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STATA September 1998 TECHNICAL STB-45 BULLETIN

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2. STATA TECHNICAL BuLLETIN A publication to promote communication among Stata users Editor Associate Editors H Joseph Newton Nicholas J Cox University of Durham Department of Statistics Francis X Diebold University of Pennsylvania Texas A amp M University Joanne M Garrett University of North Carolina College Station Texas 77843 Marcello Pagano Harvard School of Public Health 409 845 3142 J Patrick Royston Imperial College School of Medicine September 1998 409 845 3144 FAX stb O stata com EMAIL Subscriptions are available from Stata Corporation email stata stata com telephone 979 696 4600 or 800 STATAPC fax 979 696 4601 Current subscription prices are posted at www stata com bookstore stb html Previous Issues are available individually from StataCorp See www stata com bookstore stbj html for details Submissions to the STB including submissions to the supporting files programs datasets and help files are on a nonexclusive free use basis In particular the author grants to StataCorp the nonexclusive right to copyright and distribute the material in accordance with the Copyright Statement below The author also grants to StataCorp the right to freely use the ideas including communication of the ideas to other parties even if the material is never published in the STB Submissions should be addressed to the Editor Submission guidelines can be obtained from either the editor or StataCorp Copyright Statement The S
3. This table is much easier to interpret A larger proportion of blacks have diabetes than do whites or persons in the other racial category Note that the test of independence for a two way contingency table is equivalent to the test of homogeneity of row or column proportions Hence we can conclude that there is a highly significant difference between the incidence of diabetes among the three racial groups We may now wish to compute confidence intervals for the row proportions If we try to redisplay specifying ci along with row we get the following result svytab row ci confidence intervals are only available for cells to compute row confidence intervals rerun command with row and ci options r 111 There are limits to what svytab can redisplay Basically any of the options relating to variance estimation i e se ci deff and deft must be specified at run time along with the single item i e count cell row or column for which one wants standard errors confidence intervals deff or deft So to get confidence intervals for row proportions one must rerun the command We do so below requesting not only ci but also se Stata Technical Bulletin 37 svytab race diabetes row se ci format 7 4f pweight finalwgt Number of obs 10349 Strata stratid Number of strata 31 PSU psuid Number of PSUs 62 Population size 1 171e 08 Pen Sains EA E E E E Ease ae soe eras Diabetes Race no yes Total aoscenid a ieee A E
4. 0713486 dr_asian 3505409 1724349 2 033 0 073 7406157 0395339 dri_more 4855365 1842637 2 635 0 027 068703 9023701 noinsr 8983906 2974062 3 021 0 014 1 57117 2256111 inc10_01 1070703 2001414 0 535 0 606 3456811 5598216 30 Stata Technical Bulletin STB 45 Here is the same regression with odds being reported implogit comply partner dr_enthu hisp dropout dr_hisp dr_asian dri_more noinsr gt inc10_01 impvars 1 impno 10 cluster chid or Iteration no 1 complete Iteration no 2 complete output omitted Iteration no 9 complete Iteration no 10 complete Logistic Regression using imputed values Coefficients and Standard Errors Corrected N 1141 Log Likelihood for component regression no 1 650 85724 Log Likelihood for component regression no 2 650 95298 output omitted Log Likelihood for component regression no 9 650 91123 Log Likelihood for component regression no 10 651 05008 comply Odds Std Err t P gt t 95 Conf Interval AAA A A II A ee es partner 1 396997 1625327 2 874 0 018 1 073727 1 817594 dr_enthu 2 429771 3493521 6 175 0 000 1 755132 3 363727 hisp 6254777 1665807 1 762 0 112 3424225 1 142513 dropout 6009195 1297936 2 358 0 043 3686522 9795253 dr_hisp 5720362 1232004 2 593 0 029 3514255 9311373 dr_asian 704307 1214471 2 033 0 073 4768203 1 040326 dri_more 1 625047 2994372 2 635 0 027 1 071118 2 465439 noinsr 4072245 1211111 3 0
5. so also does the benefit from the conciseness of cp become more evident Acknowledgment Thanks to Fred Wolfe for helpful stimuli and responses sbe18 1 Update of sampsi Paul T Seed United Medical amp Dental School UK p seed umds ac uk The sampsi command Seed 1997 has been updated I have improved the error messages slightly It now checks for correlations outside 1 to 1 and correctly reports when correlation r1 is needed References Seed P T 1997 Sample size calculations for clinical trials with repeated measures data Stata Technical Bulletin 40 16 18 Reprinted in Stata Technical Bulletin Reprints vol 7 pp 121 125 sbe24 1 Correction to funnel plot Michael J Bradburn Institute of Health Sciences Oxford UK m bradburn icrf icnet uk Jonathan J Deeks Institute of Health Sciences Oxford UK j deeks icrf icnet uk Douglas G Altman Institute of Health Sciences Oxford UK d altman icrf icnet uk A slight error in the funnel command introduced in STB 44 has been corrected sg84 1 Concordance correlation coefficient revisited Thomas J Steichen RJRT FAX 336 741 1430 steicht rjrt com Nicholas J Cox University of Durham UK FAX 011 44 91 374 2456 n j cox durham ac uk Description concord computes Lin s 1989 concordance correlation coefficient pe for agreement on a continuous measure obtained by two persons or methods and provides an optional graphical display of the observed concordanc
6. with the estimated proportions on the diagonal The observed proportions Pre or the proportions under the null hypothesis of independence Porc Pr P c can be used for the computation of Vers and Dg For the former choice Vers becomes a matrix with diagonal elements f 1 p n and off diagonal elements PrcPst In n The former choice is used by default for the pearson and 1r statistics The latter is used when the null option is specified Note that when the p estimates are used and one of the estimates is zero the corresponding variance estimate is also zero hence the corresponding element for D3 is immaterial for the computation of A Rao and Scott s 1984 second order correction is used to produce F statistics x2 tr A Fp E with Fp F d vd where d ees and v ai L trA tr A The denominator degrees of freedom are based on a suggestion of Rao and Thomas 1989 The correction for the likelihood ratio statistic Xk is identical The Wald statistics computed by svytab with the wald and 11wald options are detailed in the earlier section titled Wald statistics References Fuller W A W Kennedy D Schnell G Sullivan H J Park 1986 PC CARP Ames IA Statistical Laboratory Iowa State University Koch G G D H Freeman Jr and J L Freeman 1975 Strategies in the multivariate analysis of data from complex surveys International Statistical Review 43 59 78 Korn E L and B I Graubard 1990 S
7. 03 yi3 2 B3 Uig uz N 0 03 y 9 if yi3 lt 0 yin if yi3 20 Where the outcomes y are observed y1 y2 and y3 are latent The task then is to use the independent data X and the observed outcome variables y to estimate the unknown parameters for all three equations Call the first two equations component Stata Technical Bulletin 31 equations and the third equation a classification equation switchr produces estimates of 61 G2 and 83 and of o and 02 which may be equal or different The classification variance o2 is unidentified and assumed to be 1 Such models have been used to explore dual labor markets the effects of school lunch programs some kids eat them some don t and unobserved cultural differences in gender bias Syntax switchr eql eq2 weight if exp ls cluster string strata string sigequal tol real itout integer noisyn integer pweights are allowed Description The user defines the two component equations eq which must be identical and the classification equation eq2 which is different The dependent variable in the classification equation is the classification variable An initial guess of the classification variable must be provided by the user for each observation switchr returns the estimated classification vector y3 with the same name as the initial guess of the classification vector Since the estimated probabilities of observations belonging to the first component regime are
8. 2 0 40 7 o o T T E E o o 0 30 7 0 050 7 ES ES 2 2 z 2 0 207 lt lt 2 ic 0 025 7 z 2 s 9 o 0 10 7 a val 0 05 7 0 000 7 0 00 7 T T T T T T T T T T T T T T T T T T T T 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 Table dimensions R C Table dimensions R C Figure 6 Unadjusted and adjusted Wald statistics under null for large variance degrees of freedom df 199 for nonsparse left and sparse right tables Sparse tables however are a different story see the right graph of Figure 6 All of the Wald statistics exhibit severe problems The Pearson Wald statistic both unadjusted and adjusted is extremely anticonservative for the smaller tables Inexplicably its behavior is worse here than it is when the variance degrees of freedom are small The log linear Wald statistic is again uniformly anticonservative The null corrected Rao and Scott statistics also exhibit some anomalies for these sparse tables simulations The null corrected Pearson is extremely anticonservative for the R 2 C 2 table rejection rate gt 0 50 at a nominal 0 05 level but conservative for the other tables The null corrected likelihood ratio statistic appears to be extremely conservative rejection rate lt 0 02 for those sparse tables in the simulation that did not contain a zero cell The default corrected statistics however do much better The default corrected Pearson has a rejection rate of
9. 6 7 or 7 6 Executing commands every time Stata is started Acknowledgment This project was supported by a grant RO1 MH54929 from the National Institute on Mental Health to Michael P Carey Joining episodes in multi record survival time data Jeroen Weesie Utrecht University Netherlands weesie weesie fsw ruu nl More complicated survival time data will usually contain multiple records observations per subject This may be due to changes in covariates to gaps in observations and to recurrent events Sometimes multiple records are used while a single record could be used Consider the following two cases entry survival failure id time time censor x1 x2 112 0 10 0 3 0 112 10 14 1 3 0 117 5 12 0 0 1 117 12 17 0 0 1 117 17 22 0 0 1 6 Stata Technical Bulletin STB 45 The subject with id 112 is described with 2 observations In her first episode the subject was at risk from time O to time 10 and was then censored She re entered at time 10 i e immediately after the end of the first episode and failed at time 14 Note that her covariates x1 and x2 did not vary between the two episodes This data representation is actually less economical than one in which subject 117 is described by a single observation as shown below Case 117 consisted of three records that could also be joined into a single record entry survival failure id time time censor x1 x2 112 0 14 1 3 0 117 5 22 1 0 1 So when is it possible to join two epis
10. In this metric an estimate of the standard error is f p 3 3 P 1 p Thus a 100 1 a confidence interval in this metric is In p 1 p ti_a 2 p 1 P where ty_ 2 is the 1 a 2 th quantile of Student s t distribution The endpoints of this confidence interval are transformed back to the proportion metric using f7 y exp y 1 exp y Hence the displayed confidence intervals for proportions are 1 ln 4 Ele danti i P 1 p Confidence intervals for weighted counts are untransformed and are identical to the intervals produced by svytotal The Rao and Scott 1984 second order correction to the Pearson statistic X equation 1 and the likelihood ratio statistic Xa equation 2 is calculated by first estimating the design effects matrix A C D5 VasD5 C C D5 VD5 C This formulation is different from that of equation 4 but it yields numerically identical results for the correction and is easier to compute Here C is a contrast matrix that is any RC x R 1 C 1 full rank matrix that is orthogonal to 1 X4 G e C 1 0 and C X 0 where Xy is a RC x R C 2 matrix of row and column main effects see the description following equation 4 V is the variance estimate for the cell proportions under the survey design i e the same estimate that would be produced by svyratio Vers is the variance estimate assuming simple random sampling Dg is a diagonal matrix
11. Prob gt chi2 0 0000 Log Likelihood 4780 8947983 Pseudo R2 0 0156 28 Stata Technical Bulletin STB 45 standard errors adjusted for clustering on provnum Robust los IRR Std Err z P gt l z 95 Conf Interval MORDE EAA q L A tl a aa e e e ed ee hs los hmo 9352302 0477849 1 311 0 190 8461103 1 033737 died 7917555 0474362 3 897 0 000 7040335 8904076 white 8854497 0641497 1 679 0 093 7682374 1 020545 age80 9840357 0629949 0 251 0 802 8679997 1 115584 type2 1 272802 0785426 3 909 0 000 1 127806 1 436439 type3 2 069855 4302092 3 500 0 000 1 377278 3 110699 gua ao A A o A AA A PSN lnalpha alpha 4339545 lnalpha _cons 1n alpha LR test against Poisson chi2 1 4107 417 P 0 0000 References Hilbe J 1994 sg16 5 Negative binomial regression Stata Technical Bulletin 18 2 5 Reprinted in Stata Technical Bulletin Reprints vol 3 pp 84 88 Logistic regression for data including multiple imputations Christopher Paul RAND Santa Monica California cpaulErand org One of the factors limiting the use of more sophisticated and less biased methods for dealing with missing data is sheer practicality Here 1 hope to help decrease the entry cost for the use of multiple imputation by providing code that allows the use of multiple imputation data for logistic regression Note that this program does not do the imputations it just automates the combination and correction of coefficients and standard e
12. and then repeatedly draw samples from the finite population This whole process should then be repeated many times This is clearly an arduous task that would require weeks of computer time I chose to do something much simpler Setting up the simulations For the simulations I generated clusters and observations within clusters using a simple parametric model I did not simulate stratified sampling or sampling weights Hence my simulations represent simple random sampling with replacement of clusters from an infinite population of clusters To produce two categorical variables z and z2 for the tabulation I first generated underlying latent variables y and ya according to a random effects model Ykij Ui eij where u N 0 pc and ej uj N 0 1 pc Hence unconditionally yg N 0 1 and the intra cluster correlation is pe To simulate the null hypothesis of independence Y and y2 were independently generated To simulate an alternative hypothesis of nonindependence y and y2 were given correlations of roughly pa by first generating independent y and y2 and then setting y y yo pay V1 pys To generate z with M categories y was categorized based on fixed normal quantiles For the nonsparse tables simulations quantiles were derived from equally spaced probabilities zk q if and only if q 1 M lt yp lt 97 q M where q 1 2 M where is the standard cumulative normal For sparse tables si
13. be separated by spaces If there are n arguments in list 7 k lists produce M nj sets of results The name cp is derived from Cartesian product Options noheader suppresses the display of the command before each repetition nostop does not stop the repetitions if one of the repetitions results in an error pause pauses output after each execution of stata_cmd This may be useful for example under Stata for Windows when cp is combined with graph Examples With the auto data cp 246 xtile mpg 1 mpg n 1 executes xtile mpg2 mpg n 2 xtile mpg4 mpg n 4 xtile mpg6 mpg n 6 and is close to for 2 4 6 1 n xtile mpg 1 mpg n 1 Stata Technical Bulletin 21 but cp length weight mpg 2 4 xtile 102 1 n 2 which executes Xtile length2 length n 2 Xtile length4 length n 4 Xtile weight2 weight n 2 xtile weight4 weight n 4 xtile mpg2 mpg n 2 xtile mpg4 mpg n 4 that is two different numbers of quantile splits for three different variables is more concise than the corresponding for statement for length weight mpg xtile 12 1 n 2 xtile 014 1 n 4 Another example is cp mpg price length displ weight regress 1 02 which executes regress mpg length regress mpg displ regress mpg weight regress price length regress price displ regress price weight As the number of combinations of items increases
14. convergence is not monotonic in the convergence criterion measure relative change in the coefficient estimates Therefore it is prudent to be conservative in the convergence criterion This program uses elapse to help with the timing of the iterations see Zimmerman 1998 The full complement of programs needed for switchr is switchr ado switchr hlp elapse ado elapse hlp _sw_lik ado and _sw_1ik2 ado 32 Saved Results Example Stata Technical Bulletin S_E_11 log likelihood value of the joint likelihood function STB 45 In this example we calculate a switching regression model of child height for age z scores on a number of variables Children s height for age is hypothesized to depend on the explanatory variables in different ways according to unobservable cultural factors and time constraints in the household gen double Guesprob O quietly summarize lnpce detail replace Guesprob 1 if Inpce gt _result 10 eq main eq regime haz docdist nursdist phardist father mother gender lnpce crop_siz urban rural Guesprob lnpce members maxfel maxfe2 highfe urban rural KZN Ecape NorP reticul elect switchr main regime pweight rsweight cl clustnum noisyn 200 sige Here is the regression for the switching equation On iter 1250 the mean absolute change in the probability vector is Average of the probability vector i 5562 2071 s 0 On iteration 1250 greatest diff is 0 000192 on phardist
15. declared by eye xpos ypos zpos this is not a perspective view 8 Stata Technical Bulletin STB 45 The grid and the eye position are required The object is presented such that the lowest 2D corner projection is in front hidlin can only represent a function not data However the program makfun may be used to generate a function summarizing real data with which hidlin may then produce a 3D representation Options xinfo yinfo and eye must all be known They define x range and step and y range and step for the grid as well as eye x y z directions i e the position from where the surface is viewed All specified values may be separated by commas and they may be expressions e g x _pi pi pi 90 going from T to m in 180 steps lines requests that only x curves be drawn when x is specified or only y curves when y is specified More precisely lines x asks to see the curves z f x yo where x varies at each successive level y of y Similarly lines y requests the curves z f ao y where y varies at successive levels of x When lines is omitted or when both x and y are specified the default is to draw both sets of curves box asks that the surface be represented as a chunk of a solid 3D object coo asks that the coordinates of the corners of the surface be displayed neg requests that z be plotted rather than z upside down view xmargin and ymargin specify the sizes of the margins around the pl
16. full understanding one can get a feeling for A It is like a ratio although remember that it is a matrix of two variances The variance in the numerator involves the variance under the true survey design and the variance in the denominator involves the variance assuming that the design was simple random sampling Recall that the design effect deff for the estimated proportions is defined as deff V Prc Vars Prc see the Methods and Formulas section of the R svymean entry in the Stata Reference Manual Hence A can be regarded as a design effects matrix and Rao and Scott call its eigenvalues the 6 s the generalized design effects Simplistically one can view the iid statistics xe and Kae as being too big by a factor of A for true survey design It is easy to compute an estimate for A using estimates for V and Vsrs But unfortunately equation 3 is not practical for the computation of a p value However one can compute simple first order and second order corrections based on it A first order correction is based on downweighting the iid statistics by the average eigenvalue of A namely one computes X2 6 X2 8 and X k X2 2 8 Stata Technical Bulletin 39 where is the mean generalized deff R 1 C 1 A 1 Gees E k 1 These corrected statistics are asymptotically distributed as Xa ne 1 A better second order correction can be obtained by using the Satterthwaite approxim
17. if you have a large dataset The standard errors computed by svytab are exactly the same as those produced by the other svy commands that can compute proportions namely svymean svyratio and svyprop Indeed svytab calls the same driver program that svymean and svyratio use For instance the estimate of the proportion of African Americans with diabetes the second proportion in the second row of the preceding table is simply a ratio estimate which we can duplicate using svyratio gen black race 2 gen diablk diabetes black 2 missing values generated g g svyratio diablk black Survey ratio estimation pweight finalwgt Number of obs 10349 Strata strata Number of strata 31 PSU psu Number of PSUs 62 Population size 1 171e 08 Ratio Estimate Std Err 95 Conf Interval Deff Loira reia A A A A diablk black 0590349 0061443 0465035 0715662 6718049 Although the standard errors are exactly the same which they must be since the same driver program computes both the confidence intervals are slightly different The svytab command produced the confidence interval 0 0477 0 0729 and svyratio gave 0 0465 0 0716 The difference is due to the fact that svytab uses a logit transform to produce confidence intervals whose 38 Stata Technical Bulletin STB 45 endpoints are always between O and 1 This transformation also shifts the confidence intervals slightly toward the null i e 0 5 which is benefic
18. not generally just zero or one the elements of y3 fall throughout the interval 0 1 Options cluster and strata invoke the robust variance calculations by using svyreg sigequal forces the variance of the two component regressions to be the same tol specifies a threshold such that when the largest relative change among the coefficients from one iteration to the next is less than tol estimates are declared to have converged The default is tol 1e 4 itout and noisyn control reporting of progress on the iterations and of intermediate output itout specifies that every iterations the convergence criterion the mean and mean change of the classification vector and the time taken for that iteration be reported The default is itout 20 noisyn specifies that every iterations the regression results on the two component regressions be reported In addition results for a modified version of the classification vector are reported These classifications results are accurate up to a constant across coefficients scaling parameter The default is noisyn 16000 Remarks To obtain these estimates switchr maximizes the likelihood function through the EM algorithm of Dempster Laird and Rubin 1977 as further articulated by Hartley 1978 This iterative method first estimates the classification vector i e the probability that a given observation is in the first component regression This estimate is obtained by reweighting the
19. obtained by typing graph bin 20 on varxplor s command line and then clicking the Enter button Still other commands are unacceptable both on the command line and as launch button assignments In particular because of limitations in Stata s macros the left quote and double quote characters must be avoided The presence of either character can trigger a variety of errors See also Remark 2 below Remarks 1 varxplor creates its list of variable names at startup and that list cannot be updated while varxplor is active So while it is possible to use varxplor s command line to create new variables they will not appear on the variable list and cannot be visited without exiting varxplor The variables counter at the top of the dialog will however be updated appropriately 2 For the same reason deleting or moving a variable would render varxplor s variable list invalid without warning Hence the Stata commands drop keep move and order are forbidden in a button cmdstr and from varxplor s command line There are ways to defeat this prohibition but they cannot be recommended 3 As mentioned above the variables counter at the top of the dialog will be updated if a new variable is created Similar remarks apply to the other pieces of information shown there For example the Sorted by item will respond to uses of the sort command from a launch button or the command line 4 The Locate command accepts wildca
20. of variables was large Reference Higbee K T 1998 sg89 Adjusted predictions and probabilities after estimation Stata Technical Bulletin 44 30 37 sg90 Akaike s information criterion and Schwarz s criterion Aurelio Tobias Institut Municipal d Investigacio Medica IMIM Barcelona atobias imim es Michael J Campbell University of Sheffield UK m j campbell sheffield ac uk Introduction It is well known that nested models estimated by maximum likelihood can be compared by examining the change in the value of 2log likelihood on adding or deleting variables in the model This is known as the likelihood ratio test McCullagh and Nelder 1989 This procedure is available in Stata using the lrtest command To assess the goodness comparisons between nonnested models two statistics can be used the Akaike s information criterion Akaike 1974 and Schwarz s criterion Schwarz 1978 Neither are currently available in Stata Editor s note A previous implementation of these tests was made available in Goldstein 1992 Criteria for assessing model goodness of fit Akaike s information criterion AIC is an adjustment to the 2log likelihood score based on the number of parameters fitted in the model For a given dataset the AIC is a goodness of fit measure that can be used to compare nonnested models The AIC is defined as follows AIC 2log likelihood 2 x p where p is the total number of parameters fitted in
21. probabilities based on the errors of the observations in the two component regressions The updated probabilities are then used to weight observations in each of the two separate component regressions This iterative procedure eventually converges to the maximum likelihood estimates of the above three equation regression model Exact standard errors in a switching regression are not available This addition provides good approximate standard errors The program can be used iteratively to obtain bootstrapped standard errors See Douglas 1996 Because the likelihood surface is not globally concave several local maxima are possible switchr can be used iteratively to find the local maximum with the highest likelihood value by searching from different starting values of the classification vector If 0 and 02 are allowed to differ the default problems can arise in which one variance is driven to zero with a very small number of observations sorted into the corresponding component regime One solution to this problem is to use the sigequal option to force the two variances to be the same Users should be aware of several caveats in using this method First estimation of switching regressions with unobserved regime separation is valid only when errors are independent and identically distributed The independence of errors across equations can be a strong assumption Second standard errors are not exact and will in general be biased downward Finally
22. rho 9 hidlin bivnor x 3 3 2 y 3 3 3 e 2 3 5 be This is a coarse graph but gives a quick first look which is shown in Figure 1 Stata Technical Bulletin 9 Figure 1 The bivariate normal density Inspection of this graph can give you an idea of a useful eye location and good values of the step sizes For example hidlin bivnor x 3 3 1 y 3 3 15 e 2 4 3 bc 1 y gives the graph in Figure 2 which is the same as that in Figure 1 except that the location of the viewing eye has been moved the grid is twice as fine and only the y lines have been drawn 3 00 2 94 0 00 2 94 3 00 0 00 Figure 2 The bivariate normal density from a different view and using a finer grid Note that when the stepsizes are very small that is when the number of grid points becomes huge graphing will become annoyingly slow if your function is very wavy or bumpy The maximum allowed is 500 by 500 but that is already visually much too dense Details on the geometry for hidlin In order to keep the number of drawing points reasonably low it is required that the ratio of the x and y components of the eye position be the same as the ratio of the xstep to the ystep Thus it is required that step stepy Leye Yeye ignoring signs However when the information provided by the user does not satisfy that condition the program adapts the x and y step to meet the requirement so that the user actually does not have to worry with th
23. statistic under null for nonsparse left and sparse right tables variance df 19 Also shown in Figure 1 are these two x statistics turned into F statistics with denominator degrees of freedom vd according to the suggestion of Rao and Thomas 1989 The left graph of the nonsparse tables simulation shows that the corrected x statistics are anticonservative i e declare significance too frequently for the smaller tables It is surprising however how well the x statistics do for the larger tables where dy R 1 C 1 approaches v The corrected F statistics do better for the smaller nonsparse tables For the nonsparse tables the null corrected F statistic is noticeably more conservative than the default corrected statistic except for the R 2 C 2 table The right graph of Figure 1 shows a sparse tables simulation for the same statistics An anomaly appears for the null corrected statistics for the R 2 C 2 table the rejection rate of the simulation is gt 0 15 at a nominal 0 05 level After the R 2 C 2 table the null corrected statistics dive to levels more conservative than the default corrected statistics Similar graphs Figure 2 can be made for the corresponding four variants of the corrected likelihood ratio statistics The graph for the nonsparse tables is essentially identical to the left graph of Figure 1 This is not surprising since the uncorrected Pearson statistic is usually numerically similar to the uncorrec
24. to adjust the F statistic by using Paaj v do 1 W vdo with Paaj F do v do 1 This is the adjustment that is done by default by svytab Note that svytest and the other svy estimation commands produce adjusted F statistics by default using exactly the same adjustment procedure See Korn and Graubard 1990 for a justification of the procedure As Thomas and Rao 1987 point out the unadjusted F statistics give anticonservative p values i e under the null the statistics are significant more often than they should be when y is not large Thomas and Rao 1987 explore the behavior of the adjusted F statistic for the log linear Wald test in simulations for simple goodness of fit tests and they find that even the adjusted statistic is anticonservative when y is small This conclusion for the log linear Wald statistic is borne out by my simulations which are detailed in the next section The adjusted Pearson Wald statistic however behaves reasonably under the null in most cases Evaluating the statistics via simulations At this point in the article you the reader are at the same point where I was after I read all the papers and coded up a bunch of the possible statistics I had a number of questions 1 Should one use pre Or Pore to compute Vsrs in the second order Rao and Scott correction for X and X R 2 It is next to certain that one should adjust for the degrees of freedom y npsy L of the design base
25. to the adjusted statistic Note svytab uses the tabdisp command see R tabdisp to produce the table As such it has some limitations One is that only five items can be displayed in the table If you select too many items you will be warned immediately You may have to view additional items by redisplaying the table while specifying different options Examples of display options The example shown earlier is from the Second National Health and Nutrition Examination Survey NHANES II McDowell et al 1981 The strata psu and pweight variables are first set using the svyset command rather than specifying them as options to svytab see R svyset for details The default table displays only cell proportions and this makes it very difficult to compare the incidence of diabetes in white versus black versus other racial groups It would be better to look at row proportions This can be done by redisplaying the results i e the command is reissued without specifying any variables with the row option svytab row pweight finalwgt Number of obs 10349 Strata stratid Number of strata 31 PSU psuid Number of PSUs A 62 Population size 1 171e 08 zts E EE Diabetes Race no yes Total Sic A A A ee es White 968 032 1 Black 941 059 1 Other 9797 0203 1 Total 9658 0342 1 PASEAR A o SSs ete Stk Key row proportions Pearson Uncorrected chi2 2 21 3483 Design based F 1 52 47 26 15 0056 P 0 0000
26. 0 04 0 06 for all tables in the large variance degrees of freedom simulation of sparse tables Power for nonsparse and sparse tables for small v Figure 7 shows the relative power of the default and null corrected Pearson and likelihood ratio F statistics for small variance degrees of freedom v 19 Again it must be kept in mind that only relative comparisons among the statistics can be made since the alternative hypothesis was changed as the table size changed The left graph of Figure 7 shows that these four statistics all have essentially identical power for nonsparse tables 46 Stata Technical Bulletin STB 45 o Pearson Corrected F A Pearson Corrected null F o Pearson Corrected F A Pearson Corrected null F O LR Corrected F LR Corrected null F o LR Corrected F LR Corrected null F 1 00 4 i 1 00 7 0 75 7 0 75 7 E 2 3 0 50 7 3 0 50 4 a a 0 25 7 0 25 7 0 00 7 0 00 7 T T T T T T T T T T T T T T T T T T T T 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 252 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 Table dimensions R C Table dimensions R C Figure 7 Power of corrected Pearson and likelihood ratio statistics for nonsparse left and sparse right tables variance df 19 For sparse tables the null corrected statistics exhibit extremely poor power for R 2 C 2 Indeed the rejection rate for the null corrected Pearson F statistic was lower for this alternative hypothesis than it was under the null hypothesis for an ot
27. 1 Winner s ages taken from 1995 Universal Almanac The parentheses on the launch buttons are meant to remind you that the command name between them is merely the current assignment Each launch button can be reconfigured as desired see below If the launch buttons prove to be inadequate varxplor has its own command line the wide edit box positioned to the right of the Locator window Most Stata commands 4 Stata Technical Bulletin STB 45 can be issued from varxplor by typing them into that edit box and pressing the Enter key on the keyboard or clicking the Enter button at the right end of the edit box Customizing varxplor The syntax of the varxplor command is varxplor varlist E alpha b1 cmdstr b2 cmdstr b3 cmdstr b4 cmdstr b5 cmdstr If a varlist is present only those variables can be visited by varxplor otherwise all variables are available al VarXplor gt presdent dta x Last saved 1 Jul 1998 11 17 Obs 36 Vars 11 of 11 Width 51 Exit Sorted by year Help Notes inspect codebook list describe Locate vage F Refresh Variable M C DataType C Format C ValueLabel Variable Label Top year Election year PgUp winner Winning Presidential candidate Up w_party Winner s party Dn w_ht Winner s height in PgDn w_incumb Incumbent winner Bottom w_age Winner s age Figure 2 If the alpha option is present varxplor creates an alphabetized list of variable names when it is launched an
28. 111013 007309 1454306 1847994 1124614 1122685 2174543 1608106 3003281 6332944 069 000 Si 000 0966979 0691419 0248153 4104505 3169228 0119485 4091142 0318424 9657677 2 776758 5 943211 1478452 0253466 0040192 1632815 4121212 4556151 8520198 8260272 3313609 3 961569 3 444829 And now the second component regression header omitted Stata Technical Bulletin haz Coef Std Err t P gt t 95 Conf Interval docdist 0020019 0034663 0 578 0 564 0088392 0048354 nursdist 0020252 0033815 0 599 0 550 0046449 0086953 phardist 0008634 0019992 0 432 0 666 0030801 004807 father 0394215 0750347 0 525 0 600 1874295 1085865 mother 21741 1089093 1 996 0 047 0025832 4322368 gender 1480176 0693646 2 134 0 034 0111939 2848413 1npce 3266183 0553563 5 900 0 000 2174265 4358102 crop_siz 0409482 0330227 1 240 0 217 1060864 02419 urban 6 306667 2095572 30 095 0 000 5 893309 6 720024 rural 5 946315 2007892 29 615 0 000 5 550253 6 342377 _cons 9 339175 3630126 25 727 0 000 10 05523 8 623123 References Dempster A P N M Laird and D B Rubin 1977 Maximum likelihood from incomplete data via the EM algorithm Journal of the Royal Statistical Society Series B 39 1 38 Douglas S 1996 Bootstrap confidence intervals in a switching regressions model Economics Letters 53 7 15 Goldfeld S M and R E Quandt 19
29. 21 0 014 2078019 7980284 inc10_01 1 113012 2227599 0 535 0 606 7077381 1 75036 Saved Results All typical S_E_ global macros are available as are b and se vectors S_E_11 S_E_10 and S_E_prs2 are based on the unadjusted results of the last of the k component logistic regressions as the programmer is not aware of the consequence to log likelihood from multiple imputation Acknowledgments This work was performed while working on the RAND UCLA Los Angeles Mammography Promotion in Churches Project The project and the time spent developing this program were supported by the National Institutes of Health the National Cancer Institute Award No 1 RO1 CA60132 SAF Thanks to both Daniel McCaffrey and Naihua Duan for their consultation and advice regarding the mathematics of the statistics computed here Reference Rubin D B 1987 Multiple Imputation for Nonresponse in Surveys John Wiley amp Sons New York sg93 Switching regressions Frederic Zimmerman Stanford University zimmerCleland stanford edu Introduction Consider the following system in which observed values of the dependent variable come from one of two regression regimes but where it is unknown a priori which regime produced any given observation Here a third equation a classification equation determines whether a given observed dependent variable comes from regression regime 1 or regression regime 2 Yar 2 b ui uy N 0 07 Yiz ib2 uiz u2 N 0
30. 324526 type3 2 105107 0553468 28 312 0 000 1 999377 2 216429 Stata Technical Bulletin 27 Using the glm command confirms there is overdispersion the deviance based dispersion is nearly six times greater than it should be for an appropriate Poisson model glm los hmo died white age80 type2 type3 nolog f poi Residual df 1488 No of obs 1495 Pearson X2 9244 928 Deviance 7954 061 Dispersion 6 212989 Dispersion 5 345471 Poisson distribution log link los Coef Std Err z P gt z l 95 Conf Interval A a 2 O A a eee eae een eee Cae e E ee eae hmo 0707465 0239615 2 953 0 003 1177102 0237828 died 2424831 0182736 13 270 0 000 2782986 2066675 white 1356989 0274563 4 942 0 000 1895123 0818855 age80 0174995 0205141 0 853 0 394 0577064 0227073 type2 2397179 0210905 11 366 0 000 1983814 2810545 type3 7443665 0262917 28 312 0 000 6928358 7958972 _cons 2 391268 0275976 86 648 0 000 2 337177 2 445358 Next we accommodate overdispersion by the robust and cluster options in poisml and nbinreg Clustering by provider may account for some of the overdispersion poisml los hmo died white age80 type2 type3 nolog robust cluster provnum irr Poisson Estimates Number of obs 1495 Model chi2 6 947 07 Prob gt chi2 0 0000 Log Likelihood 6834 6053315 Pseudo R2 0 0648 standard errors adjusted for clustering on provnum Robust los IRR Std Err z P gt z l 95 C
31. 76 Studies in Non Linear Estimation Cambridge Ballinger 33 Hartley M J 1978 Comment Journal of the American Statistical Association 73 738 741 Zimmerman F 1998 ip24 Timing portions of a program Stata Technical Bulletin 41 8 9 Reprinted in Stata Technical Bulletin Reprints vol 7 p 92 Two way contingency tables for survey or clustered data William M Sribney Stata Corporation wsribney Ostata com The syntax for the svytab command is svytab varname varnamez weight it exp in range E strata varname psu varname fpc varname subpop varname srssubpop tab varname missing cell count row column obs se ci deff deft proportion percent nolabel nomarginals format mt vertical level pearson lr null wald llwald noadjust pweights and iweights are allowed See U 18 1 6 weight in the Stata User s Guide When any of se ci deff or deft are specified only one of cell count row or column can be specified If none of se ci deff or deft are specified any or all of cell count row and column can be specified svytab typed without arguments redisplays previous results Any of the options on the last three lines of the syntax diagram cell through noadjust can be specified when redisplaying with the following exception wald must be specified at run time Warning Use of if or in restrictions will not produce correct statistics and variance estimates for subpopulations in many cases To com
32. 89 Generalized Linear Models 2d ed London Chapman and Hall Schwarz G 1978 Estimating the dimension of a model Annals of Statistics 6 461 464 26 Stata Technical Bulletin STB 45 sg91 Robust variance estimators for MLE Poisson and negative binomial regression Joseph Hilbe Arizona State University hilbe asu edu Poisson and negative binomial regression are two of the more important routines used for modeling discrete response data Although the Poisson model has been the standard method used to model such data researchers have known that the assumptions upon which the model are based are rarely met in practice In particular the Poisson model assumes the equality of the mean and the variance of the response Hence the Poisson model assumes that cases enter each respective cell count in a uniform manner Although the model is fairly robust to deviations from the assumptions researchers now have software available to model overdispersed Poisson data Notably negative binomial regression has become the method of choice for modeling such data In effect the negative binomial assumes that cases enter each count cell with a gamma shape defined by a the ancillary or heterogeneity parameter Note that the variance of the Poisson model is simply u whereas the variance for the two parameter gamma is 2 0 Since the variance of the negative binomial is ku where k 1 a the negative binomial can be conceived as a Poisson gamma mixture model
33. The left graph of Figure 3 shows that the Fuller et al statistic is quite conservative for all except the smaller tables Recall that the Fuller et al statistic uses v denominator degrees of freedom whereas the Pearson F statistic uses vd o Pearson Corrected F A Pearson Fuller Corrected null o Pearson Corrected F A Pearson Fuller Corrected null 0 100 7 0 20 7 o o gt gt 2 2 o 0 0757 is 0 1574 o o S T T E SS E o o E 0 0507 aes 0 107 ES ES o o E E S S E 4 5 4 A 2 0 025 g 0 05 2 2 a ec 0 000 4 0 00 4 T T T T T T T T T T T T T T T T T T T T 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 Table dimensions R C Table dimensions R C Figure 3 Fuller et al 1986 correction vs svytab s default Pearson under null for nonsparse left and sparse right tables variance df 19 The right graph of Figure 3 shows the sparse tables simulation Since the Fuller et al variant is a null corrected statistic it also exhibits the same anomalous anticonservatism for the R 2 C 2 table as do the null corrected Pearson statistics in the right graph of Figure 1 One could apply Fuller et al formulas to the default correction and I have done so in my simulations but this also leads to appreciable conservatism for the larger tables The y denominator degrees of freedom of the Fuller et al variant simply appear to be too strict One could increase the denominator degree
34. The psize option of graph controls the size of the text for all the labels The default psize is 100 larger numbers give larger text Example The following commands produce the graph in Figure 1 Stata Technical Bulletin 7 set obs 20 gen x _n 0 1 invnorm uniform gen yi _n 0 5 invnorm uniform gen y2 _n 5 0 5 invnorm uniform labgraph y1 y2 x c 11 s titi labgraph example xlab ylab gt xline 7 10 yline 0 12 labtext Line y1 Line y2 labxy 10 12 7 0 labgraph example 207 T T T T T 0 5 10 15 20 Figure 1 An example of using labgraph The labels Line y1 and Line y2 will appear at approximately the requested coordinates and the type size will be set to 100 The xline and yline options put cross hairs at the requested point for the labels illustrating placement gr30 A set of 3D programs Guy D van Melle University of Lausanne Switzerland guy van melle inst hospvd ch Aside from William Gould s needleplot representations gr3 Stata has very little 3D capabilities gr3 appeared in STB 2 for Stata version 2 1 Gould 1991 and was revisited and updated to version 3 0 in STB 12 Gould 1993 It still works nicely if you set the version number to 3 0 first This insert presents three programs hidlin altitude and makfun The former two produce two different representations of a surface when you provide the equation of that surface while the third one summarizes real
35. al 1975 Two Wald statistics have been proposed The first is similar to the Pearson statistic in that it is based on Vig Nee E A where re is the estimated weighted counts for the r cth cell and r 1 R 1 and c 1 C 1 The delta method can be used to estimate the variance of Y which is Yee stacked into a vector and a Wald statistic can be constructed in the usual manner W Y InV N In Y where Jn OY AN Another Wald statistic can be developed based on the log linear model with predictors 1 Xy X2 that was mentioned earlier This Wald statistic is A Wir X ln P X2Jp V P Jp X2 X In b where Jp is the matrix of first derivatives of In p with respect to p which is of course just a matrix with Pro on the diagonal and zero elsewhere Note that this log linear Wald statistic is undefined when there is a zero proportion in the table These Wald statistics can be converted to F statistics in one of two ways One method is the standard manner divide by the x degrees of freedom do R 1 C 1 to get an F statistic with do numerator degrees of freedom and v npgy L denominator degrees of freedom This is the form of the F statistic suggested by Koch et al 1975 and implemented in the CROSSTAB procedure of the SUDAAN software Shah et al 1997 Release 7 5 and it is the method used by svytab when the noadjust option is specified along with wald or 11wald Another technique is
36. ary is stored in h Zfun The bare call makfun x y uses gx qy min y N 3 matsize quantiles and produces counts on the grid Example For the auto data we study mpg in the quartiles of price by foreign We begin by summarizing the grid variables Use auto 1978 Automobile Data summarize price Variable Obs Mean Std Dev Min Max ca tesisc A A A A A A price 74 6165 257 2949 496 3291 15906 tabulate foreign nolabel Car type Freq Percent Cum A at poe en fe Bee ee Ra ee o 52 70 27 70 27 1 22 29 73 100 00 AAA A A ee A es Total 74 100 00 Next we use a matrix to define our own choice of cutpoints for foreign and use four quartiles for price mat A 0 makfun for pri x A y 4 z mean mpg Variable Obs Mean Std Dev Min Max mpg 8 22 5845 4 769106 16 45455 30 5 12 Stata Technical Bulletin STB 45 This has generated 8 levels 2 x 4 and we may want to inspect the matrices that have been generated mat dir h1Zfun 2 4 hlYcut 3 1 hlXcut 1 1 A 1 11 A first plot of the surface is shown in Figure 4 which was obtained by typing hidlin makfun x 1 1 2 y 3200 16000 200 e 1 1000 3 c 1 00 3200 00 30 50 1 00 3200 00 22 07 1 00 16000 00 71700 20 29 16000 00 16 45 Figure 4 A first plot of the surface for the auto data The front high quarter is much too long drawing from 3200 to 8000 should be adaquate Now we adjust the grid and viewing location show the bo
37. ata com either by first using uuencode if you are working on a Unix platform or by attaching it to an email message if your mailer allows the sending of attachments In Unix for example to email the current directory and all of its subdirectories tar cf compress uuencode xyzz tar Z gt whatever mail stb stata com lt whatever Stata Technical Bulletin International Stata Distributors 51 International Stata users may also order subscriptions to the Stata Technical Bulletin from our International Stata Distributors Company Address Phone Fax Email Countries served Company Address Phone Fax Email URL Countries served Company Address Phone Fax Email Countries served Applied Statistics amp Systems Consultants P O Box 1169 Nazerath Ellit 17100 Israel 972 4 9541153 972 6 6554254 sasconsl actcom co il Israel Dittrich amp Partner Consulting Prinzenstrasse 2 D 42697 Solingen Germany 49 212 3390 200 49 212 3390 295 evhall E dpc de http www dpc de Germany Austria Italy For the most up to date list of Stata distributors visit http www stata com IEM P O Box 2222 PRIMROSE 1416 South Africa 27 11 8286169 27 11 8221377 iem hot co za South Africa Botswana Lesotho Namibia Mozambique Swaziland Zimbabwe Company Address Phone Fax Email Countries served Company Address Phone Fax Email Countries served
38. ation to the distribution of a weighted sum of x variables Here the Pearson statistic becomes X3 6 a TEED 5 where is the coefficient of variation of the eigenvalues aua o R 1 C 1 2 Since gt by tr and ye 2 tra equation 5 can be written in an easily computable form as tr Xp 6 4 XB 6 These corrected statistics are asymptotically distributed as x3 with ARCH eA CES E E o i e a X with in general noninteger degrees of freedom The likelihood ratio KR statistic can also be given this second order correction in an identical manner Two wrinkles in the Rao and Scott correction formula We would be done if it were not for two outstanding issues First how should one compute the variance estimate Vars which appears in equation 4 and in the computation of X This may seem like a stupid question since as we said earlier V srs has diagonal elements Prell Pre n and off diagonal elements prcPst n but note that here pre is the true not estimated proportion Hence the question is what to use to estimate prc the observed proportions Pre or the proportions estimated under the null hypothesis of independence Pore Pr P Rao and Scott 1984 p 53 write In practice the asymptotic significance level of X 6 a is estimated by using V for V and 7 or it for 7 In our notation Tre iS Pre Tre is the observed Pre and Tre is the estimate under the nul
39. ble appears in the bottom position of the Variables window The topmost variable name also appears in the Locator window actually edit box beside the Locate button Any variable can be located by typing its name into that window or by selecting its name from the dropdown list triggered by the downarrow at the right edge of the window Clicking Locate then shifts so that the variable named in the Locator window appears in the Variables window below in the top position if possible Immediately above the Locator window is a row of five launch buttons By default clicking a launch button issues the command named on the button for the variable whose name appears in the Locator window In Figure 1 for example clicking the button marked inspect would issue the command inspect year so that inspect year year Election year Number of Observations See eee eS Non Total Integers Integers Negative Zero E z Positive 36 36 E HES AHR REE CRESS CS SSeS Total 36 36 Missing a O O S a 1856 1996 36 36 unique values appears in the Results window Clicking the Notes button would in this case have no effect because the variable year has no notes But variable w_age does have notes that is why its name is suffixed by in the Variables window So placing the name w_age in the Locator window and clicking the Notes button prints the following in the Results window w_age
40. consists of 1 An insert article describing the purpose of the submission The STB is produced using plain TEX so submissions using TEX or IAT X are the easiest for the editor to handle but any word processor is appropriate If you are not using TEX and your insert contains a significant amount of mathematics please FAX 409 845 3144 a copy of the insert so we can see the intended appearance of the text 2 Any ado files exe files or other software that accompanies the submission 3 A help file for each ado file included in the submission See any recent STB diskette for the structure a help file If you have questions fill in as much of the information as possible and we will take care of the details 4 A do file that replicates the examples in your text Also include the datasets used in the example This allows us to verify that the software works as described and allows users to replicate the examples as a way of learning how to use the software 5 Files containing the graphs to be included in the insert If you have used STAGE to edit the graphs in your submission be sure to include the gph files Do not add titles e g Figure 1 to your graphs as we will have to strip them off The easiest way to submit an insert to the STB is to first create a single archive file either a zip file or a compressed tar file containing all of the files associated with the submission and then email it to the editor at stb st
41. d shows a check box labeled abc just below the Locator window see Figure 2 Checking that box causes varxplor to begin traversing the variable list in alphabetic order rather than in dataset order The change takes place at the next screen update caused by clicking a scroll button or the Refresh or Locate buttons In Figure 2 for example the variables are shown in dataset order but the abc box has just been checked Clicking the Locate button would switch to alphabetic order with the variable w_age in the topmost position Figure 3 shows the result The alpha option also has a more profound but less visible effect Since an alphabetic variable list is at hand the Locate operation finds variables using binary search rather than linear search starting from the top of the list As a result locating a variable is much faster whether or not the abc box is checked when the alpha option is given Alphabetizing the variable list makes startup slower but pays off in faster locate operations especially when there are many variables al VarXplor gt presdent dta x Last saved 1 Jul 1998 11 17 Obs 36 Yars 11 of 11 Width 51 Exit Sorted by year H Notes inspect codebook list describe es y graph bin 20 Refresh Variable WM abc C DataType C Format ValueLabel Variable Label w_age Winner s age w_ht Winner s height in w_incumb Incumbent winner w_party Winner s party wht_Iht Winner s ht Loser
42. d sparse right tables variance df 19 It is not reasonable to include unadjusted Wald statistics in power comparisons for small variance degrees of freedom since they do such a bad job of controlling Type I error under the null Figure 4 in this situation However it should be noted that despite this fact the power of the default corrected Pearson F statistic is either better than or about the same as the power of the unadjusted Wald statistics Power for nonsparse and sparse tables for large y Power for all statistics was similar for nonsparse tables when the variance degrees of freedom were large y 199 All of the Rao and Scott corrected statistics had essentially identical power for nonsparse tables These statistics held a slight advantage of about 5 over the adjusted Wald statistics for all but the smallest tables where the power was the same Stata Technical Bulletin 47 The sparse tables simulation again provoked erratic behavior for some of the statistics in the smaller tables Again the default corrected Pearson F statistic was superior Its power was either about the same or significantly better than the other statistics Conclusions Rather surprisingly the simulations yielded unequivocal answers to the questions that I posed earlier 1 Should one use Pre default corrected or Pore null corrected in the second order Rao and Scott correction The answer appears to be Pre Using Por results in some erratic behavior for
43. d the cohort at birth This means that the x axis is time and the y axis is age The trick here is to generate a variable of zeroes This insures all follow up times will start from the y axis y 0 Then each subjects follow up is offset in the x direction by the entry time in years grlexis zero fail fup up timein lti Age bti Time saving gr3 Time LEXIS Diagram 50 7 o 1 23 88 fup Follow up Figure 4 One possible disadvantage of the previous example is that after an event the subject may still be followed up until the end of the study However previously if the follow up is altered to the end of the study coverage time in the command line this new variable is fup2 then all the events will be assumed to be at the end of the study If the event occurs at earlier times then a new variable is created that contains the amount of follow up since study entry until the first event that the subject had grlexis zero fail fup2 up timein ev event 1ti Age bti Time saving gr4 Time LEXIS Diagram 50 7 Time Figure 5 Stata Technical Bulletin 17 References Clayton D and M Hills 1993 Statistical Models in Epidemiology Oxford Oxford University Press 1995 ssa7 Analysis of follow up studies Stata Technical Bulletin 27 19 26 Reprinted in Stata Technical Bulletin Reprints vol 5 pp 219 227 ip14 1 Programming utility numeric lists correction and extension Jeroen Weesie Utrecht Universi
44. d variance estimate V by converting the corrected x statistic into an F statistic But what should one use the v denominator degrees of Stata Technical Bulletin 41 freedom as Fuller et al 1986 have implemented in PC CARP or something like the more liberal vd degrees of freedom suggested by Rao and Thomas 1989 3 How anticonservative are the unadjusted Wald statistics Koch et al 1975 Just a bit or a lot Is the adjustment really necessary 4 How powerful are the Wald statistics compared with the Rao and Scott corrected statistics Are they about the same or are some statistics clearly better than others 5 There is yet another possibility for testing the independence of two way tables and that is to use svymlog Indeed this was the suggestion that I made to Stata users while I worked on svytab How good or bad was this recommendation 6 Is one statistic clearly better than the others Can researchers just use one statistic all the time and ignore all the others Since the theory behind all of these statistics is asymptotic recourse to theory almost certainly will not help answer any of these questions Simulations are obviously the thing to do I did several simulations that attempted to evaluate the statistics under a variety of different conditions for sparse tables and for nonsparse tables for small and for large variance degrees of freedom v under the null hypothesis of independence to evaluate Type I error and under an al
45. data in a way suitable for use by either of the 2 graphing routines it makes the function they require hidlin is a genuine 3D program with hidden line removal hence the name whereas altitude uses colors and changing symbol size to convey some sort of contour plot appearance The summary produced by makfun on real data is obtained from Stata s pctile and collapse commands Counts are shown by default but you may request any of the statistics available for collapse on any other numerical variable in the dataset The three programs use macros and matrices whose names are prefixed by hl The two graphing routines share most of their information and store in the same macros and matrices These are kept after the graph completes thus permitting a replay any time later in the same Stata session An auxiliary program hltex is used to display texts on these graphs Syntax for hidlin hidlin func xinfo 4 4 yinfo 4 eye 4 4 lines x ly box coo neg xmargin ymargin text tmag saving filename where func stands for any name of your choosing with a maximum of 6 characters The function func is of the form z f x y and must be declared in a separate ado file see the example below whose name is hlfunc the hl prefix will be stripped away User data are cleared and the function is calculated on the grid defined by xinfo xlow xhigh xstep yinfo low yhigh ystep and viewed from a position
46. djusted F statistic is produced an unadjusted statistic can be produced by specifying noadjust The unadjusted F statistic can yield extremely anticonservative p values i e p values that are too small when the degrees of freedom of the variance estimates the number of PSUs minus the number of strata are small relative to the R 1 C 1 degrees of freedom of the table where R is the number of rows and C is the number of columns Hence the statistic produced by wald and noadjust should not be used for inference except when it is essentially identical to the adjusted statistic it is only made available to duplicate the results of other software 36 Stata Technical Bulletin STB 45 llwald requests a Wald test of the log linear model of independence Koch et al 1975 Note that the statistic is not defined when there are one or more zero cells in the table The adjusted statistic the default can produce anticonservative p values especially for sparse tables when the degrees of freedom of the variance estimates are small relative to the degrees of freedom of the table Specifying noadjust yields a statistic with more severe problems Neither the adjusted nor the unadjusted statistic is recommended for inference the statistics are only made available for pedagogical purposes and to duplicate the results of other software noadjust modifies the wald and 11wald options only It requests that an unadjusted F statistic be displayed in addition
47. e covariance estimate Post estimation commands that rely solely on _b and _se are available Any commands requiring the off diagonal elements of the variance covariance estimate either will not work or will be wrong Try matrix get vce and you will see what is missing implogit typed without argument does not replay the previous results Description implogit uses the Rubin 1987 corrections of coefficients and standard errors for logistic regressions with data that contain multiple imputations Multiple imputation variables must be ordered in a specific way and named in a special fashion see varlist above implogit proceeds by performing k logistic regressions where k is the number of imputations done cycling through the different imputations in each regression Results are saved and when done coefficients are averaged and standard errors are Stata Technical Bulletin 29 corrected Results are then reported Standard errors are corrected based on the following formula in which k is the number of imputations done and runs from 1 to k Var 8 SE 6 1 a TAY In most regards implogit behaves as the standard Stata Logit command The procedure reports unexponentiated coefficients and their corrected standard errors Options impvars no of vars indicates the number of variables included that contain multiple imputations They must be the last variables specified in varlist If your model contains 2 variables for w
48. e of the measures concord 22 Stata Technical Bulletin STB 45 also provides statistics and optional graphics for Bland and Altman s 1986 limits of agreement loa procedure The loa a data scale assessment of the degree of agreement is a complementary approach to the relationship scale approach of pe This insert documents enhancements and changes to concord and provides the syntax needed to use new features A full description of the method and of the operation of the original command and options is given in Steichen and Cox 1998 This revision does not change the implementation of the underlying statistical methodology or modify the original operating characteristics of the program Syntax concord varl var2 weight it exp in range summary graph ccc loa snd snd var replace noref reg by byvar level graph_options New and modified options noref suppresses the reference line at y 0 in the loa plot This option is ignored if graph loa is not requested reg adds to the loa plot a regression line that fits the paired differences to the pairwise means This option is ignored if graph loa is not requested snd snd_var replace saves the standard normal deviates produced for the normal plot generated by graph loa The values are saved in variable snd_var If snd_var does not exist it is created If snd_var exists an error will occur unless replace is also specified This option is ignored if graph loa is not re
49. e rho_c se of rho_c gt bias correction rho_c se of rho_c bias correction ct dp 0 708 0 116 0 935 ct yp 0 849 0 065 0 991 ct ip 0 836 0 073 0 963 ct at 0 819 0 079 0 965 ct ap 0 754 0 102 0 945 dp yp 0 857 0 064 0 957 dp ip 0 923 0 034 0 992 dp at 0 935 0 030 0 995 dp ap 0 901 0 040 0 981 yp ip 0 934 0 029 0 969 yp at 0 933 0 031 0 980 yp ap 0 867 0 056 0 944 ip at 0 977 0 010 0 997 ip ap 0 929 0 032 0 995 at ap 0 936 0 027 0 983 The pattern of agreement between different measures is generally good although Cassidy s tubes stand out as in relatively poor agreement with other methods References Anderson E W and N J Cox 1978 A comparison of different instruments for measuring soil creep Catena 5 81 93 Steichen T J and N J Cox 1998 sg84 Concordance correlation coefficient Stata Technical Bulletin 43 35 39 20 Stata Technical Bulletin STB 45 ip27 Results for all possible combinations of arguments Nicholas J Cox University of Durham UK FAX 011 44 91 374 2456 n j cox durham ac uk Various commands in Stata allow repetition of a command or program for different arguments In particular for repeats one or more commands using items from one or more lists The lists can be of variable names of numbers or of other items An essential restriction on for is that the number of items must be the same in each list Thus for price weight mpg gen 1 log mpg log transforms each of the named variab
50. eae Ss Se a A White 0 9680 0 0320 1 0000 0 0020 0 0020 0 9638 0 9718 0 0282 0 0362 Black 0 9410 0 0590 1 0000 0 0061 0 0061 0 9271 0 9523 0 0477 0 0729 Other 0 9797 0 0203 1 0000 0 0076 0 0076 0 9566 0 9906 0 0094 0 0434 Total 0 9658 0 0342 1 0000 0 0018 0 0018 0 9619 0 9693 0 0307 0 0381 A A A A A i E Key row proportions standard errors of row proportions 95 confidence intervals for row proportions Pearson Uncorrected chi2 2 21 3483 Design based F 1 52 47 26 15 0056 P 0 0000 In the above table we specified a 7 4f format rather than use the default 6 0g format Note that the single format applies to every item in the table If you do not want to see the marginal totals you can omit them by specifying nomarginal If the above style for displaying the confidence intervals is obtrusive and it can be in a wider table you can use the vertical option to stack the endpoints of the confidence interval one over the other and omit the brackets the parentheses around the standard errors are also omitted when vertical is specified If you would rather have results expressed as percentages like the tabulate command use the percent option If you want to play around with these display options until you get a table that you are satisfied with first try making changes to the options on redisplay i e omit the cross tabulated variables when you issue the command This will be much faster
51. evar to draw the symbols saving filename this will save the resulting graph in filename gph If the file already exists it is deleted and the new graph will be saved xlab and ylab have the same syntax as in the graph command If these options are not specified the labels will contain the maximum and minimum values on the axes btitle and 1title are titles for the bottom and top left portions of the graph The default is the variable name in brackets followed by follow up or timein depending on the axes title adds a title at the top of the graph symbol controls the plotting symbol of the failed events The integer provided corresponds to 0 dot 1 large circle 4 small circle 2 square 5 diamond 3 triangle 6 plus nolines omits the lines that represent the follow up time box is the bounding box parameters As usual the lexis diagram has all the follow up lines at 45 degrees from the horizontal This can be achieved by setting up a square bounding box for example box 2500 20000 2500 20000 The first number is top y coordinate second is bottom y coordinate third is left x coordinate and fourth is right x coordinate Stata Technical Bulletin 15 numbers gives the option that instead of the failure codes the line number will be plotted For small datasets this may give clarity noise gives a little information about the two variables on the x and y axes Examples The simplest plot displays follow up off
52. ght gt graph displ weight biv spearman length displ weight gt spearman length displ Number of obs 74 Spearman s rho 0 8525 Test of Ho length and displ independent Pr gt tl 0 0000 gt spearman length weight Number of obs 74 Spearman s rho 0 9490 Test of Ho length and weight independent Pr gt t 0 0000 gt spearman displ weight Number of obs 74 Spearman s rho 0 9054 Test of Ho displ and weight independent Pr gt t 0 0000 Finally we show how to take more control over the output from progname concord Steichen and Cox 1998 calculates the concordance correlation coefficient which measures the extent to which two variables are equal This is the underlying Stata Technical Bulletin 19 question when examining different methods of measurement or measurements by different people when applied to the same phenomenon the ideal is clearly that they are equal Two variables can be highly correlated and close to some line y a bz but equality is more demanding as a should be 0 and b should be 1 concord takes two variables at a time so biv is useful in getting all the pairwise concordance correlations An example dataset comes from Anderson and Cox 1978 who analyzed the measurement of soil creep slow soil movement on hillslopes at 20 sites near Rookhope Weardale in the Northern Pennines England The dataset is in the accompanying file rookhope dta The general slowness
53. ham ac uk Syntax biv progname varlist weight it exp in range asy con echo header header_string hstart own own_command_name pause quiet progname_options Description biv displays bivariate results from a Stata command or program progname for each pair of distinct variables in the varlist For p variables there will be p p 1 2 such pairs if the order of the variables is immaterial and p p 1 otherwise The simplest cases are biv progname biv progname varlist In the first case the varlist defaults to _a11 Options asy flags that the results of progname varl var2 may differ from those of progname var2 varl and that both sets are wanted con suppresses the new line that would normally follow the variable names echoed by echo Thus other output typically from the user s own program may follow on the same line echo echoes the variable names to the monitor header header_string specifies a header string that will be displayed first before any bivariate results hstart specifies the column in which the header will start The default is column 21 own own_command_name allows users to insert their own command dealing with the output from progname pause pauses output after each execution of progname This may be useful for example under Stata for Windows when progname is graph quiet suppresses output from progname This is likely to be useful only if the user arranges that output is picked u
54. hat readers are familiar with the Methods and Formulas section of the R svymean entry of the Stata Reference Manual For a table of R rows by C columns with cells indexed by r c let 2 1 if the hijth element of the data is in the r cth cell Y re hij 0 otherwise where h 1 L indexes strata i 1 np indexes PSUs and j 1 mps indexes elements in the PSU Weighted cell counts the count option are L Nh Mhi Nrc 5 5 5 Whij Y rc hij h 1 i 1 j 1 where wy are the weights if any If a variable pi is specified with the tab option Ne becomes Nh Mhi L r ED 5 5 Whij Thij Y rc hij h 1 i 1 j 1 48 Stata Technical Bulletin STB 45 Let gt R R C c 1 r 1 Estimated cell proportions are Pre Nre N Estimated row proportions are Drow re Na Ne Estimated column proportions are Deol re Nre Nuc Nrc is a total and the proportion estimators are ratios and their variances can be estimated using linearization methods as outlined in R svymean svytab computes the variance estimates using the same driver program that svymean svyratio and svytotal use Hence svytab produces exactly the same standard errors as these commands would Confidence intervals for proportions are calculated using a logit transform so that the endpoints lie between O and 1 Let p be an estimated proportion and an estimate of its standard error Let f P In p 1 H be the logit transform of the proportion
55. hat the magnitude of the difference is independent of the magnitude of the individual measures They proposed that these assumptions be checked visually using a plot of the casewise differences against the casewise means of the two measures and by a normal probability plot for the differences In a 1995 paper they proposed an additional visual tool that was not implemented in the loa plot in the initial release of concord that is a regression line fitting the paired differences to the pairwise means This additional tool is provided now when option reg is specified As indicated above the default graph options were changed to accommodate the regression line Third as a direct result of adding the regression line the reference line at y O in the loa plot was made optional Specification of option noref will suppress this reference line and reduce potential visual clutter Fourth option snd has been added to allow the user to save the standard normal deviates produced for the normal plot generated by graph loa As indicated above the values can be saved in either a new or existing variable Following Stata convention option modifier replace which cannot be abbreviated must be provided to overwrite an existing variable Lastly it has come to our attention that two of the p values printed in the output were not explained in the initial insert These p values are for the test of null hypothesis Ho pe 0 The first of these p values results when
56. herwise similar simulation Figure 1 right graph This is puzzling I can only say that the behavior of the null corrected statistics appears to be very erratic for sparse R 2 C 2 tables in these simulations The default corrected statistics show no such erratic behavior for sparse R 2 C 2 tables The default corrected Pearson for example has a slightly inflated rejection rate under the null 0 07 but good power under this alternative gt 0 50 Figure 8 compares the power of the adjusted Wald statistics with that of the default corrected Pearson F statistic for small variance degrees of freedom v 19 For nonsparse tables the default corrected Pearson is more powerful than the adjusted Wald statistics except for the R 2 C 2 table for which the powers are the same The differences are particularly dramatic for larger tables Sparse tables Figure 8 right graph also show this fall off for larger tables o Pearson Corrected F A Log linear Wald Adjusted F o Pearson Corrected F A Log linear Wald Adjusted F o Wald Pearson Adjusted F o Wald Pearson Adjusted F 1 00 7 1 00 4 0 75 7 0 75 7 3 3 3 0 50 3 0 50 a a 0 25 7 0 25 7 0 00 4 0 00 4 T T T T T T T T T T T T T T T T T T T T 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 Table dimensions R C Table dimensions R C Figure 8 Power of adjusted Wald statistics versus svytab s default Pearson variant for nonsparse left an
57. hich data have been imputed impvars 2 should be specified and they should be the last 2 variables in varlist impvars default is 1 impno no of imputations is the number of imputations done for each imputed variable and thus the number of iterations of regressions k that will be required If there is more than one variable with multiple imputations they all must have the same number of imputations robust specifies the Huber White sandwich estimator of variance is to be used in place of the traditional calculation see U 26 10 Obtaining robust variance estimates robust combined with cluster allows observations which are not independent within cluster cluster varname specifies that the observations are independent across groups clusters but not necessarily within groups varname specifies to which group each observation belongs e g cluster personid in data with repeated observations on individuals See U 26 10 Obtaining robust variance estimates cluster can used with pweights to produce estimates for unstratified cluster sampled data but see help svylogit for a command especially designed for survey data Specifying cluster implies robust or reports odds ratios exponentiated coefficients and their standard errors etc rather than unexponentiated coefficients Examples Data for these examples are from the RAND UCLA Los Angeles Mammography Promotion in Churches Program baseline survey conducted in 1995 Data we
58. hlmakfun function declaration program as hidlin makfun or altitude makfun see the example below This hlmakfun program should not be modified it knows how to use the saved matrices to reconstruct the surface and has the form of the hlfun required by hidlin or altitude Options x matname indicates how the x variable is to be cut The argument is either a number of quantiles with a default of y_N 3 in which case xtile is used or a matrix containing the desired x cutpoints Note that intervals are half open low high as for xtile and with m intervals or quantiles there are m 1 cutpoints y matname is similar to the x option z zexpression indicates which summary is to be produced with choices being either freq or statistic varname with a default of freq with choices for statistic being the same as with collapse ground is the z value to be used when an x y cell is empty and the zexpression cannot be evaluated The default is 0 smooth requests that computed z values be smoothed using surrounding cells each with a weight of 1 and the target cell with a weight of 2 as shown below 1 1 1 1 2 1 1 1 1 For cells located outside the grid or where a cell s contents are unknown ground a weight of 0 is used Thus for a corner cell at most 3 neighbors are available and for a cell elsewhere on an edge there are at most 5 neighbors The original h Zfun matrix is copied into matrix h Zful and the smoothed summ
59. hods developed by Rao and Scott 1981 1984 The theory behind this correction is quite advanced and I will only sketch out a little of it later in this article But understanding the theory behind the correction is not necessary to use and interpret the statistic Just interpret the p value next to the Design based F statistic as you would the p value for the Pearson x statistic for ordinary data i e data that are assumed independent and identically distributed iid Complicating this simple command is the fact that I did not just implement one statistic for the test of independence but rather four statistics with two variants of each for a total of eight statistics This was done because the literature on the subject has not indicated that there is a single superior choice However I evaluated these eight in simulations along with several other variants of these statistics and every statistic except the one chosen for the default of this command had a black mark against it So it made the choice of a default very easy Based on these simulations I would advise a practical researcher to just use the default statistic and never bother with any of the others The options that give these eight statistics are pearson the default 1r null a toggle for displaying variants of the pearson and Ir statistics wald 1lwald and noadjust a toggle for displaying variants of the wald and 11wald statistics The options wald and 11wald
60. ial since the untransformed confidence intervals tend to be on average biased away from the null See the Methods and formulas section at the end of this article for details The Rao and Scott correction for chi squared tests Two statistics commonly used for iid data for the test of independence of R x C tables R rows and C columns are the Pearson x statistic R C XP n 5 S Pre Porc Bore 1 r 1c 1 and the likelihood ratio x statistic RC X n 2n 5 2 fo Orc In Bre Pore 2 r 1 c 1 where n is the total number of observations Py is the estimated proportion for the cell in the rth row and cth column of the table and Porc is the estimated proportion under the null hypothesis of independence i e Porc Pr P c the product of the row and column marginals ee Pre and P e ae Prc For iid data both of these statistics are distributed asymptotically as X R 1 C 1 Note that the likelihood ratio statistic is not defined when one or more of the cells in the table are empty The Pearson statistic however can be calculated when one or more cells in the table are empty the statistic may not have good properties in this case but the statistic still has a computable value One can estimate the variance of pre under the actual survey design For instance in Stata this variance can be computed using linearization methods using svymean or svyratio With this variance estimate available the question then becomes how to
61. ibility of implementing a similar F statistic for two way tables but state that its properties have not been studied Note that Rao and Thomas s discussion concerns F statistics produced from the first order corrected X 2 statistics and not from the second order corrected X statistics But there is no reason that one should not consider similar transforms of the second order corrected X 6 statistics into F statistics 40 Stata Technical Bulletin STB 45 Fuller et al 1986 in the PC CARP software take the stricter approach with the second order corrected Ke 6 and turn it into an F statistic with v denominator degrees of freedom This strictness is partially balanced by the fact that rather than d tr A tr A numerator degrees of freedom they use d min tr A ts R 1 C 1 where t3 tr A tr A v 8 Hence d becomes slightly bigger in this formulation trivially so when v is large but noticeably bigger when v is small It should also be noted that Fuller et al use the null hypothesis estimates Pore to compute V srs In a later section we evaluate Fuller et al s variant along with the F statistic suggested by Rao and Thomas 1989 for the second order corrected statistic The results were surprising or at least they surprised me Wald statistics Prior to the work by Rao and Scott 1981 1984 Wald tests for the test of independence for two way tables were developed by Koch et
62. imultaneous testing of regression coefficients with complex survey data use of Bonferroni statistics The American Statistician 44 270 276 Stata Technical Bulletin 49 McDowell A A Engel J T Massey and K Maurer 1981 Plan and operation of the Second National Health and Nutrition Examination Survey 1976 1980 Vital and Health Statistics 15 1 National Center for Health Statistics Hyattsville MD Rao J N K and A J Scott 1981 The analysis of categorical data from complex sample surveys chi squared tests for goodness of fit and independence in two way tables Journal of the American Statistical Association 76 221 230 1984 On chi squared tests for multiway contingency tables with cell proportions estimated from survey data Annals of Statistics 12 46 60 Rao J N K and D R Thomas 1989 Chi squared tests for contingency tables In Analysis of Complex Surveys ed C J Skinner D Holt and T M F Smith Ch 4 89 114 New York John Wiley amp Sons Shah B V B G Barnwell and G S Bieler 1997 SUDAAN User s Manual Release 7 5 Research Triangle Park NC Research Triangle Institute Thomas D R and J N K Rao 1987 Small sample comparisons of level and power for simple goodness of fit statistics under cluster sampling Journal of the American Statistical Association 82 630 636 50 Stata Technical Bulletin STB 45 STB categories and insert codes Inserts in the STB are presently categor
63. in the second main eq n Log likelihood is 194 Note subpop subpopulation is same as full population subpop 1 indicates observation in subpopulation subpop O indicates observation not in subpopulation Survey linear regression pweight rsweight Strata lt one gt PSU clustnum Subpopulation no of obs Subpopulation size 2864 2623753 Number o Number o Number o Populati F 12 Prob gt F R square f obs f strata f PSUs on size 179 d 0 00001 2864 1 191 2623753 53542 88 0 0000 0 9852 1npce members maxfel maxfe2 highfe urban rural KZN ECape NorP reticul elect _cons 173144 0150417 004693 0027249 1936183 3 940108 4 789063 9713577 4252319 6130657 2623947 0620349 4 361922 0084625 001121 0054297 0004576 0198772 0110183 0144696 0119679 0162149 0163161 0136669 0084462 0535379 ow o ow tol 000 000 5 1898365 0128304 0154031 0036276 15441 3 961842 4 817605 9949648 4572162 6452496 2893531 0786953 4 256317 1564514 017253 0060172 0018223 2328265 3 918374 4 760521 9477507 3932476 5808817 2354364 0453744 4 467527 docdist nursdist phardist father mother gender 1npce crop_siz urban rural _cons 1222716 0472442 010398 1235845 0475992 2337818 630567 3970924 6485643 3 369163 4 69402 0129649 0
64. ines x xmar 15 ymar 22 tex tmag 70 global hltexc GvM Finally we get Figure 6 by hidlin makfun xye b 1 x xm 15 ym 22 t tm 70 Average mpg in the quartiles of price by foreign Domestic 22 1 22 2 17 3 16 5 Foreign 30 5 27 2 24 6 20 3 Ii Ns hidlin makfun x 1 1 025 y 3200 8000 50 e 1 2000 5 box lines x xmar 15 ymar 22 tex tmag 70 Figure 6 Using texts on graphs Stored Results All results are stored in globals or matrices whose names start with Al hl globals hlprog h1X1i hlYLi hlXma hlYma hlMag hlXfa hlYfa hlXsh hlYsh h1X hlY hlE hiXn hlYn hin hlNmax hlBox hlCoo hlNeg hltex hl matrices h1Cx h1Cy h1Cz h1Wk h1Pj progname for plotted function func 0 1 indicating which curves are to be drawn 10 default or specified margin values 100 default or specified text magnification gph scaling factors gph shifts xinfo yinfo eye number of z steps y steps total max indicators for corresponding options 1x4 gph coordinates of the corners 1x4 true z value of the corners 2x3 working xinfo and yinfo these may differ from the request because either the object has been oriented differently or because of geometric considerations 2x3 projection matrix from 3D into 2D Note that typing hidlin clean or altitude clean will remove all these stored results from memory These commands invoke the utility hlc
65. is limitation The reason for implementing such a constraint is that all 2D projected points now have fixed horizontal axis coordinates i e all points on the screen align on verticals As a consequence the next point to be drawn is easily identified as visible or invisible according to its position with respect to the current upper and lower edges of the graphed portion These edges are permanently updated as new points are computed and because they have fixed horizontal coordinates their storage is very economical There are indeed N Ny 1 fixed coordinates where N is the number of steps along x i e range step and Ny the number of steps along y Thus even on a 500 by 500 grid there are only 1001 points to memorize for the lower edge and 1001 for the upper edge When a curve becomes invisible a partial segment is drawn from the last visible point to the approximate position where it disappears This position is obtained via linear interpolation as the intersection of the previous visible edge and the segment 10 Stata Technical Bulletin STB 45 joining the last point to the next invisible one Naturally a similar interpolation is performed when the curve goes from invisible to visible These details are exhibited in Figure 3 which incidentally was created entirely in Stata Hidlin example showing 3 lines may reappear hidden d INTERPOLATION 2 curve 2 curve 1 visible 2 24 curve 3 xP x1 a
66. it Akaike s Information Criterion AIC and Schwarz s Criterion SC AIC sc 2 Log Likelihood Num Parameters SN e A E A A a 226 57724 246 02772 214 57724 6 Now we drop age from the model and include history of hypertension ht and uterine irritability Continued on next page Stata Technical Bulletin xi logit low lwt i race smoke ht ui i race Iteration Iteration Iteration Iteration Iteration 0 1 2 3 4 Irace_1 3 Log Likelihood 117 336 Log Likelihood 102 68681 Log Likelihood 102 11335 Log Likelihood 102 10831 Log Likelihood 102 10831 Logit Estimates Log Likelihood 102 10831 naturally coded Irace_1 omitted Number of obs chi2 6 Prob gt chi2 Pseudo R2 189 30 46 0 0000 0 1298 Irace_2 Irace_3 smoke ht 0167325 0068034 Zu 1 324562 5214669 2 9261969 4303893 2 1 035831 3925611 2 1 871416 6909051 2 904974 4475541 2 0562761 9378604 0 95 Conf 0300669 3025055 0826495 2664256 5172672 027784 1 781897 Interval 003398 346618 769744 805237 225565 782164 894449 mlfit Criteria for assessing logit model fit Akaike s Information Criterion AIC and Schwarz s Criterion SC sc 2 Log Likelihood Num Parameters ee Pe cesta teen ea hes A a ee el ee ee See See e ec A 218 21662 240 90885 204 21662 25 Although both models are nonnested we should use the AIC and or SC s
67. ized as follows General Categories an announcements ip instruction on programming cc communications amp letters os operating system hardware amp dm data management interprogram communication dt datasets qs questions and suggestions gr graphics tt teaching in instruction zz not elsewhere classified Statistical Categories sbe biostatistics amp epidemiology ssa survival analysis sed exploratory data analysis ssi simulation amp random numbers sg general statistics sss social science amp psychometrics smy multivariate analysis sts time series econometrics snp nonparametric methods svy survey sampling sqc quality control sxd experimental design sqv analysis of qualitative variables szz not elsewhere classified srd robust methods amp statistical diagnostics In addition we have granted one other prefix stata to the manufacturers of Stata for their exclusive use Guidelines for authors The Stata Technical Bulletin STB is a journal that is intended to provide a forum for Stata users of all disciplines and levels of sophistication The STB contains articles written by StataCorp Stata users and others Articles include new Stata commands ado files programming tutorials illustrations of data analysis techniques discus sions on teaching statistics debates on appropriate statistical techniques reports on other programs and interesting datasets announcements questions and suggestions A submission to the STB
68. l Porc So Rao and Scott leave this as an open question Because of the question of whether to use Pre Or Porc to compute Vars svytab can compute both corrections By default when the null option is not specified only the correction based on re is displayed If null is specified two corrected statistics and corresponding p values are displayed one computed using f and the other using Porc Simulations evaluating the performance of each of these correction methods are discussed later in this article The second wrinkle to be ironed out concerns the degrees of freedom resulting from the variance estimate V of the cell proportions under the survey design The customary degrees of freedom for t statistics resulting from this variance estimate are V Npsu L where npsy is the total number of PSUs and L is the total number of strata Hence one feels that one should use something like y degrees of freedom as the denominator degrees of freedom in an F statistic Thomas and Rao 1987 explore this issue not for two way contingency tables but for simple goodness of fit tests They took the first order corrected X 6 and turned it into an F statistic by dividing it by its degrees of freedom dy R 1 C 1 The F statistic was taken to have numerator degrees of freedom equal to do and denominator degrees of freedom equal to vdo This is much more liberal than using just v as denominator degrees of freedom Rao and Thomas 1989 mention the poss
69. land Timberlake Consultants 47 Hartfield Crescent West Wickham Kent BR4 9DW United Kingdom 44 181 4620495 44 181 4620493 info timberlake co uk http www timberlake co uk United Kingdom Eire Timberlake Consulting S L Calle Montecarmelo n 36 Bajo 41011 Seville Spain 34 5 428 40 94 34 5 428 40 94 timberlake zoom es Spain Timberlake Consultores Lda Praceta do Com rcio 13 9 Dto Quinta Grande 2720 Alfragide Portugal 351 0 1 471 9337 351 0 1 471 9337 351 0 931 6272 55 timberlake co Omail telepac pt Portugal Company Address Phone Fax Email URL Countries served STB 45 Unidost A S Rihtim Cad Polat Han D 38 Kadikoy 81320 ISTANBUL Turkey 90 216 4141958 90 216 3368923 info Ounidost com http abone turk net unidost Turkey
70. lean References Gould W 1991 gr3 Crude 3 dimensional graphics Stata Technical Bulletin 2 6 8 Reprinted in Stata Technical Bulletin Reprints vol 1 pp 35 38 1993 gr3 1 Crude 3 dimensional graphics revisited Stata Technical Bulletin 12 12 Reprinted in Stata Technical Bulletin Reprints vol 2 pp 42 43 14 Stata Technical Bulletin STB 45 gr31 Graphical representation of follow up by time bands Adrian Mander MRC Biostatistical Research Unit Cambridge adrian manderO mrc bsu cam ac uk This command is a graphical addition to the lexis command introduced in STB 27 Clayton and Hills 1995 The lexis command splits follow up into different time bands and is used for the analysis of follow up studies It is more informative to draw the follow up since all statistical analyses are incomplete without extensive preliminary analysis Preliminary analysis usually can be plotting data or doing simple tabulations or summary statistics This command has the same basic syntax as the lexis command with a few additions Follow up starts from timein to timeout and is usually graphically represented by a straight line With no additional information follow up is assumed to start from the same point in time graphically this is assumed to be time 0 This can be offset using the update option by another variable e g date of birth perhaps or date of entry into the cohort For further information about Lexis diagrams see Clayt
71. les as does for price weight mpg logp logw logm l va gen 2 log 1 The items in the first list match up one by one with those in the second list This insert describes a construct cp think Cartesian product that takes between one and five lists and some Stata command With cp the number of items in each list is unrestricted and cp executes the command in question for all combinations of items from the lists For example it can tackle problems of the form do such and such for all n X ng pairs formed from the n items in list and the na items in list2 The construct is designed primarily for interactive use The underlying programming is simply that of nested loops Programmers should avoid building cp into their programs as their own loops will typically work faster The restriction to five lists is not a matter of deep principle but rather reflects a guess about what kinds of problems arise in practice cp could lead to a lot of output Consider the effects on paper and patience your own and your institution s Syntax cp list list2 list3 ceo noheader nostop pause stata cmd Description cp repeats stata_cmd using all possible n tuples of arguments from between one and five lists each possible argument from one list each possible pair of arguments from two lists and so forth In stata_cmd 1 indicates the argument from listl 2 the argument from list2 and so forth The elements of each list must
72. lfa x2 x1 yP y1 alfa y2 y1 where alfa y3 y1 y3 y1 y2 y4 Figure 3 Some details of the hidden line algorithm Syntax for altitude altitude func xinfo 4 4 yinfo 4 nquant symb 4 neg xmargin ymargin text tmag saving filename The function is calculated on the grid defined by xinfo xlow xhigh xstep yinfo ylow yhigh ystep which are required The computed z value altitude is then divided into nquant quantiles which are displayed on the grid using symbol symb The successive quantile levels are represented with different colors and increasing sizes of the symbol so that the appearance truly yields contour effects The legend relative to quantile colors and sizes is shown in the right margin Options Most options are the same as for hidlin xinfo and yinfo are required while two options are specific for altitude nquant declares the desired number of quantiles with a maximum of 20 The default is set to 16 because 8 pens are used e 8 colors thus providing two full pen color cycles symb specifies the choice of graphing symbol numbered as for gph the default is 4 0 dot 1 large circle 4 small circle 2 square 5 diamond not translucid 3 triangle 6 plus The lowest quantile is always represented by a dot so you always know where the surface is at its minimum Example hibivnor The contour graph for the bivariate normal distributi
73. mulations the quantile cut points were varied so that one category was infrequent This frequency was chosen so that zero cells were generated in tables roughly half of the time 42 Stata Technical Bulletin STB 45 R x C tables were generated with 2 lt R C lt 5 The intra cluster correlation was pe 0 25 for all reported simulations For the simulations representing small variance degrees of freedom 20 clusters y 19 ranging in size from 30 to 70 observations where chosen for a total of approximately 1 000 observations The cluster sizes were randomly generated once and then left fixed for subsequent simulations With v 19 and table degrees of freedom dy R 1 C 1 ranging from 1 to 16 we should be able to see what happens when dy approaches v Note that y 19 is not unrealistic The NHANES II data shown earlier have y 31 For the simulations representing large variance degrees of freedom 200 clusters y 199 ranging in size from 3 to 10 observations where chosen for a total of approximately 1300 observations The approximate correlation p between the latent variables that was used to generate an alternative hypothesis was chosen based on R and C and on the type of simulation sparse or nonsparse small or large 1 to give power of around 0 5 to 0 9 for most of the statistics Because of this arbitrariness only the relative power of the statistics can be assessed That is absolute assessments of power across different sim
74. multi record survival time data 3 gr29 labgraph placing text labels on two way graphs 6 gr30 A set of 3D programs T gr31 Graphical representation of follow up by time bands 14 ip14 1 Programming utility numeric lists correction and extension 17 ip26 Bivariate results for each pair of variables in a list 17 ip27 Results for all possible combinations of arguments 20 sbe18 1 Update of sampsi 21 sbe24 1 Correction to funnel plot 21 sg84 1 Concordance correlation coefficient revisited 21 sg89 1 Correction to the adjust command 23 sg90 Akaike s information criterion and Schwarz s criterion 23 sg91 Robust variance estimators for MLE Poisson and negative binomial regression 26 sg92 Logistic regression for data including multiple imputations 28 sg93 Switching regressions 30 svy7 Two way contingency tables for survey or clustered data 33 STB 45 2 Stata Technical Bulletin STB 45 dm60 Digamma and trigamma functions Joseph Hilbe Arizona State University hilbe O asu edu The digamma and trigamma functions are the first and second derivatives respectively of the log gamma function Several numeric approximations exist but the ones used in digamma and trigamma seem particularly accurate see Abramowitz and Stegun 1972 I have prepared two versions of each program one where the user specifies a new variable name to contain the calculated values from those listed in an existing variable the other an immediate command fo
75. n the Stata Reference Manual for a description of these options tab varname specifies that counts should instead be cell totals of this variable and proportions or percentages should be relative to i e weighted by this variable For example if this variable denotes income then the cell counts are instead totals of income for each cell and the cell proportions are proportions of income for each cell See the Methods and formulas section at the end of this article Stata Technical Bulletin 35 missing specifies that missing values of varname and varnamez are to be treated as another row or column category rather than be omitted from the analysis the default cell requests that cell proportions or percentages be displayed This is the default if none of count row or column are specified count requests that weighted cell counts be displayed row or column requests that row or column proportions or percentages be displayed obs requests that the number of observations for each cell be displayed se requests that the standard errors of either cell proportions the default weighted counts or row or column proportions be displayed When se or ci deff or deft is specified only one of cell count row or column can be selected The standard error computed is the standard error of the one selected ci requests confidence intervals for either cell proportions weighted counts or row or column proportions deff or deft
76. odes El and E2 The following 4 conditions should be met 1 The episodes El and E2 belong to the same subject are to be counted as sequential 2 they are subsequent i e the ending time of El coincides with the entry time of E2 3 El was censored not ended by a failure and 4 meaningful covariates are identical on El and E2 These conditions are easily generalized for more than 2 episodes Why should one want to join such episodes The reasons are practical not really statistical Using multiple records when only one suffices is a waste of computer memory Using an uneconomical data representation may cause you to use approximate analytical methods when better methods would have been feasible with a more compact data representation Second most analytical commands require computing time that is proportional to the number of records observations not to the number of subjects Thus a more economical data representation reduces waiting time Syntax The command stjoin implements joining of episodes on these 4 conditions It should be invoked as stjoin varlist keep eps varlist specifies covariates that are meaningful for some analysis Unless keep is specified all other variables in the data apart from the st key variables are dropped If keep is specified all variables are kept in the data Variables not included in varlist may of course be different on episodes that meet the 4 conditions It is safe to assume that the values of
77. of mother in years lwt weight of mother lbs last menstrual period race white black other smoke smoking status during pregnancy 0 1 ptl number of previous premature labours ht history of hypertension 0 1 ui has uterine irritability 0 1 ftv number of physician visits in first semester bwt actual birth weight We will fit a logistic regression model The first model includes age weight of mother at last menstrual period 1wt race and smoke as predictor variables for the birth weight low As we can see age is a nonstatistically significant variable xi logit low age lwt i race smoke i race Irace_1 3 naturally coded Irace_1 omitted Iteration 0 Log Likelihood 117 336 Iteration 1 Log Likelihood 107 59043 Iteration 2 Log Likelihood 107 29007 Iteration 3 Log Likelihood 107 28862 Iteration 4 Log Likelihood 107 28862 Logit Estimates Number of obs 189 chi2 5 20 09 Prob gt chi2 0 0012 Log Likelihood 107 28862 Pseudo R2 0 0856 low Coef Std Err z P gt I z 95 Conf Interval PES pai A A A e E o O e e A age 0224783 0341705 0 658 0 511 0894512 0444947 lwt 0125257 0063858 1 961 0 050 0250417 9 66e 06 Irace_2 1 231671 5171518 2 382 0 017 2180725 2 24527 Irace_3 9432627 4162322 2 266 0 023 1274626 1 759063 smoke 1 054439 3799999 2 775 0 006 3096526 1 799225 _cons 3324516 1 107673 0 300 0 764 1 838548 2 503451 mlfit Criteria for assessing logit model f
78. of the process a few mm yr and the difficulty of obtaining a measurement without disturbance of the process combine to make measurement a major problem Six methods of measurement give 15 concordance correlation coefficients Left to its own devices concord would produce a fair amount of output for these 15 so we write a little program picking up the most important statistics from each run The documentation for concord shows that the concordance correlation is left behind in global macro S_2 its standard error in global macro S_3 and the bias correction factor in global macro S_8 The brief program dispcon uses display to print these out after each program run The biv options used are quiet to suppress the normal output from concord echo to echo variable names con to suppress the new line supplied by default so that the output from dispcon will continue on the same line and header to supply a header string program define dispcon 1 version 5 0 2 display 6 3f 8_2 9 3f S_3 13 3f S_8 3 end describe using rookhope Contains data soil creep Rookhope Weardale obs 20 8 Jun 1998 12 53 vars 6 size 560 1 ip float 7 9 0g inclinometer pegs mm yr 2 at float 9 08 Anderson s tubes mm yr 3 ap float 9 08 aluminium pillars mm yr 4 yp float 7 9 0g Young s pits mm yr 5 dp float 9 08 dowelling pillars mm yr 6 ct float 9 08 Cassidy s tubes mm yr Sorted by biv concord ct dp yp ip at ap qui echo con o dispcon h
79. on which includes in two of its log y functions the derivative necessitates the use of the digamma function Y The latter is not one of Stata s built in functions hence a good approximation is needed I have used a simple numerical approximation to the derivative it appears to work quite well over the region of values used in calculating scores If we define 6 exp xb o the scores used for the Poisson and negative binomial with offset log exposure o are given by Poisson y o y 1 a 1 a Negative binomial a y 1 a In 1 a y y 1 a Waa Unlike Stata s nbreg command nbinreg initializes values using Poisson estimates This takes a little longer but it may be worth it Example We illustrate the use of poisml and nbinreg commands on the 1996 Arizona Medpar data on DRG 475 the dataset is included on the diskette in the file medpar dta poisml los hmo died white age80 type2 type3 nolog irr Poisson Estimates Number of obs 1495 Model chi2 6 947 07 Prob gt chi2 0 0000 Log Likelihood 6834 6053315 Pseudo R2 0 0648 los IRR Std Err z P gt Iz l 95 Conf Interval ps A A A E A A eS hmo 9316981 0223249 2 953 0 003 8889537 9764978 died 784677 0143389 13 270 0 000 7570707 81329 white 8731055 0239723 4 942 0 000 8273626 9213775 age80 9826527 0201582 0 853 0 394 9439271 1 022967 type2 1 270891 0268037 11 366 0 000 1 219427 1
80. on and Hills 1993 Syntax grlexis2 timein fail fup it exp ls update varname event evar saving filename xlab ylab ltitle string btitle string title string symbol nolines numbers noise box The variable timein contains the entry time for the time scale on which the observations are being expanded The variable fail contains the outcome at exit this may be coded 1 for failure or a more specific code for type of failure such as icd may be used it must be coded O for censored observations The variable fup contains the observation times Remarks If there are missing values in the timein variable that line is deleted If there are missing values however in the update variable then the update variable is set to zero Proper handling of missing data values requires additional editing of the dataset or use of the if option On occasion the command will be unable to cope with large x or y axis values and will overwrite the axis the label is on In this case it is suggested that the xlab or ylab options be used Options update specifies variables which are entry times on alternative time scales These variables will be appropriately incremented thus allowing further expansion in subsequent calls event If the subjects are followed up for the entire time but the events do not stop follow up then the event option suppresses the drawing of a symbol at the end of a line and instead uses the values in
81. on can be produced using altitude bivnor x 3 3 06 y 3 3 12 s 5 graph not shown Usually satisfactory stepsizes are 100 steps along x and 50 steps along y with certainly no need for more Using the ranges of the example above this might have been requested as x 3 3 6 100 y 3 3 6 50 since expressions are permitted Note that the altitude representation provides a good indication of where to sit for viewing with hidlin The x and y directions for Figures 1 and 2 are respectively 2 along x 3 along y and 2 along x 4 along y which are easy to visualize on the altitude plot Only the z direction of the eye may need repeated trials Stata Technical Bulletin 11 Syntax for makfun makfun x y x matname y matname z zexpression ground smooth where x and y are any two existing variables makfun generates a function z f x y on an xy grid based on specified cutpoints or on quantiles of existing data in memory The data is preserved but 3 matrices are created and left behind on exit the x and y cutpoints are in h Xcut and hlYcut and the z values are in hlZfun The aim was to provide an interface to the 3D programs hidlin or altitude which can only plot functions not data but it turns out that makfun has general utility because h Zfun stores a nice 3D summary of real data smoothed if so desired The graphical representation of this summary is obtained either from hidlin or altitude via the included
82. onf Interval Ai ee A A se hmo 9316981 0480179 1 373 0 170 8421819 1 030729 died 784677 0510591 3 726 0 000 6907216 8914128 white 8731055 0620901 1 908 0 056 7595114 1 003689 age80 9826527 0620691 0 277 0 782 8682285 1 112157 type2 1 270891 079558 3 829 0 000 1 124146 1 436791 type3 2 105107 4528658 3 460 0 001 1 380886 3 209156 nbinreg los hmo died white age80 type2 type3 nolog irr Negative Binomial Estimates Number of obs 1495 Model chi2 6 151 20 Prob gt chi2 0 0000 Log Likelihood 4780 8947983 Pseudo R2 0 0156 los IRR Std Err z P gt lz 95 Conf Interval EEEE At So Se a ee e en e ii los hmo 9352302 0494308 1 267 0 205 843197 1 037309 died 7917555 0323761 5 710 0 000 7307758 8578237 white 8854497 060065 1 793 0 073 775215 1 01136 age80 9840357 0458491 0 345 0 730 8981542 1 078129 type2 1 272802 06397 4 800 0 000 1 1534 1 404564 type3 2 069855 1562708 9 636 0 000 1 785153 2 399961 A AA A AR AA lnalpha alpha 4339545 lnalpha _cons 1n alpha LR test against Poisson chi2 1 4107 417 P 0 0000 Now we look at negative binomial regression with robust and clustering effect of provider Note that in this case the p values are quite similar to that of the robust Poisson model likewise adjusted by the clustering effect nbinreg los hmo died white age80 type2 type3 nolog irr robust clust provnum Negative Binomial Estimates Number of obs 1495 Model chi2 6 151 20
83. ons are used If the null option is selected then a statistic corrected using proportions under the null is displayed as well See the following discussion for details lr requests that the likelihood ratio test statistic for proportions be computed Note that this statistic is not defined when there are one or more zero cells in the table The statistic is corrected for the survey design using exactly the same correction procedure that is used with the pearson statistic Again either observed cell proportions or proportions under the null can be used in the correction formula By default the former is used specifying the null option gives both the former and the latter Neither variant of this statistic is recommended for sparse tables For nonsparse tables the 1r statistics are very similar to the corresponding pearson statistics null modifies the pearson and 1r options only If it is specified two corrected statistics are displayed The statistic labeled D B null D B stands for design based uses proportions under the null hypothesis i e the product of the marginals in the Rao and Scott 1984 correction The statistic labeled merely Design based uses observed cell proportions If null is not specified only the correction that uses observed proportions is displayed See the following discussion for details wald requests a Wald test of whether observed weighted counts equal the product of the marginals Koch et al 1975 By default an a
84. ot They are expressed as a percentage of the graphing area Default margins are 10 for both x and y 1 e 10 text requests that stored texts be displayed This option invokes the auxiliary program hltex tmag asks for a text magnification the default being 100 The magnification applies to all texts shown by hltex saving stores the graph in filename which must be a new file Example of a function declaration Below is a program defining the bivariate normal density surface It generates the data not the graph It is invoked by hlbivnor x y z in where x and y are any two existing variables and z is created or replaced as necessary Note that the code in this program preceding the actual declaration should appear in any h func and that any parameter you wish to easily access should be declared in a global macro In the present function the correlation p between x and y is needed and the program assumes independence p 0 if rho is empty loc x 1 loc y 2 loc z 37 cap confirm var z if _rc qui gen z mac shift 3 loc in opt parse LDE o actual start of function declaration if rho glo rho 0 loc r 1 rho 2 need parentheses loc c 2 _pi sqrt r delimit qui replace z exp 0x 72 2x rhox x y y 72 2xr Cc in 3 delimit cr end Once the function is declared the 3D representation may be obtained for example by global
85. p and shown in some way through the own option progname _options are the options of progname if such exist 18 Stata Technical Bulletin STB 45 Explanation biv displays bivariate results for each pair of distinct variables in the list of variables supplied to it It is a framework for some command or program call it generically progname that produces results for a pair of variables In some cases perhaps the majority in statistical practice the order of the variables is immaterial for example the correlation between x and y is identical to the correlation between y and x In other cases the order of the variables is important for example the regression equation of y predicted from x is not identical to the converse For the latter case biv has an asy option think asymmetric spelling out that results are desired for x and y as well as for y and z biv might be useful in various ways Here are some examples 1 Some bivariate commands such as spearman and ktau take just two variables thus if you want all the pairwise correlations that could mean typing a large number of commands Actually for spearman there is another work around use for and egen to rank the set of variables in one fell swoop and then use correlate 2 To get a set of scatter plots you could use graph matrix but that may not be quite what you want Perhaps you want each scatter plot to show variable names or you would prefer a slow movie with each plot f
86. pute estimates for a subpopulation use the subpop option Editor s note The ado files for this command can be found in the stata directory on the STB 45 diskette Introduction This command produces two way tabulations with tests of independence for complex survey data or for other clustered data Do not be put off by the long list of options for svytab It is a simple command to use Using the svytab command is just like using tabulate to produce two way tables for ordinary data The main difference is that svytab will compute a test of independence that is appropriate for a complex survey design or for clustered data Here is an example 34 Stata Technical Bulletin STB 45 svyset strata stratid Svyset psu psuid svyset pweight finalwgt svytab race diabetes pweight finalwgt Number of obs 10349 Strata stratid Number of strata 31 PSU psuid Number of PSUs 62 Population size 1 171e 08 DIR NA AA Diabetes Race no yes Total ee OO om SNS aan ee ee White 851 0281 8791 Black 0899 0056 0955 Other 0248 5 2e 04 0253 Total 9658 0342 1 TE poke ie n et Se A Key cell proportions Pearson Uncorrected chi2 2 21 3483 Design based F 1 52 47 26 15 0056 P 0 0000 The test of independence that is displayed by default is based on the usual Pearson x statistic for two way tables To account for the survey design the statistic is turned into an F statistic with noninteger degrees of freedom using the met
87. quested graph_options have been modified slightly To accommodate the optional regression line the default graph options for graph loa now include connect 111 1 symbo1 o andpen 35324 for the lower confidence interval limit the mean difference the upper confidence interval limit the data points and the regression line if requested respectively along with default titles and labels The user is still not allowed to modify the default graph options for the normal probability plot but additional labeling can be added Explanation Publication of the initial version of concord resulted in a number of requests for new or modified features Further a few deficiencies in the initial implementation were identified by users The resulting changes are embodied in this version First the initial implementation did not allow special characters such as parentheses to be included in the labels on the optional graphs Such characters are now allowed when part of an existing label string i e those labels created via Stata s label command Because of parser limitations special characters are not allowed and will result in an error when included in a passed option string Second Bland and Altman 1986 suggested that the loa confidence interval would be valid provided the differences follow a normal distribution and are independent of the magnitude of the measurement They argued that the normality assumption should be valid provided t
88. r which the user simply types a number after the command Syntax digamma varname lif exp in range generate newvar trigamma varname lif exp in range Senerate newvar digami trigami Examples We find the values of the digamma and trigamma functions for x 1 2 10 set obs 10 obs was 0 now 10 gen x _n digamma x g dx trigamma x g tx list x dx tx La 1 577216 1 645019 2 2 4227843 6449341 3 3 9227843 3949341 4 4 1 256118 283823 5 5 1 506118 221323 6 6 1 706118 181323 Fe T7 1 872784 1535452 8 8 2 015641 133137 9 9 2 140641 117512 10 10 2 251753 1051663 Reference Abramowitz M and I Stegun 1972 Handbook of Mathematical Functions New York Dover A tool for exploring Stata datasets Windows and Macintosh only John R Gleason Syracuse University loesljrg ican net Surely describe is one of the first commands issued by new Stata users and one of the first invoked by Stata veterans when they begin to examine a new dataset Simple forms of the list summarize tabulate and graph commands enjoy a similar status and for good reason These commands are central to the processes of learning about Stata for new users and of understanding an unfamiliar dataset for all users This insert presents varxplor a tool that might be viewed as an interactive form of the describe command in much the same sense that Stata s Browse window is an interactive form of the list command
89. rds For example placing w_ in the Locator window and clicking Locate will search for variable names that begin with the characters w_ 5 The default launch button assignments are defined by a local macro near the top of the varxplor ado file Any other set of five one word Stata commands can be used as the defaults The default variable placeholder character is defined by a nearby global macro that too can be changed if necessary 6 One default button assignment is Notes which displays notes associated with the variable in the Locator window Observe that Notes is not Stata s notes command but varxplor s own internal routine for displaying notes Also it might seem curious that another launch button defaults to the describe command This is because the contents of varxplor s Variables window cannot be directly copied to the Results screen and hence to a log file invoking describe solves that problem 7 Rather than typing varxplor from the command line some users may prefer to click a menu item or press a keystroke combination The included file vxmenu do arranges for that Typing do vxmenu on Stata s command line adds an item named Xplor to Stata s top level menu Afterward one mouse click launches varxplor Windows users can also use the Alt X keystroke shortcut To make this arrangement permanent add the line do vxmenu to the file profile do alternatively copy the contents of vxmenu do into profile do See U 5 7
90. re sampled in clusters based on churches chid The outcome of interest is respondent compliance with AMA cancer screening guidelines for breast cancer comply More than 18 of respondents failed to report income Income was imputed using a Bayesian bootstrap method not shown or discussed here In this example all variables are 0 1 indicator variables Income greater than 10 000 inc10 is imputed 10 times and stored as inc10_01 inc10_10 use stbimp clear implogit comply partner dr_enthu hisp dropout dr_hisp dr_asian dri_more noinsr gt inc10_01 impvars 1 impno 10 cluster chid Iteration no 1 complete Iteration no 2 complete output omitted Iteration no 9 complete Iteration no 10 complete Logistic Regression using imputed values Coefficients and Standard Errors Corrected N 1141 Log Likelihood for component regression no 1 650 85724 Log Likelihood for component regression no 2 650 95298 output omitted Log Likelihood for component regression no 9 650 91123 Log Likelihood for component regression no 10 651 05008 comply Coef Std Err t P gt t 95 Conf Interval nee toe SA ae tee ee ens ee ea oh he ee ee eee partner 3343246 1163444 2 874 0 018 0711354 5975138 dr_enthu 8877968 1437799 6 175 0 000 5625442 1 21305 hisp 4692397 2663255 1 762 0 112 1 07171 1332306 dropout 5092944 2159917 2 358 0 043 9979015 0206872 dr_hisp 5585531 2153716 2 593 0 029 1 045758
91. requests that the design effect measure deff or deft be displayed for either cell proportions counts or row or column proportions See R svymean for details The mean generalized deff is also displayed when deff or deft is requested see the following discussion for an explanation of mean generalized deff proportion or percent requests that proportions the default or percentages be displayed nolabel requests that variable labels and value labels be ignored nomarginals requests that row and column marginals not be displayed format fmt specifies a format for the items in the table The default is 46 0g See U 19 5 Formats controlling how data is displayed vertical requests that the endpoints of confidence intervals be stacked vertically on display level specifies the confidence level i e nominal coverage rate in percent for confidence intervals The default is level 95 or as set by set level see U 26 4 Specifying the width of confidence intervals pearson requests that the Pearson x statistic be computed By default this is the test of independence that is displayed The Pearson x statistic is corrected for the survey design using the second order corrections of Rao and Scott 1984 and converted into an F statistic One term in the correction formula can be calculated using either observed cell proportions or proportions under the null hypothesis i e the product of the marginals By default observed cell proporti
92. rful are the Wald statistics compared with the Rao and Scott corrected statistics The Rao and Scott corrected statistics are significantly more powerful than the adjusted Wald statistics for small to moderate variance degrees of freedom especially for large tables 5 How good is svymlog for a test of independence At best it is as good as the adjusted log linear Wald statistic which is to say fairly bad 6 Is one statistic clearly better than the others All of the statistics except the default corrected Pearson F statistic collected black marks in the simulations The default corrected Pearson F statistic was slightly anticonservative for small tables when the variance degrees of freedom were small but other than that it did remarkably well It exhibited reasonably true Type I error for small sparse tables when other statistics behaved erratically However these simulations only used one particular model of sparse tables so it would be unwarranted to generalize this observation to all sparse tables The corrected likelihood ratio F statistic is an equally good choice for nonsparse tables but it is no better so there is no reason to ever use it over the corrected Pearson F statistic Hence I recommend the use of the default pearson statistic of svytab in all situations Conversely I recommend ignoring all the other statistics in all situations unless you have a particular pedagogical interest in them Methods and formulas We assume here t
93. rrors for multiply imputed data in the logistic regression context For a complete discussion of multiple imputation see Rubin 1987 Logistic regression for data including multiple imputations implogit depvar varlist weight lif exp in range impvars no of vars impno no of imputations robust cluster varname level 4 or depvar may not contain multiple imputation data varlist may contain multiple imputation data with the following conditions variables containing imputed data must be the last variables in varlist and imputed variables must have variable names following special conventions that is they must have fewer than 5 characters and have _01 _xx appended to them where xx is the number of imputations done Even though an imputed variable may have many individual variables to repres ent it include it only once in varlist For example suppose the variable incom was imputed 5 times It should be labeled incom_01 incom_02 incom_03 incom_04 incom_05 In the command list only one say incom_01 The program will iterate through the numbers and take care of the rest If you r variables are not named properly the program will not work fweights and pweights are allowed implogit does not share features with all estimation commands Because of the external variance adjustments implicit in the corrections to the standard errors and the programmer s limited skill in matrix algebra this program does not post a full varianc
94. s ht winner Winning Presidential candidate Figure 3 The options b1 cmdstr b5 cmdstr configure the five launch buttons in left to right order The argument cmdstr is effectively just a string to be passed to Stata s command processor the first word of that string is used to decorate the button More precisely when a launch button is clicked it is as though cmdstr has been entered on Stata s command line with the variable name in the Locator window substituted wherever a certain placeholder appears in cmdstr the default placeholder is the character For example to make Button 4 launch the list command with the nolabel option start varxplor with Stata Technical Bulletin 5 varxplor b4 list nolabel gt The fourth button in Figures 2 and 3 reflects this startup option The character will be replaced with the variable name in the Locator window when Button 4 is clicked Note that the default setup for Button 4 is equivalent to either b4 summarize or b4 summarize they are the same because varxplor automatically appends when cmdstr consists of a single word To force a null variable list use for example b4 summarize note the blank space preceding the comma Also note that certain commands cannot be assigned to a launch button For example an option such as b5 graph 7 bin 20 is unacceptable to Stata s parser because of the embedded parentheses However the desired effect can be
95. s of freedom of the Fuller et al variant to vd but since the numerator degrees of freedom for the Fuller et al variant equation 8 are larger than the numerator degrees of freedom calculated according to Rao and Scott s 1984 formulas this leads to a uniformly anticonservative statistic So although the theory behind the Fuller et al 1986 variant appears compelling simulations show it to be problematic 44 Stata Technical Bulletin STB 45 Unadjusted and adjusted Wald statistics Figure 4 shows the behavior of the unadjusted Wald statistics Koch et al 1975 under the null hypothesis of independence for nonsparse and sparse tables for v 19 Note the scale of the left axis As the table degrees of freedom d R 1 C 1 approach the variance degrees of freedom y 19 the rejection rate approaches 1 Clearly this behavior makes an unadjusted Wald statistic unsuitable for use in these situations o Log linear Wald Unadjusted F A Wald Pearson Unadjusted F o Log linear Wald Unadjusted F A Wald Pearson Unadjusted F 1 00 7 1 00 4 o o gt gt 2 2 iD 0 7574 0 7574 Q 2 o o a E E o o 5 0 50 7 0 50 7 ES ES o o g E lt 2 E E 0 25 4 3 0 25 4 3 2 T d 0 05 7 0 05 7 0 00 7 0 00 7 T T T T T T T T T T T T T T T T T T T T 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 22 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 Table dimensions R C Table dimensions R C Figure 4 Unadjus
96. saved how sorted and so on The Variables window is at the bottom It is divided into three sections the middle one shows a list of current variable names a multi purpose display panel is located to the right of the names and to the left is a stack of six scroll buttons used to navigate the variable list The contents of the multi purpose display are controlled by the radio buttons above it To show the data types of variables rather than variable labels for example click the Data Type button and then click any of the six scroll buttons or the Refresh button to avoid scrolling the variable list al VarXplor gt presdent dta x Last saved 1 Jul 1998 11 17 Obs 36 Vars 11 of 11 Width 51 Exit Sorted by year Help Notes inspect codebook summarize describe Locate year bd Refresh Variable C Data Type Format C ValueLabel Variable Label Top year Election year PgUp winner Winning Presidential candidate Up w_party Winner s party Dn w_ht Winner s height in PgDn w_incumb Incumbent winner Bottom w_age Winner s age Figure 1 If more than six variables are available the scroll buttons traverse the variable list in an obvious manner Clicking Dn for example shifts downward one position in the variable list that is moves the variables one position upward in the Variables window Clicking PgDn shifts six positions downward in the variable list and clicking Bottom shifts so that the last varia
97. set by some starting time date in the y direction The automatic labeling of axes is between minimum and maximum points and they are labeled as time in and follow up In brackets the actual variables used are displayed grlexis2 timein fail fup imein Time in LEXIS Diagram p 88 7 23 1 fup Follow up Figure 1 Taking the same dataset the follow up lines can now be offset in the x direction Previously time in may be the age of the person entering the cohort and datein may contain the dates that the subject entered the cohort Now the follow up times are more meaningful grlexis2 timein fail fup up datein imein Time in LEXIS Diagram l ae 23 1 1 60 fup Follow up Figure 2 The following command just adds some of the options to improve the finished graph xlab and ylab must have numbers as arguments to these options and no best guess system is used as in all other Stata graphs The numbers option allows the drawing of text next to the events representing the line number in the dataset The title options are similar to the usual graph options grlexis2 timein fail fup up datein numbers xlab 0 30 60 ylab 0 20 40 60 10 gt ltitle Time in btitle Follow up title my graph 16 Stata Technical Bulletin STB 45 Time in my graph ye 2 304 dl eee i 8 9 40 7 20 7 6 o T 1 o 30 60 Follow up Figure 3 Take the same dataset but this time timein are the event times and everyone entere
98. sparse tables at least in the simulations I ran For nonsparse tables it does not matter which is used they both yield similar statistics 2 What should one use the y denominator degrees of freedom as Fuller et al 1986 have implemented in PC CARP or something like the more liberal vd degrees of freedom suggested by Rao and Thomas 1989 The Fuller et al variant is too conservative for all but the smallest tables The Rao and Thomas suggestion appears better although it produces slightly anticonservative statistics for the smallest tables 3 How anticonservative are the unadjusted Wald statistics Koch et al 1975 They can be dangerously anticonservative For large tables and small variance degrees of freedom i e a small to moderate number of PSUs they can reject the null hypothesis most of the time even though the null hypothesis of independence is true Only when the variance degrees of freedom are very large gt 1000 and the unadjusted and adjusted statistics are approximately equal would the use of the unadjusted statistic be justified The adjusted log linear Wald statistics appear to be uniformly anticonservative for small to moderate variance degrees of freedom The Pearson Wald statistic the wald option of svytab appears to have reasonable properties under the null hypothesis in this situation However like the Rao and Scott null corrected statistics it can exhibit erratic behavior in small sparse tables 4 How powe
99. such variables are chosen at random among the values of these variables on the joined episodes eps 4 specifies the minimum elapsed time between exit and re entry so that subsequent episodes are to be counted as sequential eps defaults to 0 gr29 labgraph placing text labels on two way graphs Jon Faust Federal Reserve Board faust Ofrb gov labgraph is an extension of the graph two way version command that allows one to place a list of text labels at specified x y coordinates on the graph Thus one can label points of special interest or label lines on the graph Labeling lines may be especially useful in rough drafts differing line styles and a legend are probably preferred for more polished graphs All graph options are supported two new options are supplied and one graph option is modified The two new options are for specifying labels and their locations labtext string string specifies a semicolon delimited list of text labels labxy real real l real real specifies a semicolon delimited list of x y coordinates for the labels You must state an x y pair for each labtext string The label will appear centered at y where is the value of the x axis variable in the labgraph command that is closest to the requested x coordinate The trim option of graph is modified trim controls the size of text labels and defaults to 8 in graph In labgraph trim defaults to 32 the maximum allowed by graph
100. tata Technical Bulletin STB and the contents of the supporting files programs datasets and help files are copyright by StataCorp The contents of the supporting files programs datasets and help files may be copied or reproduced by any means whatsoever in whole or in part as long as any copy or reproduction includes attribution to both 1 the author and 2 the STB The insertions appearing in the STB may be copied or reproduced as printed copies in whole or in part as long as any copy or reproduction includes attribution to both 1 the author and 2 the STB Written permission must be obtained from Stata Corporation if you wish to make electronic copies of the insertions Users of any of the software ideas data or other materials published in the STB or the supporting files understand that such use is made without warranty of any kind either by the STB the author or Stata Corporation In particular there is no warranty of fitness of purpose or merchantability nor for special incidental or consequential damages such as loss of profits The purpose of the STB is to promote free communication among Stata users The Stata Technical Bulletin ISSN 1097 8879 is published six times per year by Stata Corporation Stata is a registered trademark of Stata Corporation Contents of this issue page dm60 Digamma and trigamma functions 2 dm61 A tool for exploring Stata datasets Windows and Macintosh only 2 dm62 Joining episodes in
101. tatistics to compare them As we can see from the results the second model presents considerably lower AIC and SC values AIC 218 22 SC 240 91 than the first model AIC 226 58 SC 246 03 As we said earlier there is no way to test if the difference between the two AICs is statistically significant The correctness of the implementation of calculation methods of AIC and SC statistics was assessed by doing the example with S PLUS and SAS respectively and identical results were obtained Saved results mlfit saves the following results in the S_ macros Acknowledgments S_E_aic AIC statistic S E_sc SC statistic S E_11 log likelihood value S E_112 2 log likelihood value S_E_np number of parameters fitted in the model S_E_nobs number of observations This work was done while Aurelio Tobias was visiting the Institute of Primary Care University of Sheffield UK Aurelio Tobias was funded by a grant from the British Council and from the Research Stimulation Fund by ScHARR University of Sheffield References Akaike H 1974 A new look at statistical model identification IEEE Transactions on Automatic Control 19 716 722 Goldstein R 1992 srd12 Some model selection statistics Stata Technical Bulletin 6 22 26 Reprinted in Stata Technical Bulletin Reprints vol 1 pp 194 199 Hosmer D W and S Lemeshow 1989 Applied Logistic Regression New York John Wiley amp Sons McCullagh P and J A Nelder 19
102. ted Wald statistics under null for nonsparse left and sparse right tables variance df 19 o Log linear Wald Adjusted F A Wald Pearson Adjusted F o Log linear Wald Adjusted F A Wald Pearson Adjusted F 0 100 7 0 30 74 o o gt gt 2 2 lo 0 075 7 10 o o S roy T T e 0 20 7 E ES E 0 0507 A z T d ES o o E E S S 0 107 3 0 025 4 3 gt T E E 0 054 0 000 4 0 00 4 T T T T T T T T T T T T T T T T T T T T 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 Table dimensions R C Table dimensions R C Figure 5 Adjusted Wald statistics under null for nonsparse left and sparse right tables variance df 19 The adjusted Pearson Wald statistic Figure 5 behaves much better For nonsparse tables the observed rejection rate is close to the nominal 0 05 level For sparse tables the statistic is very anticonservative for the R 2 C 2 table like the null corrected statistics and also very anticonservative for some of the larger tables In agreement with the observations of Thomas and Rao 1987 the adjusted log linear Wald statistic is almost uniformly anticonservative and is especially poor for sparse tables Note that the simulation results for the log linear Wald statistic are effectively based on fewer replications for sparse tables Figures 3 and 4 right graphs since the statistic was often undefined because of a zero cell in the table Using svymlog for a test of independence The s
103. ted likelihood ratio statistic when tables are not sparse Stata Technical Bulletin 43 o LR Corrected chi2 A LR Corrected F o LR Corrected chi2 A LR Corrected F O LR Corrected null chi2 LR Corrected null F o LR Corrected null chi2 LR Corrected null F 0 100 4 0 20 4 0 075 7 0 157 0 050 4 Rejection rate at nominal 0 05 level Rejection rate at nominal 0 05 level 0 10 7 0 025 7 0 05 7 0 000 7 0 00 7 T T T T T T T T T T T T T T T T T T T T 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 Table dimensions R C Table dimensions R C Figure 2 Variants of the likelihood ratio statistic under null for nonsparse left and sparse right tables variance df 19 In the sparse tables simulations for the likelihood ratio statistics right graph of Figure 2 there are many instances in which these statistics are not defined because of a zero cell Of those sparse tables for which the statistics could be computed the null corrected likelihood ratio statistics display severe conservatism and the default corrected likelihood ratio statistics exhibit unsatisfactory anticonservatism especially for the smaller tables e g rejection rates gt 0 1 for R 2 C 2 and R 2 C 3 The Fuller et al PC CARP variant Figure 3 compares the statistic implemented by Fuller et al 1986 in the PC CARP software with the default corrected Pearson F statistic svytab s default statistic
104. ternative hypothesis of nonindependence to evaluate power There is one point about simulations for tests of independence I cannot emphasize strongly enough It is essentially impossible to do simulations that definitively prove anything in general This is because there is an infinite number of distributions that one could assume for the underlying true cell proportions Contrast this to the case of for example a maximum likelihood estimator in which one can use the assumed likelihood function as the distribution for the simulations Hence evaluation of the statistics should focus on failure If a statistic shows undesirable properties e g anticonservative p values under the null or poor power under an alternative for a particular simulation then it would be reasonable to assume that the statistic may fail in this manner in at least some similar situations with real data Another shortcoming of the following simulations must be mentioned These statistics are intended for survey data A common paradigm for the theoretical development of many survey estimators is that of sampling from a fixed finite population Under this paradigm the properties of an estimator are evaluated by considering repeated sampling from the same fixed finite population under the same survey design Hence to do simulations following this paradigm one should first generate a finite population from an assumed distribution of the population i e a superpopulation
105. the model Lower values of the AIC statistic indicate a better model and so we aim to get the model that minimizes the AIC Schwarz s criterion SC provides a different way to adjust the 2log likelihood for the number of parameters fitted in the model and for the total number of observations The SC is defined as SC 2log likelihood p x In n where p is again the total number of parameters in the model and n the total number of observations in the dataset As for the AIC we aim to fit the model that provides the lowest SC We should note that both the AIC and SC can be used to compare disparate models although care should be taken because there are no formal statistical tests to compare different AIC or SC statistics In fact models selected can only be applied to the current dataset and possible extensions to other populations of the best model chosen based on the AIC or SC statistics must be done with caution Syntax The m1fit command works after fitting a maximum likelihood estimated model with one of the following commands clogit glm logistic logit mlogit or poisson The syntax is mlfit 24 Stata Technical Bulletin STB 45 Example We tested the mlfit command using a dataset from Hosmer and Lemeshow Hosmer and Lemeshow 1989 on 189 births at a US hospital with the main interest being in low birth weight The following ten variables are available in the dataset low birth weight less than 2 5 kg 0 1 age age
106. the test is performed using the asymptotic point estimate and variance The second occurs when Fisher s z transformation is first applied While not particularly applicable to the measurement question at hand failure to reject this hypothesis indicates serious disconcordance between the measures The more interesting hypothesis Ho pe 1 is not testable The user is advised to use the confidence intervals for pe to assess the goodness of the relationship Stata Technical Bulletin 23 Saved Results The system S_ macros are unchanged Acknowledgments We thank Richard Hall and Richard Goldstein for comments that motivated many of these changes and additions References Bland J M and D G Altman 1986 Statistical methods for assessing agreement between two methods of clinical measurement Lancet 1 307 310 1995 Comparing methods of measurement why plotting difference against standard is misleading Lancet 346 1085 1087 Lin L FK 1989 A concordance correlation coefficient to evaluate reproducibility Biometrics 45 255 268 Steichen T J and N J Cox 1998 sg84 Concordance correlation coefficient Stata Technical Bulletin 43 35 39 sg89 1 Correction to the adjust command Kenneth Higbee Stata Corporation khigbee stata com The adjust command Higbee 1998 has been improved to handle a larger number of variables in the variable list Previously it would produce an uninformative error message when the number
107. ty Netherlands weesie Oweesie fsw ruu nl I recently encountered a bug in numlist see Weesie 1997 that may occur in numeric lists with negative increments In this new version of numlist this bug was fixed In addition I improved the formatting of output to reduce the need for using explicit formatting Finally I replaced the relatively slow sorting algorithm with a Stata implementation of nonrecursive quicksort for numbers see Wirth 1976 The sorting commands qsort qsortidx are actually separate utilities that may be of some interest by themselves to other Stata programmers Some testing however indicated that a quicksort in Stata s macro language becomes quite slow for complex lists For instance sorting a macro with 1 000 random numbers took so long that I initially thought the main loop did not terminate due to some bug in my code This is clearly stretching Stata s language beyond its design and purpose I hope that Stata Corporation will one day apply its very fast sorting of numbers in variables to numbers in strings and macros References Weesie J 1997 ip14 Programming utility Numeric lists Stata Technical Bulletin 35 14 16 Reprinted in Stata Technical Bulletin Reprints vol 6 pp 68 70 Wirth N 1976 Algorithms Data Structures Programs Englewood Cliffs NJ Prentice Hall Bivariate results for each pair of variables in a list Nicholas J Cox University of Durham UK FAX 011 44 91 374 2456 n j cox dur
108. ulations cannot be made For all simulations 1 000 replications were run Simulations of the null for nonsparse and sparse tables for small v Simulations of the null hypothesis of independence for small v should be a good trial of the denominator degrees of freedom for the Rao and Scott corrected F statistics and also a good trial of the unadjusted versus adjusted Wald statistics Figure 1 shows the observed rejection rate at a nominal 0 05 level for four variants of the Rao and Scott corrected Pearson statistic Shown are the two second order corrected x statistics X from equation 5 The one labeled null is corrected using Porc to compute Vz in design effects matrix A and I refer to this as the null corrected statistic The other one uses Pre and I refer to this as the default corrected statistic since it is svytab s default o Pearson Corrected chi2 A Pearson Corrected F o Pearson Corrected chi2 A Pearson Corrected F o Pearson Corrected null chi2 Pearson Corrected null F O Pearson Corrected null chi2 Pearson Corrected null F 0 100 4 0 20 4 0 075 4 0 15 4 Rejection rate at nominal 0 05 level Rejection rate at nominal 0 05 level 0 050 4 Zz e 0 107 0 025 7 0 05 4 0 000 4 0 00 4 T T T T T T T T T T T T T T T T T T T T 2 2 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 232 2 3 2 4 2 5 3 3 3 4 3 5 4 4 4 5 5 5 Table dimensions R C Table dimensions R C Figure 1 Variants of the Pearson
109. ull size 3 You write a program to do some bivariate work biv provides the basic scaffolding of looping round a set of names to get all the distinct pairs Thus your program can concentrate on what is specific to your problem biv also allows the minimal decoration of a one line header pausing after each run of progname and suppressing the program s output and processing it with the user s own program Note that biv could lead to a lot of output if p is large and or the results of progname are bulky If p is 100 a modest number of variables in many fields there are 4 950 pairs if the order of the variables is immaterial and 9 900 pairs otherwise Users should consider the effects on paper and patience their own and their institution s Examples In the auto dataset supplied with Stata we have several measures of vehicle size Scatter plots for these would be obtained by biv graph length weight displ xlab ylab With Stata for Windows the user may prefer biv graph length weight displ xlab ylab pause to allow enough time to peruse the graphs The patterns in these scatterplots are basically those of monotonic relationships with some curvature These might be expected not only from experience but also on dimensional grounds With monotonicity and some lack of linearity the Spearman correlation is a natural measure of strength of relationship biv graph length displ weight gt graph length displ gt graph length wei
110. use it to estimate the true distribution of the statistics Ke and Xf Rao and Scott 1981 1984 showed that asymptotically Xx and Beam are distributed as R 1 C 1 Xan Y A amp W 3 k 1 where the W are independent x variables and the are the eigenvalues of A X VersX2 X VX2 4 where V is the variance of the prc under the survey design and Vsrs is the variance of the Pre that one would have if the design were simple random sampling namely Vsrs has diagonal elements Prell Pre n and off diagonal elements PrcPst n X takes a bit of explaining Rao and Scott do their development in a log linear modeling context So consider 1 X4 X2 as predictors for the cell counts of the R x C table The X matrix of dimension RC x R C 2 contains the R 1 main effects for the rows and the C 1 main effects for the columns The X2 matrix of dimension RC x R 1 C 1 contains the row and column interactions Hence fitting 1 X X2 gives the fully saturated model i e fits the observed values perfectly and 1 X gives the independence model The X matrix is the projection of X onto the orthogonal complement of the space spanned by the columns of X 1 where the orthogonality is defined with respect to Vers i e X Vss X 0 I do not expect anyone to understand from this brief description how this leads to equation 3 see Rao and Scott 1984 for the proofs However even without a
111. varxplor resembles Stata s Variables window except that more information is available a given variable can be more easily located and more can be done once a variable is located Note that varxplor uses the dialog programming features new in Version 5 0 for Windows and Macintosh only and so is restricted to those platforms We begin by demonstrating some features of varxplor and delay presentation of its formal syntax First varxplor provides much of the same information as describe Most importantly there is a Variables window that shows variable names variable labels value label assignments data types and output formats Unlike the describe command only one of those categories of information is visible at a time but in return one gains the ability to scroll about in the list of variables in either dataset order or alphabetical order to rapidly locate any variable and with a single mouse click to execute commands such as Stata Technical Bulletin 3 summarize or list on that variable The set of commands that can be so executed is configurable better still varxplor has its own rendition of Stata s command line from which most Stata commands can be issued To illustrate use the dataset presdent dta included with this insert issue the command varxplor and a dialog box resembling Figure 1 will appear The top portion of the dialog displays general information about presdent dta a count of variables and observations date last
112. vymlog command can be used to conduct a test of independence for two way tables One merely does the following xi svymlog z1 i z2 Svytest I Stata Technical Bulletin 45 For those readers not familiar with xi note that the I variables are dummies for the z2 categories Note also that svytest by default computes an adjusted F statistic This command sequence using svymlog was included in all the simulations The results are easy to describe for every nonsparse tables simulation svymlog yielded the same results as the adjusted log linear Wald statistic For sparse tables svymlog was uniformly and seriously anticonservative Simulations of the null for nonsparse and sparse tables for large v Since all of the theory for the various statistics is asymptotic as the number of PSUs clusters goes to infinity one expects that all the statistics should be well behaved under the null for nonsparse tables at least Simulations of nonsparse tables with y 199 bear this out for all statistics except for the unadjusted Wald statistics which are surprisingly anticonservative for some of the larger tables see the left graph of Figure 6 o Log linear Wald Unadjusted F A Wald Pearson Unadjusted F o Log linear Wald Unadjusted F A Wald Pearson Unadjusted F o Log linear Wald Adjusted F Wald Pearson Adjusted F o Log linear Wald Adjusted F Wald Pearson Adjusted F 0 100 7 _ _ 0 5074 o o gt gt O a o 0 075 7 Lo 3
113. with noadjust yield the statistics developed by Koch et al 1975 which have been implemented in the CROSSTAB procedure of the SUDAAN software Shah et al 1997 Release 7 5 Based on simulations which are detailed later in this article I recommend that these two unadjusted statistics only be used for comparative purposes Other than the survey design options the first row of options in the syntax diagram and the test statistic options the last row of options in the diagram most of the other options merely relate to different choices for what can be displayed in the body of the table By default cell proportions are displayed but it is likely that in many circumstances it makes more sense to view row or column proportions or weighted counts Standard errors and confidence intervals can optionally be displayed for weighted counts or cell row or column proportions The confidence intervals are constructed using a logit transform so that their endpoints always lie between 0 and 1 Associated design effects deff and deft can be viewed for the variance estimates The mean generalized deff Rao and Scott 1984 is also displayed when deff or deft is requested this deff is essentially a design effect for the asymptotic distribution of the test statistic see the discussion of it below Options The survey design options strata psu fpc subpop and srssubpop are the same as those for the svymean command see R svyset and R svymean i
114. with the assumption of log likelihood criterion of case independence still retained The use of the Huber White robust standard error sandwich estimator allows one to model data which may otherwise violate the log likelihood assumption of the independence of cases Essentially the method adjusts the standard errors to accommodate extra correlation in the data The parameter estimates are left unadjusted Because the robust estimator can be used in such a manner for correlated data it has been the standard method used by GEE programs to display standard errors Stata has implemented the robust and cluster options with many of its regression routines but they have not yet been made part of Stata s poisson and nbreg ado files I have written programs which otherwise emulate the poisson and nbreg commands but add the robust cluster and score options The programs called poisml and nbinreg were written using Stata s ML capabilities poisml calls mypoislf ado and nbinreg calls nbinlf ado for log likelihood calculations Robust estimators are themselves calculated using the so called score function In Stata this is defined as the derivative of the log likelihood function with respect to B the parameter estimates When determining the score for an ancillary parameter such as is the case with the negative binomial one must calculate the derivative of the LL function with respect to that parameter here termed For the negative binomial LL functi
115. x and coordinates and only draw the x lines giving Figure 5 global xye x 1 1 025 y 3200 8000 50 e 1 2000 5 hidlin makfun xye b c 1 x 1 00 3200 00 1 00 3200 00 22 07 1 00 8000 00 20 29 8000 00 16 45 Figure 5 A better view of the surface in Figure 4 Adding texts In the previous graph we would like to add some details with the text option We first clear any texts in memory hltex clean mat li hlZfun hlZfun 2 4 cel c2 c3 c4 ri 22 066668 22 214285 17 333334 16 454546 r2 30 5 27 25 24 571428 20 285715 Suppose we want to show the z levels on the graph The utility mat2mac copies a row of a matrix into a global macro mat2mac hlZfun 1 tx1 6 1f copy row 1 into tx1 format 6 1 tx1i 2250 22 2 17 3 16 5 Stata Technical Bulletin 13 mat2mac hlZfun 2 tx2 6 1f tx2 30 5 27 2 24 6 20 3 copy row 2 into tx2 format 6 1 Next we define a number of texts global hltexl mag 80 global hltexr mag 80 Foreign tx2 hidlin makfun xye b 1 x xm 15 ym 22 t tm 70 global hltext1 mag 100 Average mpg Domestic tx1 in the quartiles of price by foreign global hltexb2 hidlin makfun xye global hltexb1 box l

STATA September 1998 TECHNICAL STB-45 BULLETIN

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