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R for Programmers - matloff - University of California, Davis

1. 6 7 Matrices 6 7 1 General OperatiOnS ee 6 7 2 Matrix Row and Column Names 6 7 3 Matrix Indexing ee 6 8 Sensing the Number of Rows and Columns of a MatrIX o 6 9 Treating a Vector As a One Column Matrix 2 2 ee ee ee 6 10 Adding Deleting Elements of Vectors and Matrices o o 6 11 Matrix Row and Column Mean Functions oaoa e 6 12 Linear Algebra Operations on Vectors and Matrices o o 5 6 6 1 7 1 Creation 10 11 11 12 12 12 13 16 16 17 17 18 18 19 20 20 20 22 22 23 24 24 25 25 26 7 2 List Tags and Values and the unlist Function o o e 7 3 Issues of Mode Precedencel ee a a a Cee ye a o Ge a A ia a aaa a a Boe dea da Saud 76 Indexingof Lists ios a a a a a Sd MI Si eota AAA 7 8 Recursive Lists 0 ooo omo sos a o a eee a E E a 8 Data Frames 8 1 A Second R Example Session e 8 2 List Representation 8 3 Matrix Like OperatlOnsS ee 8 3 1 rowMeans and colMeaasOl a 8 3 2 rbindQ and cbmdO os se ea a ea a a a E E e a 8 3 3 Indexing sor aar ieda ar a A a EN 8 4 Creating a New Data Frame from Scratch aooaa a fe ty a We A de AE A ee ta a eh es 8 6 The Factor Factor s orana i ae t o e a es ue age Geis tester ae adh te bate a e Sad Phe oe hore 9 Factors and Tables 10 Mis
2. pick from Urn 1 and put in Urn 2 if runif 1 lt nb1 n1 nb2 lt nb2 1 pick from Urn 2 if runif 1 lt nb2 n2 count lt count 1 return count nreps est P pick blue from Urn 2 But here is how we can do it without loops sim4 lt function nreps nbl 10 10 blue marbles in Urn 1 nb2 6 6 blue marbles orig in Urn 2 nl lt 18 number of marbles in Urn 1 at 1st pick n2 lt 13 number of marbles in Urn 2 at 2nd pick u lt matrix c runif 2 nreps nrow nreps ncol 2 simfun lt function rw nbl nl nb2 ny2 n2 if rw 1 lt nb1 n1 nb2 lt nb2 1 if rw 2 lt nb2 n2 b lt 1 else b lt 0 return b z lt apply u 1 simfun nb1 n1 nb2 ny2 n2 return mean z est P pick blue from Urn 2 Here we have set up a matrix u with two columns of U 0 1 random variates The first column is used for our simulation of drawing from Urn 1 and the second for the drawing from Urn 2 Our function simfun works on one repetition of the experiment We have set up the call to apply to go through all of the nreps repetitions Actually on my machine this second approach was actually slower So one must not assume that using apply will necessarily speed things up Note though that in a parallel version of R Section 32 we d likely get quite a speedup 14 3 Built In Random Variate Generators R has functions to generate variates from a number of different distributions For
3. 1 2 De 1 4 La 2 5 3 3 6 gt m lt matrix c 1 2 3 4 5 6 nrow 2 byrow T gt m 1 2 3 Ly 1 2 3 Zip 4 5 6 T is an abbreviation for TRUE Since we specified the matrix entries in the above example we would not have needed to specify ncol just nrow would be enough For instance gt y lt matrix c 1 2 3 4 nrow 2 25y 1 1 3 2 Note that when we then printed out y R showed us its notation for rows and columns For instance 2 means column 2 as can be seen in this check gt yi2 12 1 3 4 Another way we could have built y would have been to specify elements individually gt y lt matrix nrow 2 ncol 2 gt y 1 1 1 gt y 2 1 2 gt y 1 2 3 gt y 2 2 4 RAY 1 2 1 1 ELA 4 We can perform various operations on matrices e g matrix multiplication matrix scalar multiplication and matrix addition 21 gt y x y ordinary matrix multiplication pi 2 j 7 19 2 110 22 gt 3xy zA z2 3 9 25 6 12 gt yty pl F2 pl 2 6 2i 4 8 For linear algebra operations on matrices see Section Again keep in mind and when possible exploit the notion of recycling Section 6 4 For instance gt x lt 1 2 gt y lt c 1 3 4 10 gt Xxy 1 1 6 4 20 Since x was shorter than y it was recycled to the four element vector e 1 2 1 2 then multiplied elementwise with y 6 7 2 Matrix Row and Column Names
4. A 2 Updating Use updatepackages either for specific packages or if no argument is specified then all R packages 104
5. 55000 TRUE gt class ulj 1 character The return value of unlist is a vector in this case a vector of mode character i e a vector of character strings 7 3 Issues of Mode Precedence Let s look at this a bit more closely gt x Sabe 2a 2 de TT 3 Here the list x has two elements with x abe 2 and x de 5 Just for practice let s call names gt names x 1 abc de Now let s try unlist gt ulx lt unlist x gt ulx abc de 2 5 gt class ulx 1 numeric So again unlist returned a vector but R noticed that all the values were numeric so it gave ulx that mode By contrast with ulj above though one of the values was numeric R was forced to take the least common denominator and make the vector of mode character This sounds like some kind of precedence structure and itis As R s help for unlist states Where possible the list elements are coerced to a common mode during the unlisting and so the result often ends up as a character vector Vectors will be coerced to the highest type of the components in the hierarchy NULL lt raw lt logical lt integer lt real lt complex lt character lt list lt expression pairlists are treated as lists 27 But there is something else to deal with here Though ulx is a vector and not a list R did give each of the elements a name We can remove them by settings their names to NULL seen in Section 6 6 gt name
6. Why use anything else As the Cantonese say yauh peng yauh leng both inexpensive and beautiful Its virtues e a public domain implementation of the widely regarded S statistical language R S is the de facto standard among professional statisticians e comparable and often superior in power to commercial products in most senses e available for Windows Macs Linux e in addition to enabling statistical operations it s a general programming language so that you can automate your analyses and create new functions e object oriented and functional programming structure e your data sets are saved between sessions so you don t have to reload each time e open software nature means it s easy to get help from the user community and lots of new functions get contributed by users many of which are prominent statisticians I should warn you that one submits commands to R via text rather than mouse clicks in a Graphical User Interface GUD If you can t live without GUIs you should consider using one of the free GUIs that have been developed for R e g R Commander or JGR See Section 34 2 below Note that R definitely does have graphics tons of it But the graphics are for the output e g plots not for the input Though the terms object oriented and functional programming may pique the interests of computer scien tists they are actually quite relevant to anyone who uses R The term object oriented can be explained by
7. One can write multiple fields For instance gt cat file v 1 2 xyz n would produce a file v consisting of a single line 1 2 xyz 15 5 3 Writing a List to a File You have various options here One would be to convert the list to a data frame as in Section 8 5 and then call write table 57 15 5 4 Writing to a File One Line at a Time Use writeLines See Section 15 6 Directories Access Permissions Etc R has a variety of functions for dealing with directories file access permissions and the like Here is a short example Say our current working directory contains files x and y as well as a subdirectory z Suppose the contents of x is 12 13 and y contains us The following code sums up all the numbers in the non directory files here tot lt 0 ndatafiles lt 0 for d in dir if file info d S isdir ndatafiles lt ndatafiles 1 x lt scan d quiet T tot lt tot sum x cat there were ndatafiles nondirectory files with a sum of tot n Type gt files to get more information on permissions etc The functions getwd and setwd can be used to determine or change the current working directory The notation for parent directory in Linux systems does work on them 15 7 Accessing Files on Remote Machines Via URLs Functions such as read table scan and so on accept file names as arguments For example I placed a file z on my Web page with the
8. or equivalent operation and this will fail if one predictor is an exact linear combination of the others or is so within roundoff error If so R will remove one of the predictors and you will see NA listed as the corresponding estimated coefficient 36 2 Generalized Linear Models Here we assume that some function of the regression function m t rather than m t itself has a linear form In R the function that handles such models is glm The named argument family specifies which function of m t has a linear form 36 2 1 Logistic Regression Probably the most famous generalized linear model is the logistic model which is applied when Y is a boolean quantity coded by the values 1 and O Here the quantity In m t 1 m t is assumed to be equal to Bo Bit Bt for some population values 6 This is equivalent to saying 1 1 e Bo Prt1 Brtr 3 m t P Y 1 X t This is an intuitively appealing model as it produces values in 0 1 appropriate for modeling a probability function and is a monotonic function in the linear form One calls glm to fit a generalized linear model In the logistic case we specify the argument fam ily binomial e g glm x 1 x 2 family binomial 97 36 2 2 The Log Linear Model Consider the example ct in Section and in particular the data frame of counts ctdf We can perform a log linear model analysis then we can use glm to regress the counts ctdf
9. x03 z 1 First the subset function would take the data frame x03 and cull out all those records for which the variable z has the value 1 The resulting new frame would be fed into nrow the function that counts the number of rows in a frame The net effect would be to report a count of z 1 in the original frame A common theme in R programming is the avoidance of writing explicit loops Instead one exploits R s functional programming and other features which do the loops internally They are much more efficient which can make a huge timing difference when running R on large data sets 3 How to Run R R has two modes interactive and batch The former is the typical one used 3 1 Interactive Mode You start R by typing R on the command line in Linux or on a Mac or in a Windows Run window You ll get a greeting and then the R prompt gt You can then execute R commands as you ll see in the quick sample session discussed in Section 4 Or you may have your own R code which you want to execute say in a file z r You could issue the command gt source z r which would execute the contents of that file Note by the way that the contents of that file may well just be a function you ve written In that case executing the file would mean simply that the R interpreter reads in the function and stores the function s definition in memory You could then execute the function itself by calling it from the R comm
10. 3 3 4 gt v 1 2 1 8 15 2 12 10 3 20 2 gt for m in u tv 4 z lt get m print lm z 2 7 z 1 ob Call lm formula z 2 zl 1 Coefficients Intercept ZO 1 0 6667 1 5000 Call lm formula z 2 zl 1 Coefficients Intercept Zl 1 23 286 1 07 The reader is welcome to make his her own refinements here 12 4 Return Values By the way you often don t need the return call The last value computed will be returned by default In the oddcount example in Section 5 instead of writing return k we could simply write This is true for nonscalars too recall that a scalar is really a one element vector anyway e g r lt function x y c xty x y 8 2 11 5 1 V v 48 12 5 If Else The syntax for if else is like this gt if r 4 x lt 1 lt 2 else x lt 3 y lt 4 Note that the braces are necessary even for single statement bodies for the if and else and the newlines are important too For instance the left brace before the else is what the parser uses to tell that this is an if else rather than just an if this would be easy for the parser to handle in batch mode but not in interactive mode However if you place the else on the same line as the if this problem will not occur See also the ifelse function discussed in Section IT 12 6 Local and Global Variables Say a variable z appearing
11. 34 64 50 35 40 Note that I have separated fields here by spaces As you can see other than the first record which contains the names of the columns i e the variables each line contains the three exam scores for one student This is the classical two dimensional file notion 1 e each line in our file contains the data for one observation in a statistical dataset The idea of a data frame is to encapsulate such data along with variable names into one object As mentioned I ve specified the variable names in the first record Our variable names didn t have any embedded spaces in this case but if they had we d need to quote any such name e g Exam 1 Exam 2 Exam 3 Suppose the second exam score for the third student had been missing Then we would have typed 50 NA 40 in that line of the exams file In any subsequent statistical analyses R would do its best to cope with the missing data in the obvious manners We may have to set the option na rm T If for instance we had wanted to find the mean score on Exam 2 R would find the mean among all students except the third We first read in the data from the file exams into a data frame which we ll name testscores gt testscores lt read table exams header TRUE The parameter header TRUE tells R that we do have a header line for the variable names so R should not count that first line in the file as data In R the components of an object are accesse
12. For example gt z lt matrix c 1 2 3 4 nrow 2 gt z 1 2 1 1 3 2 2 4 gt colnames z lt c a b gt Z ab 1 13 2 2 4 gt colnames z 1 Tan mpn The function rownames works similarly 6 7 3 Matrix Indexing The same operations we discussed in Section 6 5 apply to matrices For instance gt Z EY 721 L 3 1 1 1 1 2 2 1 0 3 1 3 0 1 4 4 0 0 gt z c 2 3 22 oror Here s another example gt y lt matrix c 11 21 31 12 22 32 nrow 3 ncol 2 gt y 1 2 Ls FLI 12 2121 22 31321 32 gt y 2 3 1 2 Le ee 22 Bak 32 gt y 23 21 1 22 32 You can copy a smaller matrix to a slice of a larger one Y 1 2 1 4 Zip 2 5 3y 3 6 y 2 3 lt matrix c 1 1 8 12 nrow 2 gt y 1 2 1 4 r 8 3y 1 12 gt x lt matrix nrow 3 nco1 3 gt x 2 3 2 3 lt cbind 4 5 2 3 2 E BLD 21 01734 1 NA NA NA 12 NA 4 2 3 NA 5 3 6 8 Sensing the Number of Rows and Columns of a Matrix The numbers of rows and columns in a matrix can be obtained through the nrow and ncol functions e g gt Xx 11 2 1 1 4 2 2 5 3 3 6 gt nrow x 1 3 These functions are useful when you are writing a general purpose library function whose argument is a matrix By being able to sense the number of rows and columns in your code you alleviate the caller of the burden of supplying that information as two addit
13. character x Pa Y Wee 2 yn gt as numeric y 1 124 gt q lt as list x gt q 1 gt r lt as numeric q gt E 124 You can see all of this family by typing gt methods as The unclass function converts a class object to an ordinary list 18 Stopping Execution You can write your code to check for various anomalies specific to your application and if one is found call stop to stop execution 19 Functions for Statistical Distributions R has functions available for various aspects of most of the famous statistical distributions Prefix the name by d for the density p for the cdf q for quantiles and r for simulation The suffix of the name indicates the distribution such as norm unif chisq binom exp etc For example for the chi square distribution 65 gt mean rchisq 1000 different 2 find mean of 1000 chi square 2 variates 1 1 938179 gt qchisq 0 95 1 find 95th percentile of chi square 2 1 3 841459 An example of the use of rnorm to generate random normally distributed variates is in Section 14 as well as one for rbinon for binomial Bernoulli random variates The function dnorm gives the normal density pnorm gives the normal CDF and qnorm gives the normal quantiles The d series for density gives the probability mass function in the case of discrete distributions The first argument is a vector indicating at which points we wish to find th
14. code but for speed If speed is an issue such as when working with large data sets or long running simulations one must avoid explicit loops as much as possible because R can do them a lot faster than you can To this end there is the apply function and its variants 11 4 1 Applying the Same Function to All Rows or Columns of a Matrix The arguments of apply are the matrix data frame to be applied to the dimension 1 if the function applies to rows 2 for columns and the function to be applied For example here we apply the built in R function mean to each column of a matrix z 43 2 2 11 2 1 1 1 4 2 2 5 37 3 6 gt apply z 2 mean 11 2 3 Here is an example of working on rows using our own function gt f lt function x x c 2 8 gt y lt apply z 1 f gt y 1 2 3 lle 00 51 0007 15 50 2 1 0 5 0 625 0 75 You might be surprised that the size of the result here is 2 x 3 rather than 3 x 2 If the function to be applied returns a vector of k components the result of applyQ will have k rows You can use the matrix transpose function t to change it As you can see the function to be applied needs at least one argument which will play the role of one row or column in the array In some cases you will need additional arguments which you can place following the function name in your call to applyO For instance suppose we have a matrix of 1s and Os and want to create a vector as
15. example 38 2 The boot Function The bootstrap is a resampling method for performing statistical inference in analytically intractable situa tions If we have an estimator but no standard error we can get one by resampling from our sample data many times calculating the estimator each time and then taking the standard deviation of all those gener ated values You could just use sample for this but R has a package boot that automates the procedure for you To use the package you must first load it gt library boot Inside that package is a function boot that will do the work of bootstrapping Suppose for example we have a data array y of length 100 from which we wish to estimate a population median using y and have a standard error as well We could do the following First we must define a function which defines the statistic we wish to compute which in this case is the me dian This function will be called by boot it is named statistic in the list of boot s formal parameters We could define it as follows gt mdn lt function x i return median x i It may seem to you that all this is doing is to call R s own median function and thus may wonder why we need to define our own new function But it is definitely needed with the key being our second parameter i When we call boot the latter will generate a specified number of indices see below sampled randomly with replacement fr
16. example Section the command points testscores Exam1l testscores Exam3 pch would superimpose onto the current graph the points of the exam scores from that example using signs to mark them As with most of the other graphics functions there are lots of options e g point color background color etc 72 23 7 The legend Function A nice function is legend which is used to add a legend to a multicurve graph For instance gt legend 2000 31162 legend CS lty 1 would place a legend at the point 2000 31162 in the graph with a little line of type 1 and label of CS Try it 23 8 Adding Text the text and mtext Functions Use the text function to place some text anywhere in the current graph For example text 2 5 4 abc would write the text abc at the point 2 5 4 in the graph The center of the string in this case b would go at that point In order to get a certain string placed exactly where you want it you may need to engage in some trial and error R has no undo command though the ESS interface to R described below does For that reason you might want to put all the commands you re using to build up a graph in a file and then use source to execute them But you may find the locator function to be a much quicker way to go See Section To add text in the margins use mtext 23 9 Pinpointing Locations the locator Function Typing locator 1
17. example rbinom gen erates binomial or Bernoulli random variates P If we wanted to say find the probability of getting at least 4 heads out of 5 tosses of a coin we could do this gt x lt rbinom 100000 5 0 5 gt length x x gt 4 100000 1 0 18791 There are also rnorm for the normal distribution rexp for the exponential runif for the uniform rgamma for the gamma rpois for the Poisson and so on SA sequence of independent 0 1 valued random variables with the same probability of 1 for each is called Bernoulli 54 14 3 1 Obtaining the Same Random Stream in Repeated Runs By default R will generate a different random number stream from run to run of a program If you want the same stream each time call set seed e g gt set seed 8888 or your favorite number as an argument 15 Input Output 15 1 Reading from the Keyboard You can use scan gt z lt scan dee ZAS 3e 2 4 Read 3 items gt z ITAAS 2 Use readline to input a line from the keyboard as a string gt w lt readline abc de f gt w 1 abc de f 15 2 Printing to the Screen In interactive mode one can print the value of a variable or expression by simply typing the variable name or expression In batch mode one can use the print function e g print x The argument may be an object It s a little better to use cat instead of print as the latter can print only one expression and
18. example we will predict b from a They are loaded dynamically as you use them gt gt gt a 5 12 13 555 b 10 28 30 gt gt gt lmout r lm v2 vl1 data r data_frame vl a v2 b This is somewhat more complex than it would have been if done directly in R What are the issues here First since Python syntax does not include the tilde character we needed to specify the model formula via a string Since this is done in R anyway this is not a major departure Second we needed a data frame to contain our data We created one using R s data frame function but note that again due to syntax clash issues RPy converts periods in function names to underscores so we need to call rdata_frame Note that in this call we named the columns of our data frame v1 and v2 and then used these in our model formula The output object is a Python dictionary as can be seen gt gt gt lmout Hory pivot 1 2 qr array 1 73205081 17 32050808 0 57735027 6 164414 0 57735027 0 78355007 qraux 1 5773502691896257 1 6213286481208891 rank 2 tol 9 999 You should recognize the various attributes of Im objects there For example the coefficients of the fitted regression line which would be contained in Imout coefficients if this were done in R are here in Python as Imout coefficients So we can access those coefficients accordingly e g gt gt gt lmout coef
19. follows For each row of the matrix the corresponding element of the vector will be either 1 or 0 depending on whether the majority of the first c elements in that row are 1 or 0 Here c will be a parameter which we may wish to vary We could do this gt copymaj lt function rw c maj lt sum rw l c c return ifelse maj gt 0 5 1 0 gt x lt matrix c 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 nrow 4 gt x 11 21 31 41 5 1 1 0 1 1 0 Di 1 1 1 1 0 35 1 0 0 1 1 4 0 1 1 0 gt apply x 1 copymaj 3 Ty 20 gt apply x 1 copymaj 2 13 01 50 50 Here the values 3 and 2 form the actual arguments for the formal argument c in copymaj So the general form of apply is apply m dimcode f fargs where m is the matrix dimcode is 1 or 2 according to whether we will operate on rows or columns f is the function to be applied and fargs is an optional list of arguments to be supplied to f Note carefully that in writing C itself its first argument must be a vector that will be supplied by the caller as a row or column ofm As R moves closer and closer to parallel processing functions like apply will become more and more important For example the clusterApply function in the snow package gives R some parallel processing capability by distributing the submatrix data to various network nodes with each one basically running apply on its submatrix and then collect the re
20. from R 32 Parallel R B24 RDPI eo Fe avd ee Aha he ek eae ee ee ee de a Ba eee a E ai B2 stalan s eor eee de a eoa Shee ee ee eae a Mead Soe Mio Hees hy oe apts a boa heey hae ee ae ate Gee a a A iaa ico eee ens E ea se E 32 2 3 Overview of Available Functi0ns o 32 2 4 More Snow Examples e 32 2 5 Parallel Simulation Including the Bootstrap 0 82 2 0 Example 02 i250 doe Vek Pha eh Aa EEA eRe Eee ead 82 82 83 83 83 83 83 84 85 85 85 85 85 86 86 32 2 7 To Learn More about snhoW 0 02 ee 33 Using R from Python 34 Tools 34 1 Using R from emacs 2 ee 34 2 GUIS for R orina a da E RA a 35 Inference on Simple Means and Proportions 36 Linear and Generalized Linear Models 36 1 Linear Regression Analysis ee 36 2 Generalized Linear Models e 36 2 1 Logistic Regression 2 ee 36 2 2 The Log Linear Model 2 0 0 0 0 200000 e 36 2 3 The Return Value of glmQ 2 2 ee 36 3 Some Generic Functions for All Linear Models 37 Principal Components Analysis 38 Sampling Subsets 38 1 The sampleQ Function ee 38 2 The boot Function aa s assisas taco tats po raaka aara danska 39 To Learn More 39 1 R s Internal Help Facilities aoaaa a 39 1 1 The help and example Functions n o aaa a 39 1 2 If You Don t Kno
21. gt integrate function x x 2 0 1 0 3333333 with absolute error lt 3 7e 15 There are R packages such as odesolve for differential equations ryacas to interface R with the Yacas symbolic math system and so on 21 String Manipulation R has a number of string manipulation utilities such as e grep Searches for a substring like the Linux command of the same name e nchar Finds the length of a string e paste Assembles a string from parts e sprintf Assembles a string from parts e substr Extracts a substring e strsplit Splits a string into substrings 21 1 Example of nchar substr Testing for a Specified Suffix in a File Name tests whether the file name fn has the suffix suff e g abc in x abc testsuffix lt function fn suff nef lt nchar fn nchar gives the string length dotpos lt ncf nchar suff 1 dot would start here if there is one now check that suff is at the end of the name return substr fn dotpos ncf suff 21 1 1 Example of paste sprintf Forming File Names Suppose I wish to create five files q1 pdf through q5 pdf consisting of histograms of 100 random N 0 i variates I could execute the code The main point here is the string manipulation creating the file names fname Don t worry about the graphics operations or check Section 23 15 for details 67 for i in 1 5 fname lt paste q i pdf pdf fname hist rnorm 100 sd i de
22. gt matrix z12 x ncol 2 1 2 Le 1 T 2 2 4 37 3 9 4 4 16 Sp 5 25 6 6 36 Tey 7 49 8 8 64 11 2 Filtering Another idea borrowed from functional programming is filtering which is one of the most common opera tions in R 40 11 2 1 On Vectors For example gt 2 18 527 378 gt w lt z z z gt 8 gt w 1 5 3 8 Here is what happened above We asked R to find the indices of all the elements of z whose squares were greater than 8 then use those indices in an indexing operation on z then finally assign the result to w Look at it done piece by piece SoZ D 2 3081 gt Z fil amp 2 gt z z gt 8 1 TRUE FALSE TRUE TRUE Evaluation of the expression z z gt 8 gave us a vector of booleans Let s go further gt z c TRUE FALSE TRUE TRUE 1 5 o B This example will place things into even sharper focus lt 6 5 2 37 8 j lt z z gt 8 Zz J J TRUE FALSE TRUE TRUE y lt 0 1 2 30 5 y 3 gt gt gt 1 gt gt 1 30 5 1 We may just want to find the positions within z at which the condition occurs We can do this using which gt which zx z gt 8 1 13 4 Here s an extension of an example in Section 6 5 x is an array of numbers mostly in nondecreasing order but with some violations of that order nviol returns the number of indices i for which x 1 1 lt x i nviol lt function x diff
23. languages would be highly useful RPy is probably the most popular of these RPy is a Python module that allows access to R from Python For extra efficiency it can be used in conjunction with NumPy You can build the module from the source available from http rpy sourceforge net or down load a prebuilt version If you are running Ubuntu simply type sudo apt get install python rpy To load RPy from Python whether in Python interactive mode or from code execute from rpy import This will load a variable r which is a Python class instance Running R from Python is in principle quite simple For instance running gt gt gt r hist r rnorm 100 from the Python prompt will call the R function rnorm to produce 100 standard normal variates and then input those values into R s histogram function hist As you can see R names are prefixed by r reflecting the fact that Python wrappers for R functions are members of the class instance rf By the way note that the above code will if not refined produce ugly output with your possibly volumi nous data appearing as the graph title and the X axis label You can avoid this by writing for example gt gt gt r hist r rnorm 100 main xlab RPy syntax is sometimes less simple than the above examples would lead us to believe The problem is that there may be a clash of R and Python syntax Consider for instance a call to the R linear model function Im0 In our
24. make use of Is s pattern argument this tool becomes even more powerful 16 1 3 Saving a Collection of Objects with the save Function Calling save on a collection of objects will write them to disk for later retrieval by load 59 16 1 4 Listing the Characteristics of an Object with the names attributes and class Functions An object consists of a gathering of various kinds of information with each kind being called an attribute The names function will tell us the names of the attributes of the given object For a data frame for ex ample these will be the names of the columns For a regression object these will be coefficients residuals and so on Calling the attributes function will give you all this plus the class of the object itself To just get the class call class 16 1 5 The exists Function The function exists returns TRUE or FALSE depending on whether the argument exists Be sure to quote the argument e g gt exists acc 1 TRUE shows that the object acc exists 16 1 6 Accessing an Object Via Strings The call get u will return the object u An example appears on page 48 16 2 Generic Functions As mentioned in my introduction R is rather polymorphic in the sense that the same function can have different operation for different classes One can apply plot for example to many types of objects getting an appropriate plot for each The same is true for print and summa
25. paul RGraphics rgraphics html Web page for the book R Graphics by Paul Murrell Chapman and Hall 2005 Chapters 1 4 and 5 are available there plus all the figures from the book and the R code which generated them elhttp www biostat harvard edu carey CompMeth StatVis dem pdf By Vince Carey of the Harvard Biostatistics Dept Lots of pictures but not much explanation 39 2 5 For Specific Statistical Topics e Practical Regression and Anova using R by Julian Faraway online book http www cran r project org doc contrib Faraway PRA pdf 39 2 6 Web Search for R Topics Lots of resources here e Various R search engines are listed on the R home page http www r project org Click on Search e You can search the R site itself by invoking the function RSiteSearch from within R It will interact with you via your Web browser e I use RSeek http www rseek orgalot e also uselfinzi psych upenn edu 103 A Installing Updating R A 1 Installation There are precompiled binaries for Windows Linux and MacOS X at the R home page www r project Just click on Download CRAN Or if you have Fedora Linux just type yum install R In Ubuntu Linux do sudo apt get install r base On Linux machines you can compile the source yourself by using the usual configure make make install sequence If you want to install to a nonstandard directory say a b c run configure as configure prefix a b c
26. tests in one and two mean situa tions It returns an object of class htest which includes various components type gt t test for details There is a similar function prop test for proportions 36 Linear and Generalized Linear Models R has a very rich set of facilities for linear models At least two entire books have been written on this one aspect of R But we ll give some of the basics here 36 1 Linear Regression Analysis In statistical regression analysis we try to predict a response variable Y by one or more predictor variables x XB pee Xx The regression function is defined to be m t E Y X t1 XW tp 1 where t is the vector t1 tk Typically we model m t as linear in the i e we assume that WMA ty te Bo Bila Bete 2 Here the 8 are population values to be estimated via our sample data In our example in Section 8 1 let s try to predict the third exam score from the first Our goal here may not be prediction per se but rather to see whether the two exams are highly correlated In R we can use Im linear model function to fit a linear model here meaning that we will find the values of c and d for which c d Exam best predicts Exam3 gt fitl lt lm Exam3 Examl data testscores gt fitl coefficients Intercept Examl 3 7008841 0 7458898 We find that c 3 7 and d 0 75 The notation Exam3 Examl means that we wish to predict Exam3
27. the shell script Rslaves sh replacing SR_HOME bin R no init file slave no save lt 1 gt Shn 2 log 2 gt amp 1 else SR_HOME bin R no init file slave no save lt 1 gt dev null 2 gt amp 1 by SR_HOME bin R slave no save lt 1 gt Shn 2 S log 2 gt amp 1 else SR_HOME bin R slave no save lt 1 gt dev null 2 gt 41 86 You ll need to arrange for the directory a b e not a b c Rmpi to be added to your R library search path I recommend placing a line libPaths a b c in a file Rprofile in your home directory 32 1 2 Usage Fire up MPI and then in R load in Rmpi by typing gt library Rmpi Then start Rmpi gt mpi spawn Rslaves This will start R on all machines in the group you started MPI on Optionally you can specify fewer machines via the named argument nslaves The first time you do this try this test mpi remote exec paste I am mpi comm rank of mpi comm size The available functions are similar to and call those of such as e mpi comm size Returns the number of MPI processes including the master that spawned the other processes The master will be rank 0 e mpi comm rank Returns the rank of the process that executes it e mpi send mpi recv The usual send receive operations e mpi bcast mpi scatter mpi gather The usual broadcast scatter and gather operations e Etc Details are available at ttp
28. trace gy browser This would have the same effect as placing the command browser in our source code for gy but would be quicker and more convenient than inserting such a line saving the file and rerunning source to load in the new version of the file It would also be quicker and more convenient to undo by simply running gt untrace gy You can turn tracing on or off globally by calling tracingState with the argument TRUE to turn it on FALSE to turn it off Recall too that these boolean constants in R can be abbreviated T and F 26 3 Performing Checks After a Crash with the traceback and debugger Functions Say your R code crashes when you are not running the debugger There is still a debugging tool available to you after the fact You can do a post mortem by simply calling traceback You can get a lot more if you set R up to dump frames on a crash gt options error dump frames If you ve done this then after a crash run gt debugger You will then be presented with a choice of levels of function calls to look at For each one that you choose you can take a look at the values of the variables there After browsing through one level you can return to the debugger main menu by hitting n 79 26 4 The debug Package The debug package provides a more usable debugging interface than R s built in facilities do It features a pop up window in which you can watch your progress as you step through
29. will tell R that you will click in 1 place in the graph Once you do so R will tell you the exact coordinates of the point you clicked on Call locator 2 to get the locations of 2 places etc Warning Make sure to include the argument You can combine this for example with text e g gt text locator 1 nv 75 23 10 Changing Character Sizes the cex Function The cex character expand function allows you to expand or shrink characters within a graph very useful You can use it as a named parameter in various graphing functions text 2 5 4 abe cex 1 5 would print the same text as in our earlier example but with characters 1 5 times normal size 73 23 11 Operations on Axes You may wish to have the ranges on the X and Y axes of your plot to be broader or narrower than the default You can do this by specifying the xlim and or ylim parameters in your call to plot or points For example ylim c 0 90000 would specify a range on the Y axis of 0 to 90000 This is especially useful if you will be displaying several curves in the same graph Note that if you do not specify xlim and or ylim then draw the largest curve first so there is room for all of them 23 12 The polygon Function You can use polygon to draw arbitrary polygonal objects with shading etc For example the following code draws the graph of the function f x 1 e then adds a rectangle that approximates the area under the cu
30. x b y lt cut x b return as vector table y 10 Missing Values Data sets in the real world tend to have problems Observed values can be incorrect and are often missing altogether R designates the latter case by NA One can test for this condition by using is na When applied to a vector e g gt z lt c 5 NA 12 gt is na z 1 FALSE TRUE FALSE this function can be used to identify all the missing values which then can be avoided in one s analysis Thus for instance the mean function has such an option gt mean z 1 NA gt mean z na rm T LEI SNS 38 11 Functional Programming Features Functional programming has several benefits Clearer more compact code Potentially much faster execution speed Less debugging since you write less code Easier transition to parallel programming 11 1 Elementwise Operations on Vectors Suppose we have a function f that we wish to apply to all elements of a vector x In many cases we can accomplish this by simply calling fQ on x itself 11 1 1 Vectorized Functions As we saw in Section 6 3 many Operations are vectorized such as and gt gt u lt 0c 5 2 8 a lt C1 37 9 gt utv pr 6 5 17 gt u gt y 1 TRUE FALSE FALSE The key point is that if an R function uses vectorized operations it too is vectorized i e it can be applied to vectors in an elementwise fashion For instance gt w lt function x retur
31. Freq against the factors ctdf VoteX and ctdf VoteLast setting family poisson gt g lt glm Freq Vote for X Vote Last Time family poisson data ctdf Here we have chosen to fit the saturated model 36 2 3 The Return Value of glm The function glm returns an object of type glm a subclass of Im The latter provides us with a number of member variables and functions such as discussed in Sec 36 3 In addition there are various glm specific variables and functions such as e iter is the number of iterations used e converged is a logical variable indicating whether convergence occurred 36 3 Some Generic Functions for All Linear Models These will work on all the linear models e vcov will return the estimated covariance matrix for our estimated coefficients e fitted will return the fitted values i e the predicted Y values for the X s in our sample e coef returns the estimated coefficients 37 Principal Components Analysis R includes two functions for principal components analysis princomp and prcomp The latter is pre ferred as it has better numerical accuracy though the former is included for compatibility with S In its simplest form the call is gt pre lt prcomp m where m is a matrix or data frame 98 38 Sampling Subsets 38 1 The sample Function We can use the sample function to do sampling with or without replacement from a finite set This is handy in simulations for
32. In Section 8 1 we read in a dataset from a file exams gt testscores lt read table exams header TRUE The parameter header TRUE told R that we did have a header line so R should not count that first line in the file as data This is an example of the use of named arguments The function read table has a number of arguments some of which are optional which means that we must specify which arguments we are using by using their names e g header TRUE above Again Python programmers will find this familiar The ones you don t specify all have default values 51 13 Writing Fast R Code A central theme in R programming is avoidance of explicit loops instead relying on R s rich functionality to do the work for you Not only does this save you programming and debugging time it produces faster code since R s functions have been written for efficiency This can be of the utmost importance in applications with large data sets or large amounts of computation For instance let s rewrite our function oddcount in Section 5 gt oddcount lt function x return length which x 2 1 Let s test it gt oddcount c 1 5 6 2 19 1 3 There is no explicit loop in this version of our oddcount We used R s vector filtering to avoid a loop and even though R internally will loop through the array it will do so much faster than we would with an explicit loop in our R code In essence the looping is done in C
33. R for Programmers Norman Matloff University of California Davis 2007 8 N Matloff December 4 2008 IMPORTANT NOTICE This document is no longer being maintained My book on R program ming The Art of R Programming is due out in August 2011 You are welcome to use an early draft at http heather cs ucdavis edu matloff 132 NSPpart pdf it was about 50 com plete and contains bugs but should be useful Licensing This work dated December 4 2008 is licensed under a Creative Commons Attribution No Derivative Works 3 0 United States License Subsequent works by the author that make use of part or all of this material will not be covered by the license Copyright is retained by N Matloff in all non U S jurisdictions rerequisites AL a gt 5 a UN What Is R 2 3_ How to Run R 3 1 Why Use R for Your Statistical Work Interactive Model osie e do a a a a a a a Aen 3 2 Running Rin Batch Mode e 4 A First R Example Session 5 Minutes Functions a Short Programming Example Scalars Vectors Arrays and Matrices Declarations 2 ee 6 2 Generating Useful Vectors with seq andrepO o oo ee eee 6 3 Vector Arithmetic and Logical Operations 0 000000 02 eee 6 4 Recycling lt 2 ase age OG aoe Baa Peed ease ead ae oe Pe doe Paced 6 5 Vector Indexing yesos s 3 ke eds a ee we ae eR ee A a A N 6 6 Vector Element Names
34. ULL gt names x lt NULL gt x 1 12 4 We can even reference elements of the vector by name e g x lt 0 1 2 4 names x lt c a b ab x b NOvovoy 6 7 Matrices A matrix is a vector with two additional attributes the number of rows and number of columns 6 7 1 General Operations Multidimensional vectors in R are called arrays A two dimensional array is also called a matrix and is eligible for the usual matrix mathematical operations Matrix row and column subscripts begin with 1 so for instance the upper left corner of the matrix a is denoted a 1 1 The internal linear storage of a matrix is in column major order meaning that first all of column 1 is stored then all of column 2 etc One of the ways to create a matrix is via the matrix function e g gt y lt matrix c 1 2 3 4 nrow 2 ncol 2 gt y 20 Here we concatenated what we intended as the first column the numbers 1 and 2 with what we intended as the second column 3 and 4 That was our data in linear form and then we specified the number of rows and columns The fact that R uses column major order then determined where these four numbers were put Though internal storage of a matrix is in column major order we can use the byrow argument in matrix to TRUE in order to specify that the data we are using to fill a matrix be interpreted as being in row major order For example gt m lt matrix c 1 2 3 4 5 6 nrow 3 gt m
35. and line e g gt 12 3 2 Running R in Batch Mode Sometimes it s preferable to automate the process of running R For example we may wish to run an R script that generates a graph output file and not have to bother with manually running R Here s how it could be done Consider the file z r which produces a histogram and saves it to a PDF file 12 pdf xh pdf set graphical output file hist rnorm 100 generate 100 N 0 1 variates and plot their histogram dev off close the file Don t worry about the details the information in the comments marked with suffices here We could run it automatically by simply typing R CMD BATCH vanilla lt z r The vanilla option tells R not to load any startup file information and not to save any 4 A First R Example Session 5 Minutes We start R from our shell command line and get the greeting message and the gt prompt R Copyright 2005 The R Foundation for Statistical Computing Version 2 1 1 2005 06 20 ISBN 3 900051 07 0 Type q to quit R gt Now let s make a simple data set a vector in R parlance consisting of the numbers 1 2 and 4 and name it x gt x lt c 1 2 4 The standard assignment operator in R is lt However there are also gt and even the assign function The c stands for concatenate Here we are concatenating the numbers 1 2 and 4 Or more precisely we are concatenating three one element vect
36. are called factors in R A factor is basically a vector of mode character intended to represent values of a categorical variable such as the ct VoteX variable above The factor class includes a component levels which in the case of ct VoteX are Yes No and Not Sure Of course all of the above would still work if our original data frame ct we had three factors or more We get counts on a single factor in isolation as well e g gt y lt factor c a bi Mat mam mm gt z lt table y gt Zz y ab 32 gt as vector z 1 3 2 Note the use here of as vector to extract only the counts Among other things this gives us an easy way to determine what proportion of items satisfy a certain condition For example 37 A A 1213 37470 gt table x 5 FALSE TRUE 4 2 So our answer is 2 6 The function table is often used with cut To explain what the latter does first consider the call y lt cut x b labels F where x is a vector of observations and b defines bins which are the semi open intervals b 1 b 2 b 2 b 3 Then y j will be the index i such that x j falls into bin i For instance gt cut 1 8 c 0 17 1 1 1 12 A 4 7 8 labels F LS The function cut has many many other options but in our context here the point is that we can pipe the output of cut into talbe thus getting counts of the numbers of observations in each bin bincounts lt function
37. args i e individualargs i and optionally one can give additional arguments for following fQ in the argument list for clusterApply Q Here for instance is how we can assign an ID to each worker node like MPI rank gt myid lt 0 gt clusterExport cls myid gt setid lt function i myid lt lt i note superassignment operator gt clusterApply cls 1 2 setid 1 2 gt clusterCall cls function return myid 1 Recall that the way snow works is to have a master node the one from which you invoke functions like parApply and then a cluster of worker nodes Suppose the function you specify as an argument to parApply0 is f Q and that calls g Then f itself its code is passed to the cluster nodes but g is not Therefore you must first pass g to the cluster nodes via a call to clusterExport Don t forget to stop your clusters before exiting R by calling stopCluster clustername There are various other useful snow functions See the user s manual for details 32 2 4 More Snow Examples In the first example we do a kind of one level Quicksort breaking the array into piles Quicksort style then having each cluster node work on its pile then consolidate We assume a two node cluster T don t see a provision in snow itself that does this 90 sorts the array x on the cluster cls qs lt function cls x pvt lt x 1 pivot chunks lt list
38. ation y division y exponentiation SS y modular arithmetic S S y integer division y test for equality y test for less than or equal y test for greater than or equal y boolean and for scalars y boolean or for scalars y boolean and for vectors vector x y result y boolean or for vectors vector x y result x boolean negation XXX KM KKK KKM KM KX Xx KM ox The boolean values are TRUE and FALSE They can be abbreviated to T and F but must be capitalized These values change to 1 and 0 in arithmetic expressions e g 50 TRUE gt 1 lt 2 3 lt 4 gt 1 lt 2 3 lt 4 5 lt 1 gt 1 lt 2 TRUE TRUE gt 1 lt 2 1 TRUE There are set operations e g v x lt 3 1 2 5 y lt c 5 1 8 9 gt union x y 1 2 5 8 9 gt intersect x y 1 5 gt setdiff x y 1 2 gt setdiff y x 8 9 gt setequal x y FALSE gt setequal x c 1 2 5 TRUE gt 2 sins x note that plain in doesn t work TRUE gt 2 Sins y FALSE v You can invent your own operators Just write a function whose name begins and ends with Here is an operator for the symmetric difference between two sets i e all the elements in exactly one of the two operand sets SsdfS lt function a b sdfxy lt setdiff x y sdfyx lt setdiff y x return union sdfxy sdfyx oe ole y ZV v x Ssdf 1 8 N wo 12 10 Named Arguments
39. be ES gt 2s Lsa 1 13 In such contexts it is often useful to use the length function gt z lt c 5 12 13 gt z l length z 1 1 5 12 Note that this is more general than using z 1 2 In a program with general length vectors we could use this pattern to exclude the last element of a vector Here is a more involved example of this principle Suppose we have a sequence of numbers for which we want to find successive differences i e the difference between each number and its predecessor Here s how we could do it gt K 65 VOC 12 1 555851 77245 gt y lt x 1 x length x 2 Y ie Bs BAS Here we want to find the numbers 15 12 3 8 15 7 etc The expression x 1 gave us the vector 15 8 11 24 and x length x gave us 12 15 8 11 Subtracting these two vectors then gave us the differ ences we wanted 19 Make careful note of the above example This is the R way of doing things By taking advantage of R s vector operations we came up with a solution which avoids loops This is clean compact and likely much faster when our vectors are long We often use R s functional programming features to these ends as well 6 6 Vector Element Names The elements of a vector can optionally be given names For instance gt x lt c 1 2 4 gt names x NULL gt names x lt c a b ab gt names x 11 ar BY Tar gt x We can remove the names from a vector by assigning N
40. chunks 1 lt x x lt pvt low pile chunks 2 lt x x gt pvt high pile now parcel out the piles to the clusters which sort the piles rcvd lt clusterApply cls chunks sort lx lt length x lel lt length rcvd 1 1c2 lt length revd 2 y lt vector length 1x if lel gt 0 y 1l 1c1 lt revd 1 E Chee gt 00 YEGIL sis lt Bevel 2 return y The second example implements the Shearsort sorting algorithm Here one imagines the nodes laid out as an n x n matrix they may really have such a configuration Here is the pseudocode for i 1 to log2 n 2 1 if i is odd sort each even row in descending order sort each odd row in ascending order else sort each column is ascending order And here is the Snow code is lt function cls dm n lt nrow dm numsteps lt ceiling log2 nx n 1 for step in l numsteps if step 1 attach a row ID to each row so will know odd even augdm lt cbind 1 n dm parcel out to the cluster members for sorting dm lt parApply cls augdm 1 augsort dm lt t dm recall need to transpose after apply else dm lt parApply cls dm 2 sort return dm augsort lt function augdmrow nelt lt length augdmrow if augdmrow 1 2 0 return sort augdmrow 2 nelt decreasing T else return sort augdmrow 2 nelt 32 2 5 Parallel Simulation Including the Bootstrap If you wish to use snow on sim
41. contents ja N 58 and accessed 1t from within R running on my home machine gt z lt read table http heather cs ucdavis edu matloff z gt Z V1 V2 1 A 2 2 3 4 You can also read the file one line at a time as in Section 15 4 16 Object Oriented Programming 16 1 Managing Your Objects 16 1 1 Listing Your Objects with the Is Function The Is command will list all of your current objects A useful named argument is pattern which enables wild cards For example gt 1s 1 acc Nace05 binomci cmeans divorg tay PTI TELES a E genxc genxnt sa as whos 13 outi outi 100 outl 25 guti 50 Toutt 75 out2 19 out2 100 out2 25 Out2 50 out2 75 par set prpdf 25 ratbootci simonn vecprod x zout Zout 100 31 Zzout 125 2o0ut3 zouts Zout 50 Rot 75 gt ls pattern ut pII Touti outil 100 Gttl 25 outi 50 Touti 75 Gutz 7 outs 100 out2 25 out2 50 eut2 75 Zout Zour 100 13 zout 125 zout3 ZOUt 5 Zout 50 zout 75 16 1 2 Removing Specified Objects with the rm Function To remove objects you no longer need use rm For instance gt rm a b X y 2Z uuu would remove the objects a b and so on One of the named arguments of rm is list which makes it easier to remove multiple objects For example gt rm list 1s would assign all of your objects to list thus removing everything If you
42. cran r project org web packages Rmpi index html Site for download of package and manual e http ace acadiau ca math ACMMaC Rmpi sample html Nice tutorial But we forego details here as snow provides a nicer programmer interface to be described next 87 32 2 snow snow runs on top of Rmpi or directly via sockets allowing the programmer to more conveniently express the parallel disposition of work For instance just as the ordinary R function apply Q applies the same function to all rows of a matrix the snow function parApply does that in parallel across multiple machines different machines will work on different rows 32 2 1 Installation Follow the same pattern as described above for Rmpi If you plan to have snow run on top of Rmpi you ll of course need the latter too Again I needed to change a shell script RSOCKnode sh replacing S RPROG R vanilla lt lt EOF gt OUT dev null 2 gt 41 amp by S RPROG R no save no restore lt lt EOF gt OUT dev null 2 gt amp 1 amp 32 2 2 Starting snow Make sure snow is in your library path see material on Rmpi above Then load snow gt library snow One then sets up a cluster by calling the snow function makeCluster The named argument type of that function indicates the networking platform e g MPI PVM or SOCK The last indicates that you wish snow to run on TCP IP sockets that it creates itself rather than going
43. ctor tmp iseq value 3 invalid factor level NAs generated gt d X1 X2 lt NA gt xyz 2 5 ab 3 12 yabc 4 13 lt NA gt Why didn t d 1 1 change Well since the second column was a character vector data frame treated it as a factor and thus demoted the first column to factor status too Then when we tried to assign the value 3 to d 1 1 R told us that 3 was not one of the official values levels for this factor This can be avoided by setting stringsAsFactors to false v d lt data frame cbind c 0 5 12 13 c xyz ab yabc NA stringsAsFactors F d X1 X2 0 xyz 5 ab 12 yabe 13 lt NA gt d 1 1 lt 3 d X1 X2 3 xyz 5 ab 3 12 yabc 4 13 lt NA gt VV amp WD t v N See Section 15 3 34 8 7 Extended Example Data Preparation In a study of engineers and programmers sponsored by U S employers for permanent residency I considered the question How many of these workers are the best and the brightest i e people of extraordinary ability f The government data is limited The admittedly imperfect way to determine whether a worker is of ex traordinary ability was to look at the ratio of actual salary to the government prevailing wage for that job and location If that ratio is substantially higher than 1 0 by law it cannot be less than 1 0 one can reasonably assume that this worker has a high level of talent I used R to prepare and analyze the data and will pre
44. ctors and Tables Consider the data frame say in a file ct dat VoteX VoteLastTime Yes Yes Yes No No No Not Sure Yes No No where in the usual statistical fashion each row represents one subject under study In this case say we have asked five people a Do you plan to vote for Candidate X and b Did you vote in the last election The first line in the file is a header Let s read in the file gt ct lt read table ct dat header T gt ct 36 VoteX VoteLastTime 1 Yes Yes 2 Yes No 3 No No 4 Not Sure Yes 5 No No We can use the table function to convert this data to contingency table format i e a display of the counts of the various combinations of the two variables gt cttab lt table ct gt cttab VoteLastTime Votex No Yes No 2 0 Not Sure 0 1 Yes I 1 The 2 in the upper left corner of the table shows that we had for example two people who said No to a and No to b The 1 in the middle right indicates that one person answered Not Sure to a and Yes to b We can in turn change this to a data frame not the original one but a data frame version of the contingency table gt ctdf lt as data frame cttab gt ctdf VoteX VoteLastTime Freq 1 No No 2 2 Not Sure No 0 3 Yes No 1 4 No Yes 0 5 Not Sure Yes 1 6 Yes Yes 1 This is useful for instance in the log linear model Section 36 2 2 Note that in our original data frame the two columns
45. curve x 2 1 0 5 0 5 23 15 Graphical Devices and Saving Graphs to Files R has the notion of a graphics device The default device is the screen If we want to have a graph saved to a file we must set up another device For example if we wish to save as a PDF file we do something like the following Warning This is actually too tedious an approach and a shortcut will be presented later on But the reader should go through this long way once to understand the principles gt pdf d1l2 pd This opens a file which we have chosen here to call d12 pdf We now have two devices open as we can confirm gt dev list X11 pdf 2 3 The screen is named X11 when R runs on Linux it is device number 2 here Our PDF file is device number 3 Our active device is now the PDF file gt dev cur pdt 3 All graphics output will now go to this file instead of to the screen But what if we wish to save what s already on the screen We could re establish the screen as the current device then copy it to the PDF device 3 gt dev set 2 X11 2 gt dev copy which 3 pdt 3 Note carefully that the PDF file is not usable until we close it which we do as follows gt dev set 3 pdt 3 gt dev off X11 2 We could also close the device by exiting R though it s probably better to proactively close The above set of operations to print a graph can become tedious but there is a shortcut 75 gt dev
46. d via the operator For example the vector of all the Exam1 scores is testscores Exam1 as we confirm here gt testscores Examl 1 62 74 50 62 39 60 48 80 49 49 100 30 61100 82 37 54 65 36 20 97 60 80 70 50 60 24 60 75 77 71 25 93 80 92 75 26 27 55 39 30 44 86 35 95 98 50 50 34 100 57 99 67 TT 70 53 38 The 1 means that items 1 19 start here the 20 means that items 20 38 start here etc We will illustrate operations on this data in the following sections 8 2 List Representation You will have a better understanding of data frames if you keep in mind that technically a data frame is implemented as a list of equal length vectors Recall that R s list construct was covered in Section 7 Each column is one element of the list 31 For instance in Section the data frame testscores first column is referenced as testscores Exam1 which is list notation Recall that elements of vectors can have names The rows of a data frame can have names too So a data frame does have a bit more structure than a general list of vectors 8 3 Matrix Like Operations Many matrix operations can also be used on data frames 8 3 1 rowMeans and colMeans gt colMeans testscores Examl Exam2 Exam3 62 14545 51 27273 50 05455 8 3 2 rbind and cbind The rbind and cbind matrix functions introduced in Section work here too We can also create new columns from old ones e g we can add a variable which is the differenc
47. df A draft of John Maindonald s book he also has scripts data etc on his full site http wwwmaths anu edu au johnm duction by M Hlynka of the University of Windsor ttp www2 uwindsor ca hlynka HlynkaIntroToR pdf A nice short first intro ttp www math ilstu edu dhkim Rstuff Rtutor html A general tutorial but with lots of graphics and good examples from real data sets very nice job by Prof Dong Yun Kim of the Dept of Math at Illinois State University draft of an R simulation based textbook on statistics by Shravan Vasishth ttp ww ling uni potsdam de vasishth VasishthFS vasishthFS pdfi A elhttp www medepi net epir index html A set of tutorials by Dr Tomas Aragon Though they are aimed at a epidemiologist readership there is much material here Chapter ing with R Data Objects is definitely readable by general audiences 2 Work elhttp cran stat ucla edu doc contrib Robinson icebreaker pal a general tutorial by Prof Andrew Robinson excellent 39 2 2 Especially for Reference ttp www mayin org ajayshah KB R index html R by Example a qu 4 pages very handy f icebreakeR ick handy R reference card e http www stats uwo ca computing R mcleod default htm A I McLeod s R Lexicon 39 2 3 Especially for Programmers e http zoonek2 free fr UNIX 48_R 02 htm1 The programming section of Zoonekynd s ot utorial includes so
48. ding from the Keyboard PAG see ne ee ee ee ee a ae as dad a ues ae Mechs Bnet Bind ean Bares fk Pe aS oe Sod a Bed paa eae eet 46 47 47 47 47 48 49 49 49 50 50 51 52 52 52 52 54 55 15 5 2 Writing to a Text File Using CatOl o o ee ee 57 dole Bier Ge Eek ea ea Hse ede BO ee 57 Brace We ENP See ie cas eng ee Bg A ee ee 58 15 6 Directories Access Permissions Etc 2 0 aa a a o 58 a wR eh wie aod a eR a 58 16 Object Oriented Programming 59 a Pw OR ao a ade aed Rha Od ha oe da Paes 59 ig ata wits cee es Ge eh Cs ee eee 59 ee ee ee 59 Ana Spee sden tees 59 pad Edi Ras edad ee ee ee ee 60 E ede am bea Bone r e 60 i Dae dePa ka eased woe OG doe 2a 4 o Pare a 60 16 2 Generic Functions 60 hal de as a dha ck ved db dea ee ada dob 61 Shae ee eee Bo doo ee Bake ata ee a 62 ths ety ho eh J aes ae ee eG ee ee ec e 63 65 65 65 20 Math Functions 66 21 String Manipulation 67 o 67 paci eua he Soe Haw hoe 67 21 1 2 Example of grepQl ea g eaea ee ee 68 21 1 3 Example of strsplitQ 2 a 69 22 Sorting 69 23 Graphics tid ie ia dot 23 2 Plotting Multiple Curves on the Same Graph o E a dew Pama a Paced Mea a Sd Ree Bd ay aoa Grd eRe ee eee ee i eee ee Soe dhe ado a ee oat aed es ui aid dd ee eee a ee ee Ib od as ty ae Bn oe ee Oe eee to ee Horie Ge eee poe be iaa OE aw eh a w bared eh o Ak ONE ee fe deck eh E eed RE ate at pd die wee Boe Boats d
49. e between Exams 1 and 2 gt testscores Diff21 lt testscores Exam2 testscores Examl 8 3 3 Indexing One can also refer to the rows and columns of a data frame using two dimensional array notation including indexing For instance in our example data frame testscores here testscores 2 3 would refer to the third score for the second student testscores 2 would refer to the set of all scores for the second student testscores c 1 2 5 would refer to the set of all scores for the first second and fifth students testscores 10 13 would refer to the set of all scores for the tenth through thirteenth students testscores 2 would refer to the set of all scores for all students except the second 8 4 Creating a New Data Frame from Scratch We saw above how to create a data frame by reading from a data file We can also create a data frame directly using the function data frame For example 32 gt z lt data frame cbind c 1 2 c 3 4 gt Zz X1 X2 Le 13 2 2 4 Note again the use of the cbind function We can also coerce a matrix to a data frame e g gt x lt matrix c 1 2 3 4 nrow 2 ncol 2 gt x 1 2 1 1 3 2 1 2 4 gt y lt data frame x gt y X1 X2 1 T3 2 2 4 As you can see the column names will be X1 X2 However you can change them e g gt 2 XI X2 be TS 2 2 A gt names z lt c col 1 col 2 gt E col 1 col 2 LT 3 2 2 4 8 5 Converting a L
50. e can define functions use constructs such as loops and conditionals etc 46 12 1 Use of Braces for Block Definition The body of a for if or similar statement does not need braces if it consists of a single statement 12 2 Loops 12 3 Basic Structure In our function oddcount in Section 5 the line for n in x will be instantly recognized by Python programmers It of course means that there will be one iteration of the loop for each component of the vector x with n taking on the values of those components In other words in the first iteration n x 1 in the second iteration n x 2 etc Looping with while and repeat are also available complete with break e g gt i lt 1 gt while 1 i lt it4 if i gt 10 break gt TITS Of course break can be used with for too 12 3 1 Looping Over Nonvector Sets The for construct works on any vector regardless of mode One can loop over a vector of file names for instance Say we have files x and y with contents VOD 04 WN FE and 12 13 Then this loop prints each of them 47 gt for fn in c x y print scan fn Read 6 items 1 123456 Read 3 items 1 5 12 13 R does not directly support iteration over nonvector sets but there are indirect yet easy ways to accomplish it One way would be to use lapplyQ as shown in Section 11 4 2 Another would be to use get e g gt 0 1 2 1 1 1 2 2 2
51. e cat No coefficients n cat n invisible x lt environment namespace stats gt Don t worry about the details here our main point is that the printing was dependent on context with a different print function being called for each different class You can see all the implementations of a given generic method by calling methods e g gt methods print 1 print acfx print anova 3 print aovx print aovlistx 5 print arx print Arimax 7 print arima0x print AsIs 9 print Bibtexx print by You can see all the generic methods this way gt methods class default 16 3 Writing Classes A class is named via a quoted string gt class 3 1 numeric gt class list 3 TRUE Ely tTrst gt lmout lt lm y gt class lmout 1 im x If a class is derived from a parent class the named of the derived class will be a vector consisting of two strings first one for the derived class and then one for the parent 61 Methods are implemented as generic functions The name of a method is formed by concatening the function name with a period and the class name e g print Im The class of an object is stored in its class attribute the quotation marks are necessary 16 3 1 Old Style Classes Older versions of R used a cobbled together structure for classes referred to as S3 Under this approach a class instance is created by forming a list with the elements of the list be
52. e values of the pmf For instance here is how we would find the probabilities of 0 1 or 2 heads in 3 tosses of a coin gt dbinom 0 2 3 0 5 E 0 125 05375 0 375 See the online help pages for details e g by typing gt help pnorm 20 Math Functions The usual exp log log100 sqrtQ abs etc are available as well as min which min returns the index for the smallest element max which max pmin pmax sum prod for products of multiple factors round floor ceiling sort etc The function factorial computes its namesake so that for instance factorial 3 is 6 Note that the function min returns a scalar even when applied to a vector By contrast if pmin is applied to vectors 1t returns a vector of the elementwise minima For example gt Z 1 2 1 L 2 27 5 3 3 1 6 2 gt min z 1 1 z 2 1 1 gt pmin z 1 z 2 1 2 3 2 Also some special math functions described when you invoke help with the argument Arithmetic The function combn generates combinations gt c32 lt combn 1 3 2 gt 032 1 2 3 tizi 1 1 2 2 2 3 3 gt class c32 1 matrix 66 The function also allows the user to specify a function to be called by combn on each combination Function minimization maximization can be done via nlm and optim R also has some calculus capabilities e g gt D expression exp x 2 x derivative exp x72 2 x
53. en with a 12 wherever x is odd So the first argument is c F T F T F The second argument 1 is treated as c 1 1 1 1 1 by recycling and similarly for the third argument Here is another example in which we have explicit vectors gt x lt c 5 2 9 12 gt ifelse x gt 6 2xx 3xx 1 15 6 18 24 The advantage of ifelse over the standard if then else is that it is vectorized Thus it s potentially much faster Due to the vector nature of the arguments one can nest ifelse operations In the following example involving an abalone data set gender is coded as M F or I the last meaning infant We wish to recode those characters as 1 2 or 3 gt g lt c M F F I M gt ifelse g M 1 ifelse g F 2 3 17 12231 The inner call to ifelse which of course is evaluated first produces a vector of 2s and 3s with the 2s corresponding to female cases and 3s being for males and infants The outer call results in 1s for the males in which cases the 3s are ignored Remember the vectors involved could be columns in matrices and this is a very common scenario Say our abalone data is stored in the matrix ab with gender in the first column Then if we wish to recode as above we could do it this way gt ab 1 lt ifelse ab 1 M 1 ifelse ab 1 F 2 3 11 4 Applying the Same Function to All Elements of a Matrix Data Frame and Even More This is not just for compactness of
54. et of graphics facilities The top level R home page http www r project org7 org has some colorful a and there is a very nice display of examples in the R Graph Gallery E a I cannot cover even a small part of that material here but will give you enough foundation to work the basics and learn more 23 1 The Workhorse of R Graphics the plot Function This is the workhorse function for graphing serving as the vehicle for producing many different kinds of graphs As mentioned earlier it senses from the type of the object sent to it what type of graph to make i e plot is a generic function Section 16 2 It is really a placeholder for a family of functions The function that actually gets called will depend on the class of the object on which it is called Let s see what happens when we call plot with an X vector and a Y vector which are interpreted as a set of pairs in the X Y plane For example gt plot c 1 2 3 c 1 2 4 will cause a window to pop up plotting the points 1 1 2 2 and 3 4 Here and below we will not show the actual plots The points in the graph will be symbolized by empty circles If you want a different character type specify a value for the named argument pch point character You can change the size of the character via the named argument cex see Section 23 10 As noted in Section one typically builds a graph by adding more and more to it in a succession of seve
55. example say statistical regression When you perform a regression analysis with other statistical packages say SAS or SPSS you get a mountain of output By contrast if you call the Im regression function in R the function returns an object containing all the results estimated coefficients their standard errors residuals etc You then pick and choose which parts of that object to extract as you wish R is polymorphic which means that the same function can be applied to different types of objects with results tailored to the different object types Such a function is called a generic function Consider for In C this is called a virtual function 11 instance the plot function If you apply it to a simple list of numbers you get a simple plot of them but if you apply it to the output of a regression analysis you get a set of plots of various aspects of the regression output This is nice since it means that you as a user have fewer commands to remember For instance you know that you can use the plot function on just about any object produced by R The fact that R is a programming language rather than a collection of discrete commands means that you can combine several commands each one using the output of the last with the resulting combination being quite powerful and extremely flexible Linux users will recognize the similarity to shell pipe commands For example consider this compound command nrow subset
56. ficients vl 2 5263157894736841 Intercept 2 5964912280701729 gt gt gt lmout coefficients vl1 2 5263157894736841 One can also submit R commands to work on variables in R s namespace using the function r This is convenient if there are many syntax clashes Here is how we could run the wireframe example in Section 23 16 in RPy gt gt gt r library lattice gt gt gt r assign a a gt gt gt r assign b b gt gt gt r g lt expand grid a b gt gt gt r g Var32 lt g Var1l 2 g Varl g Var2 gt gt gt r wireframe Var3 Varl Var2 g gt gt gt r plot wireframe Var3 Varl Var2 g We first used r assign to copy a variable from Python s namespace to R s We then ran expand grid with a period in the name instead of an underscore since we are running in R s namespace assigning the result to g Again the latter is in R s namespace Note that the call to wireframe did not automatically display the plot so we needed to call plot The official documentation for RPY is at http rpy sourceforge net rpy doc rpy pdf with a useful presentation available at http www daimi au dk besen TBiB2007 lecture notes rpy html 94 34 Tools 34 1 Using R from emacs There is a very popular package which allows one to run R and some other statistical packages from within emacs ESS I personally do not use it b
57. for instance is shade T which makes it all easier to see 23 17 The Rest of the Story As mentioned we are not even scratching the surface here See one of the references cited in Section 39 2 4 to learn more about R s excellent set of graphics facilities 24 The Innocuous c Function As seen before the concatenation function c does what its name implies e g gt lt olya gt y lt c 4 5 gt c x y 111 234 5 76 But when mixing modes c will apply the precedence discussed in Section 7 3 Note carefully too that by default e will recurse down through data structures resulting in a flatten operation 25 The Versatile attach Function Abstractly described the call attach x loads the namespace in the database x making those objects avail able via those names There are two main contexts for this e The database x could be a list The result is that say x u will now be referenceable as simply u The typical usage of this is for data frames which you may recall are in fact lists In the example in Section 8 1 for instance we could type gt attach testscores This command tells R that from now on when we refer for example to Exam3 we mean testscores Exam3 gt mean Exam3 1 50 05455 If we want R to stop doing that we use detach e g gt detach gt mean Exam3 Error in mean Exam3 Object Exam3 not found e If we had previously saved a collection of objects to d
58. from Examl Exam3 Examl Exam2 would mean to predict Exam3 from Exam2 and Exam2 Exam3 Examl Exam2 means to predict Exam3 from Exam2 and Exam2 with an interaction term i e E Exam3 Examl Exam2 a b Examl c Exam2 d Examlx Exam2 The interaction term would be referred to as Exam1 Exam2 by R Note that coefficients is a member variable within the Im class hence the sign as we saw in Section 7 96 Another member variable of that class is formula a string in which we specify the regression model in this case predicting Exam3 from Exam1 Note by the way that since the model is a string we can program many models in a loop using R s string manipulation facilities Section 21 Actually the fitl object contains a lot more information such as fit1 residuals a vector consisting of the prediction errors i e how far off our predicted values are from the real ones If we simply call summary as we did above it prints out but the return value of that function is also an object of class summary hn If we make sure to have our data in matrix form rather than as a data frame applying as matrix if neces sary then we can conveniently specify multiple predictors by making use of R s indexing operations For instance if we have a data matrix Z gt Im z 1 7 z 2 3 would be easier to type than gt lm z 1 z 2 z 3 Computation of the estimated coefficients requires a matrix inversion
59. gt mtrace f 80 Do this for each function at which you want a breakpoint e Then go ahead and start your program I m assuming that your program itself consists of a function Execution will pause at f and a window will pop up showing the source code for that function The current line will be highlighted in green Back in the R interactive window you ll see a prompt D 1 gt e At this point you can single step through your code by repeatedly hitting the Enter key You can print the values of variables as you usually do in R s interactive mode e You can set finer breakpoints at the line level using bpQ Once you are in for instance to set a breakpoint at line 12 in that function type D 1 gt bp 12 e To set a conditional breakpoint say at line 12 with the condition k 5 issue bp 12 k 5 e To avoid single stepping issue go which will execute continuously until the next breakpoint e To set a temporary breakpoint at line n issue go n e To restart execution of the function issue skip 1 e If there is an execution error the offending line will be highlighted e To cancel all mtrace breaks issue mtrace off To cancel one for a particular function fQ issue mtrace f tracing F e To cancel a breakpoint say at line 12 issue bp 12 F e To quit issue qqq e For more details see the extensive online help e g by typing D 1 gt bp 26 5 Ensuring Consistency with the set seed Functio
60. gument to a function In many cases the program output may be invalid though it may well be fine too say with a message fitted probabilities numerically O or 1 occurred in glm 27 Startup Files If there are R commands you would like to have executed at the beginning of every R session you can place them in a file Rprofile either in your home directory or in the directory from which you are running R The latter directory is searched for such a file first which allows you to customize for a particular project Other information on startup files is available by typing gt help Rprofile 28 Session Data As you proceed through an interactive R session R will record the commands you submit And as you long as you answer yes to the question Save workspace image put to you when you quit the session R will save all the objects you created in that session and restore them in your next session You thus do not have to recreate the objects again from scratch if you wish to continue work from before The saved workspace file is named Rdata and is located either in the directory from which you invoked this R session Linux or in the R installation directory Windows Note that that means that in Windows if you use R from various different directories each save operation will overwrite the last That makes Linux more convenient but note that the file can be quite voluminous so be sure to delete it if you are no longer worki
61. he function dot to each row indicated by the 1 with 2 meaning column of a playing the role of the first argument to dot and with c 1 1 playing the role of the second argument Now let s do this in parallel across our two machines in our cluster cls gt parApply cls a 1 dot c 1 1 1 8 10 12 14 16 18 The function clusterCall cls f args applies the given function f at each worker node in the cluster cls using the arguments provided in args The function clusterExport cls varlist copies the variables in the list varlist to each worker in the cluster cls You can use this to avoid constant shipping of large data sets from the master to the workers you just do so once using clusterExport on the corresponding variables and then access those variables as global For instance gt z lt function return x gt x lt 5 gt y lt 12 gt clusterExport cls list x y gt clusterCall cls z EEFI 1 5 121 EERE The function clusterEvalQ cls expression runs expression at each worker node in cls Continuing the above example we have 89 gt clusterEvalQ cls x lt x 1 6 6 gt clusterCall cls z 6 Note that x still has its original version back at the master The function clusterApply cls individualargs f commonargsgohere runs f at each worker node in cls with arguments as follows The first argument to f for worker i is the it element of the list individu al
62. if dog amp amp k 6 browser 26 1 2 Stepping through Our Code When you execute your code and hit a breakpoint you enter the debugger termed the browser in R The command prompt will now be something like Browse 1 instead of just gt Then you can invoke various debugging operations such as e n or Enter You can single step through the code by hitting the Enter key If it is a line level breakpoint you must hit n the first time then Enter after that e c You can skip to the end of the current context a loop or a function by typing c where You can get a stack report by typing where e Q You can return to the gt prompt i e exit the debugger by typing Q e All normal R operations and functions are still available to you So for instance to query the value of a variable just type its name as you would in ordinary interactive usage of R If the variable s name is one of the debug commands though say c you ll need to do something like print c to print it out 78 26 2 Automating Actions with the trace Function The trace function is quite flexible and powerful though it takes some initial effort to learn I will discuss some of the simpler usage forms here The call gt trace f t would instruct R to call the function t every time we enter the function r For instance say we wish to set a breakpoint at the beginning of the function gy We could do this by the command gt
63. in native machine code rather than interpretively in R code Of course R s functional programming features described in Section IT provide many ways to help us avoid explicit loops For more detailed information on improving R performance see http www statistik uni dortmund de useR 2008 tutorials useR2008introhighperfR pdf 14 Simulation Programming in R 14 1 The Basics Here is an example finding P Z lt 1 for a N 0 1 random variable Z gt count lt 0 gt for i in seq 1 100000 if rnorm 1 lt 1 0 count lt count 1 gt count 100000 1 0 832 gt count 100000 0 1 0 832 14 2 Achieving Better Speed But as noted in Section 13 you should try to use R s built in features for greater speed The above code would be better written gt x lt rnorm 100000 gt length x x lt 1 0 100000 0 52 We achieve an increase in speed at the expense of using more memory by keeping our random numbers in an array instead of generating and discarding them one at a time Suppose for example we wish to simulate sampling from an adult human population in which height is normally distributed with mean 69 and standard deviation 2 5 for men with corresponding values 64 and 2 for women We ll create a matrix for the data with column 1 showing gender 1 for male 0 for female and column 2 showing height The straightforward way to do this would be something like siml lt function n xm lt matrix n
64. ing the member variables of the class Readers who know Perl may recognize this ad hoc nature in Perl s own OOP system The class attribute is set by hand by using the attr or class function and then various generic functions are defined For instance continuing our employee example from Section 7 we could write gt j lt list name Joe salary 55000 union T gt class j lt employee gt attributes j let s check Snames 1 name salary union Sclass 1 employee Now write a generic function print employee lt function wrkr cat wrkr name An cat salary wrkr salary An cat union member wrkrSunion n Now test it gt 3 Joe salary 55000 union member TRUE Compare this to the call to the default print back in Section 7 gt j Sname Joe Ssalary 55000 Sunion TRUE gt 3 1 1 Joe 62 Here is a more involved example Here we will write an R class ut for upper triangular matrices Recall that this means that these are square matrices whose elements below the diagonal are Os For example 1 5 12 0 6 9 0 0 2 The component mat of this class will store the matrix There is no point in storing the Os so only the diagonal and above diagonal elements will be stored in column major order We could initialize storage for the above matrix for instance via the call c 1 5 6 12 9 2 The component ix of this class shows where in mat
65. instance and will serve as a case study on how to scramble if ordinary methods don t work I wanted to install a package Rmpi on our department s instructional machines in the directory home matloff R I tried using install packages first but found that the automated process could not find the MPI library on our machines The problem was that R was looking for those files in usr local lam whereas I knew they were in usr local LAM So I downloaded the Rmpi files in the packed form Rmpi_0 5 3 tar gz I unpacked that file in my directory tmp producing a directory tmp Rmpi Now if there had been no problem I could have just typed R CMD INSTALL 1 home matloff R Rmpi from within the tmp directory That command would install the package contained in tmp Rmpi placing it in home matloff R This would have been an alternative to calling install packages But as noted I had to deal with a problem Within the tmp Rmpi directory there was a configure file so I ran configure help on my Linux command line It told me that I could specify the location of my MPI files to configure as follows configure with mpi usr local LAM This is if one runs configure directly but I ran it via R R CMD INSTALL 1 home matloff R Rmpi configure args with mpi usr local LAM Well that seemed to work in the sense that R did install the package but it also noted that it had a problem with the threads library o
66. ional arguments 23 6 9 Treating a Vector As a One Column Matrix In doing matrix work you may be disconcerted to find that if you have code that deals with matrices of various sizes a matrix degenerates to a vector if 1t has only one column You can fix that by then applying as matrix For example gt u Mi 23 gt v lt as matrix u gt attributes u NULL gt attributes v Sdim 1 3 1 So as matrix converted the 3 element vector u to a 3x1 matrix v 6 10 Adding Deleting Elements of Vectors and Matrices Technically vectors and matrices are of fixed length and dimensions However they can be reassigned etc Consider mk Ka 0 127 5 7035 16 8 gt x lt c x 20 append 20 Sox ET EL 25 eo 58 20 gt x lt c x 1 3 20 x 4 6 insert 20 gt x 1 12 5 13 20 16 8 20 delete elements 2 through 4 gt x lt x 2 4 gt x 1 H 12 16 8 20 The rbind and cbind functions enable one to add rows or columns to a matrix For example obhbome You can also use these functions as a quick way to create small matrices gt q lt chind c 1 2 c 3 4 gt q 11 z2 1 dl 2 2 4 24 We can delete rows or columns in the same manner as shown for vectors above e g gt m lt matrix 1 6 nrow 3 gt m 1 2 1 1 4 2 2 5 3 3 6 gt m lt m c 1 3 gt m 1 2 T 1 4 25 3 6 6 11 Matrix Row and Column Mean Functi
67. isk using save we can now restore them to our R session by using attach 26 Debugging The R base package includes a number of debugging facilities They are nowhere near what a good debug ging tool offers but with skillful usage they can be effective A much more functional debugging package is available for R of course called debug I will discuss this in Section 26 4 26 1 The debug Function One of the tools R offers for debugging your R code is the built in function debug It works in a manner similar to C debuggers such as GDB 26 1 1 Setting Breakpoints Say for example we suspect that our bug is in the function f We enable debugging by typing gt debug f TT This will set a breakpoint at the beginning of f To turn off this kind of debugging for a function fQ type gt undebug f Note that if you simultaneously have a separate window open in which you are editing your source code and you had executed debug f then if you reload using source the effect is that of calling undebug f If we wish to set breakpoints at the line level we insert a line browser before line at which we wish to break You can make a breakpoint set in this fashion conditional by placing it within an if statement e g if k 6 browser You may wish to add an argument named say dbg to most of your functions with dbg 1 meaning that you wish to debug that part of the code The above then may look like
68. ist to a Data Frame For printing statistical calculations and so on you may wish to convert a list to a data frame straightforward code to do it converts a list lst to a data frame which is the return value wrtlst lt function ist frm lt data frame rw lt 1 for key in names 1st frm rw 1 lt key frm rw 2 lt lst key rw lt rwtl return frm But if our list has named tags and has only numeric values the following code may run faster converts a list lst that has only numeric values to a data frame which is the return value of the function lsttodf lt function lst n lt length lst create the data frame using the default column names 33 Here s frm lt data frame Vl character n V2 numeric n frm 1 lt names lst frm 2 lt as numeric unlist lst return frm 8 6 The Factor Factor If your table does have a variable i e a column in character mode you probably should set as is T in your call to read table so that this variable stays a vector rather than a factor Otherwise even your numeric columns will become factors which could cause problems as seen in our example below The same is true for creating a data frame via a call to data frame Consider gt d lt data frame cbind c 0 5 12 13 c xyz ab yabc NA d X1 X2 Q xyz 5 ab 12 yabe 13 lt NA gt gt d 1 1 lt 3 Warning message Vv S WN n lt fa
69. its output is numbered which may be a nuisance to us E g gt print abc 1 abc gt cat abc n abc The arguments to cat will be printed out with intervening spaces for instance gt x lt 12 gt cat x abc de n 12 abc de 55 If you don t want the spaces use separate calls to cat gt z lt function a b cat a cat b n gt z abc de abcde 15 3 Reading a Matrix or Data Frame From a File The function read table was discussed in Section 8 1 Here is a bit more on it e The default value of header is FALSE so if we don t have a header we need not say so e By default character strings are treated as R factors Section 9 To turn this feature off include the argument as is T in your call to read table e If you have a spreadsheet export file i e of type csv in which the fields are separated by commas in stead of spaces use read csv instead of read table There is also read xls to read core spreadsheet files e Note that if you read in a matrix via read table the resulting object will be a data frame even if all the entries are numeric You may need it as a matrix in which case do a followup call to as matrix There appears to be no good way of reading in a matrix from a file One can use read table and then convert A simpler way is to use scan to read in the matrix row by row making sure to use the byrow option in the function matr
70. ix For instance say the matrix x is orrrr orrro POORER We can read it into a matrix this way gt x lt matrix scan x nrow 5 byrow T 15 4 Reading a File One Line at a Time You can use readLines for this We need to create a connection first by calling file For example suppose we have a file z with contents NeHe Di Ww Then we can do this 56 gt lt file z r gt readLines c n 1 iy yr 3 gt readLines c n 1 1 1 4 gt readLines c n 1 1 2 6 If readLines encounters the end of the file it returns a null string 15 5 Writing to a File 15 5 1 Writing a Table to a File The function write table works very much like read table in this case writing a data frame instead of reading one In the case of writing a matrix to a file just state that you want no row or column names e g gt write table xc xcnew row names F col names F 15 5 2 Writing to a Text File Using cat The point of the word text in the title of this section is that for instance the number 12 will be written as the ASCII characters 1 and 2 as with printf with d format in C as opposed to the bits 000 00001 100 The function cat can be used to write to a file one part at a time For example gt cat abc n file u gt cat de n file u append T The file is saved after each operation so at this point the file on disk really does look like abc de
71. ling the quit function or optionally by hitting ctrl d in Linux gt q Save workspace image y n c n That last question asked whether we want to save our variables etc so that we can resume work later on If we answer y then the next time we run R all those objects will automatically be loaded This is a very important feature especially when working with large or numerous datasets see more in Section 28 15 5 Functions a Short Programming Example In the following example we define a function oddcount while in R s interactive mode and then call the function on a couple of test cases The function is supposed to count the number of odd numbers in its argument vector comment counts the number of odd integers in x oddcount lt function x k lt 0 for n in x if n 2 return k oddcount c 1 3 5 1 3 oddcount c 1 2 3 7 9 1 4 ZV OVA 3 gt 8e Here is what happened We first told R that we would define a function oddcount of one argument x The left brace demarcates the start of the body of the function We wrote one R statement per line Since we were still in the body of the function R reminded us of that by using as its prompf instead of the usual gt After we finally entered a right brace to end the function body R resumed the gt prompt 6 Scalars Vectors Arrays and Matrices Remember objects are actually considered one element vectors So there is rea
72. lly no such thing as a scalar Vector elements must all have the same mode which can be integer numeric floating point number character string logical boolean complex object etc Vectors indices begin at 1 Note that vectors are stored like arrays in C i e contiguously and thus one cannot insert or delete elements a la Python If you wish to do this use a list instead A variable might not have a value a situation designated as NA This is like None in Python and undefined in Perl though its origin is different In statistical datasets one often encounters missing data i e observa tions for which the values are missing In many of R s statistical functions we can instruct the function to skip over any missing values Arrays and matrices are actually vectors too as you ll see they merely have extra attributes e g in the matrix case the numbers of rows and columns Keep in mind that since arrays and matrices are vectors that means that everything we say about vectors applies to them too One can obtain the length of a vector by using the function of the same name e g gt x lt c 1 2 4 gt length x 1 3 Actually this is a line continuation character 16 6 1 Declarations You must warn R ahead of time that you intend a variable to be one of the vector array types For instance say we wish y to be a two component vector with values 5 and 12 If you try gt y 1 lt 5 gt y 2 l
73. lt x 1 x 1 length x 1 return length which diff lt 0 I noted in Section 2 that using the nrow function in conjunction with filtering provides a way to obtain a count of records satisfying various conditions If you just want the count and don t want to create a new table you should use this approach You can also use this to selectively change elements of a vector e g 41 gt lt OL 3872 gt x x gt 3 lt 0 gt X 1J t302 11 2 2 On Matrices and Data Frames Filtering can be done with matrices and data frames too Note that one must be careful with the syntax For instance x WN Xx UuNRA XK Again let s dissect this gt j lt x 2 gt 3 gt 3 1 FALSE TRUE TRUE gt x 3 1 1 1 2 1 wW NX Ae W Here is another example gt m lt matrix c 1 2 3 4 5 6 nrow 3 gt m ri 2 Ty 1 4 2 2 5 Sy 3 6 gt m m 1 gt ri 2 tj 2 5 2i 3 6 gt m m 1 gt 1 m 2 gt 5 TL 36 11 3 Combining Elementwise Operations and Filtering with the ifelse Function The form is ifelse b u v where b is a boolean vector and u and v are vectors The return value is a vector element i of which is u i if b i is true or v i if b i is false This is pretty abstract so let s go right to an example 42 gt x lt 1 10 gt y lt ifelse x 2 0 5 12 gt y Here we wish to produce a vector in which there is a 5 wherever x is ev
74. me It is automatically invoked by some R commends such as help and you can invoke it yourself on lengthy output For instance if you have a long vector x and wish to display it one screen at a time then instead of typing type 85 gt page x Type abc to search for the string abc in the pager output hit q to quit the pager etc 30 3 Calculating Run Time If you are not sure which of several approaches to use to get the fastest R code you can time them with the function system time An example is shown in Section 14 31 Writing C C Functions to be Called from R You may wish to write your own C C functions to be called from R as they may run much faster than if you wrote them in R Recall though that you may get a lot of speed out of R if you avoid using loops See Section 13 The SWIG package can be used for this see nttp www swig org 32 Parallel R Since many R users have very large computational needs various tools for some kind of parallel operation of R have been devised These involve parallel invocations of R communicating through a network 32 1 Rmpi The Rmpi provides an interface for R to MPI the popular message passing system 32 1 1 Installation Say you want to install in the directory a b c The easiest way to do so is gt install packages Rmpi a b c This will install Rmpi in the directory a b c Rmpi I found that in order to get it to work I needed to edit
75. me material on OOP ttp cran r project org doc FAQ R FAQ html R FAQ mainly aimed at program e http bayes math montana edu Rweb Rnotes R html Reference manual by sev eral prominent people in the R S community R tasks that may not have immediately obvious solutions 102 ttp wiki r project org rwiki doku php id tips tips Tips on miscellaneous 39 2 4 Especially for Graphics There are many extensive Web tutorials on this including ttp www sph umich edu nichols biostat_bbag march2001 pdf A slide show tutorial on R graphics very nice easy to follow by M Nelson of Esperion Therapeutics e http zoonek2 free fr UNIX 48_R 02 html The graphics section of Zoonekynd s tutorial Lots of stuff here e http www math ilstu edu dhkim Rstuff Rtutor html Again by Prof Dong Yun Kim of the Dept of Math at Illinois State University Extensive material on use of color ttp wwwmaths anu edu au johnm r usingR pdf A draft of John Maindonald s book he also has scripts data etc on his full site http wwwmaths anu edu au johnm Graphics used heavily throughout but see especially Chapters 3 and 4 which are devoted to this topic e hi public iastate edu 7emervyn stat579 r_class6_f05 pdf Prof elhttp addictedtor free fr graphiques The R Graphics Gallery a collection of graphics examples with the source code elhttp www stat auckland ac nz
76. n If you re doing anything with random numbers you ll need to be able to reproduce the same stream of numbers each time you run your program during the debugging session To do this type gt set seed 8888 or your favorite number as an argument 26 6 Syntax and Runtime Errors The most common syntax errors will be lack of matching parentheses brackets or braces When you en counter a syntax error this is the first thing you should check and double check I highly recommend that you use a text editor say Vim that does parenthesis matching and syntax coloring for R Beware that often when you get a message saying there is a syntax error on a certain line the error may well be elsewhere This can occur with any language but R seems especially prone to it 81 If it just isn t obvious to you where your syntax error is I recommend selectively commenting out some of your code thus enabling you to better pinpoint the location of the syntax problem If during a run you get a message could not find function evaluator and a particular function call is cited it means that the interpreter cannot find that function You may have forgotten to load a library or source a code file You may sometimes get messages like There were 50 or more warnings use warnings to see the first 50 These should be heeded run warnings as suggested The problem could range from nonconvergence of an algorithm to misspecification of a matrix ar
77. n our machines Sure enough when I tried to load Rmpi I got a runtime error saying that a certain threads function wasn t there I knew that our threads library was fine so I went into configure file and commented out two lines 84 if test Sac_cv_lib_pthread_main yes then MPI_LIBS MPI_LIBS lpthread fi In other words I forced it to use what I knew or was fairly sure would work I then reran R CMD INSTALL and the package then loaded with no problem 29 4 Documentation You can get a list of functions in a package by calling library with the help argument e g gt library help mvrnorm for help on the mvrnorm package 29 5 Built in Data Sets R includes a few real data sets for use in teaching research or in testing software Type the following gt library utils gt help data Here data is contained within the utils package We load that package and use help to see what s in it in this case various data sets We can load any of them but typing its name e g gt LakeHuron 30 Handy Miscellaneous Features 30 1 Scrolling through the Command History During a session you can scroll back and forth in your command history by typing ctrl p and ctrl n You can also use the history command to list your more recent commands which will be run through the pager Set the named argument max show Inf if you want to see all of them 30 2 The Pager This displays material one screen at a ti
78. n x 1 gt w u HI 639 Here w uses which is vectorized so w is vectorized as well This applies to many of R s built in functions For instance let s apply the function for rounding to the nearest integer to an example vector y gt y lt O 1 273 9 0 04 gt z lt round y gt z 11 140 The point is that the round function was applied individually to each element in the vector y In fact in Tf not use as matrix to convert your vector to a matrix and use apply An example is given in Section 11 4 3 39 gt round 1 2 i E the operation still works because the number 1 2 is actually considered to be a vector that happens to consist of a single element 1 2 Here we used the built in function round but you can do the same thing with functions that you write yourself Note that the functions can also have extra arguments e g gt f lt function elt s return elt s gt y lt c 1 2 4 gt f y 1 PL 2 305 As seen above even operators such as are really functions For example the reason why elementwise addition of 4 works here Soy Se 2 5 13 gt yt4 ly 16 2 17 is that the is actually considered a function Look at it here gt y 4 LJ 169 17 11 1 2 The Case of Vector Valued Functions The above operations work with vector valued functions too z12 lt function z return c z z 2 x Freg gt z12 x Al 1 2 3 4 5 6 7 8 1 4 9 16 25 36 49 64
79. nce matrix the R function preomp may be preferable The function diag extracts the diagonal of a square matrix useful for obtaining variances from a covariance matrix 25 7 Lists R s list structure is similar to a C struct It plays an important role in R with data frames object oriented programming and so on as we will see later 7 1 Creation As an example consider an employee database Suppose for each employee we store name salary and a boolean indicating union membership We could initialize our database to be empty if we wish j lt list Or we could create a list and enter our first employee Joe this way j lt list name Joe salary 55000 union T We could print j out aan name 1 Joe Ssalary 1 55000 Sunion 1 TRUE Actually the element names e g salary are optional One could alternatively do this gt jalt lt list Joe 55000 T gt jalt 1 Joe Here we refer to jalt s elements as 1 2 and 3 which we can also do for j above 7 2 List Tags and Values and the unlist Function If the elements in a list do have names e g with name salary and union for j above these names are called tags The value associated with a tag is indeed called its value You can obtain the tags via names 26 gt names 3 1 name salary union To obtain the values use unlist gt ulj lt unlist j gt ulj name salary union Joe
80. nd all functions are handy gt x lt 1 10 gt if any x gt 8 print yes 1 ves gt if any x gt 88 print yes gt if all x gt 88 print yes gt if all x gt 0 print yes 1 yes 6 4 Recycling When applying an operation to two vectors which requires them to be the same length the shorter one will be recycled i e repeated until it is long enough to match the longer one e g Se tig 2 y 0 F966 0 9 20 22 1 T 2 13 21 24 Warning message longer object length is not a multiple of shorter object length in c 1 2 4 c 6 O79 20 22 Here s a more subtle example gt x 1 2 Ys T 4 2 2 5 oy 3 6 gt xte 1 2 1 2 Ly 2 6 ay 4 6 3y 4 8 18 What happened here is that x as a 3x2 matrix is also a six element vector which in R is stored column by column We added a two element vector to it so our addend had to be repeated twice to make six elements So we were adding c 1 2 1 2 1 2 to x 6 5 Vector Indexing You can also do indexing of arrays picking out elements with specific indices e g A A H E O PE 12 gt y c 1 3 1 1 2 0 4 gt y 2 3 1 3 9 0 4 Note carefully that duplicates are definitely allowed e g gt x lt c 4 2 17 5 gt y lt x c 1 1 3 gt y I A 4 r7 Negative subscripts mean that we want to exclude the given elements in our output gt z lt c 5 12 13 gt z 1 exclude element 1 TA
81. ng on that particular project You can also save the image yourself to whatever file you wish by calling save image You can restore the workspace from that file later on by calling load 82 29 Packages Libraries 29 1 Basic Notions R uses packages to store groups of related pieces of software f The libraries are visible as subdirectories of your library directory in your R installation tree e g usr lib R library The ones automatically loaded when you start R include the base subdirectory but in order to save memory and time R does not automat ically load all the packages You can check which packages are currently loaded by typing gt path package 29 2 Loading a Package from Your Hard Drive If you need a package which is in your R installation but not loaded into memory yet you must request it For instance suppose you wish to generate multivariate normal random vectors The function mvrnorm in the package MASS does this So load the library gt library MASS Then mvrnorm will now be ready to use As will be its documentation Before you loaded MASS help mvrnorm would have given an error message 29 3 Downloading a Package from the Web However the package you want may not be in your R installation One of the big advantages of open source software is that people love to share Thus people all over the world have written their own special purpose R packages placing them in the CRAN reposito
82. nteractive mode by typing the name of the object and since functions are objects you can view the code for a function either one you wrote or one in R in this manner For example gt fl function a b return a b This is handy if you re using a function that you ve written but have forgotten what its arguments are for instance It s also useful if you are not quite sure what an R library function does by looking at the code you may understand it better Also a nice feature is that you can edit functions from within R In the case above I could change f1 by typing gt f1 lt edit f1 This would open the default editor on the code for f1 which I could then edit and save back to f1 The editor invokved will depend on R s internal options variable editor In Unix class systems R will set this from your EDITOR or VISUAL environment variable or you can set 1t yourself e g gt options editor usr bin vim See the online documentation if you have any problems Note that in this example I am saving the revision back to the same function Note too that when I do so I am making an assignment and thus the R interpreter will compile the code if I have any errors the assignment will not be done I can recover by the command gt x lt edit Warning Apparently comments are not preserved 12 R Programming Structures R is a full programming language similar to scripting languages such as Perl and Python On
83. om 1 100 recall 100 is our sample size here R will then i to this set of random indices when it calls mdn For example R might generate i to be the vector 3 22 59 3 14 6 Of course in boot s call to mdn the formal parameter x is our vector y here So the expression x i means y c 3 22 59 3 14 6 in other words the vector y 3 y 22 y 59 y 31 y 14 y 6 exactly the kind of thing the bootstrap is supposed to do To then call boot we do something like gt b lt boot y mdn R 200 This tells R to apply the bootstrap to the data y calculating the statistic mdn on each of 200 resamplings of y 99 Normally we would assign the result of boot to an object as we did with b above Among the components of that object are b t which is a matrix whose it row gives the value of the statistic as found on the i bootstrap resampling and b t0 which is the value of our statistic on the original data set A somewhat more sophisticated example they can become quite complex would be that in which our data is stored in a data frame say a frame d consisting of 100 rows of two columns We might be doing regression of the first column against the second Let s assume that both the predictor and response data is random 1 e this is not a fixed X regression situation An index i here of 3 22 59 3 14 6 could mean that our resampling would give us rows 3 22 59 and so on of d We could set our sta
84. on can also be used To define a generic function on a class use setMethod Let s do that for our class employee here We ll implement the show function To see what this function does consider our command above gt joe As we know in R when we type the name of a variable while in interactive mode the value of the variable is printed out gt joe An object of class employee Slot name 1 Joe Slot salary 1 55000 Slot union 1 TRUE The action here is that show is called In fact we would get the same output here by typing gt show joe Let s override that with the following code which is in a separate file and brought in using source setMethod show employee function object inorout lt ifelse object union is is not cat object name has a salary of object salary and inorout in the union n The first argument gives the name of the generic function which we will override with the second argument giving the class name We then define the new function Let s try it out gt joe Joe has a salary of 55000 and is in the union The function show has precedence over print 64 17 Type Conversions The str function converts an object to string form e g gt OL 2 4 gt class x 1 numeric gt str x num 1 3 1 2 4 There is a generic function as which does conversions e g gt x lt c 1 2 4 gt y lt as
85. ons The function mean applies only to vectors not matrices If one does call this function with a matrix ar gument the mean of all of its elements is computed not multiple means row by row or column by column since a matrix is a vector The functions rowMeans and colMeans return vectors containing the means of the rows and columns There are also corresponding functions rowSums and colSums 6 12 Linear Algebra Operations on Vectors and Matrices Multiplying a vector by a scalar works directly as seen earlier For example If you wish to compute the inner product dot product of two vectors use crossprod Note that the name is a misnomer as the function does not compute vector cross product For matrix multiplication in the mathematical sense the operator to use is not Note also that a vector is considered a one row matrix not a one column matrix and thus is suitable as the left factor in a matrix product but not directly usable as the right factor The function solve will solve systems of linear equations and even find matrix inverses For example gt a lt matrix c 1 1 1 1 nrow 2 ncol 2 gt b lt 6 2 4 gt solve a b fl 3 1 gt solve a 1 2 Lie 033 25 ES 1 D ds Usb Use t for matrix transpose qr for QR decomposition chol for Cholesky and det for determinants Use eigen to compute eigenvalues and eigenvectors though if the matrix in question is a covaria
86. ors consisting of those numbers This is because any object is considered a one element vector Thus we can also do for instance gt q lt c x x 8 which would set q to 1 2 4 1 2 4 8 Since seeing is believing go ahead and confirm that the data is really in x to print the vector to the screen simply type its name If you type any variable name or more generally an expression while in interactive mode R will print out the value of that variable or expression Python programmers will find this feature familiar For example 13 Yep sure enough x consists of the numbers 1 2 and 4 The 1 here means in this row of output the first item is item 1 of that output If there were say two rows of output with six items per row the second row would be labeled 7 Our output in this case consists of only one row but this notation helps users read voluminous output consisting of many rows Again in interactive mode one can always print an object in R by simply typing its name so let s print out the third element of x gt x 3 1 4 We might as well find the mean and standard deviation gt mean x I 2 333333 gt sd x I 2 527525 If we had wanted to save the mean in a variable instead of just printing it to the screen we could do say gt y lt mean x Again since you are learning let s confirm that y really does contain the mean of x gt y HI 2333333 As noted earlier
87. print device pdf d12 pdf x11 2 This opens the PDF file d12 pdf copies the X11 graph to it closes the file and resets X11 as the active device 23 16 3 Dimensional Plots There are a number of functions to plot data in three dimensions such as persp and wireframe which draw surfaces and cloud which draws three dimensional scatter plots There are many more For wireframe and cloud one loads the lattice library Here is an example gt a lt 1 10 gt b lt 1715 gt eg lt expand grid x a y b gt eg z lt eg x 2 eg x egSy gt wireframe z x y eg The call to expand grid creates a data frame consisting of two columns named x and y combining all the values of the two inputs Here a and b had 10 and 15 values respectively so the resulting data frame will have 150 rows We then added a third column named z as a function of the first two columns Our call to wireframe then creates the graph Note that z x and y of course refer to names of columns in eg All the points would be connected as a surface like connecting points by lines in two dimensions With cloud though the points would just be isolated For wireframe the X Y pairs must form a rectangular grid though not necessarily evenly spaced Note that the data frame that is input to wireframe need not have been created by expand grid By the way these functions have many different options A nice one for wireframe
88. ral commands So as a base we might first draw an empty graph with only axes For instance gt plot c 3 3 c 1 5 type n xlab x ylab y 66 99 draws axes labeled x and y the horizontal one ranging from x 3 to x 3 and the vertical one ranging from y 1 to y 5 The argument type n means that there is nothing in the graph itself 70 23 2 Plotting Multiple Curves on the Same Graph The plot function works in stages i e you can build up a graph in stages by issuing more and more commands each of which adds to the graph For instance consider the following x lt c 1 2 3 y lt c 1 3 8 plot x y lmout lt lm y x abline lmout VVVV Vv The call to plot will graph the three points as in our example above At this point the graph will simply show the three points along with the X and Y axes with hash marks The call to abline then adds a line to the current graph Now which line is this As we know from Section 36 1 the result of the call to the linear regression function Im is a class instance containing the slope and intercept of the fitted line as well as various other quantities that won t concern us here We ve assigned that class instance to Imout The slope and intercept will now be in Imout coefficients Now what happens when we call abline This is simply a function that draws a straight line with the function s arguments being treated as the intercep
89. row n ncol 2 for i in 1 n d lt rnorm 1 LE Muni 035 4 xm i 1 lt 1 xm i 2 lt 2 5 d 69 else xm i 1 lt 0 xm i 2 lt 2xd 64 return xm We could avoid a loop this way sim2 lt function n d lt matrix nrow n ncol 2 d 1 lt runif n d 2 lt rnorm n smpl lt function rw rw one row of d if rw 1 lt 0 5 y lt 1 x lt 2 5xrw 2 69 else y lt 0 x lt 2xrw 2 64 return c y x z lt apply d 1 smp1 return t z Here is a quick illustration of the fact that we do gain in performance gt system time sim1 1000 1 0 028 0 000 0 027 0 000 0 000 gt system time sim2 1000 1 0 016 0 000 0 018 0 000 0 000 Here is a slightly more complicated example using a classical problem from elementary probability courses Urn 1 contains 10 blue marbles and eight blue ones In Urn 2 the mixture is six blue and six yellow We draw a marble at random from Urn 1 and transfer it to Urn 2 and then draw a marble at random from Urn 2 What is the probability that that second marble is blue This quantity is easy to find analytically but we ll use simulation Here is the straightforward way sim3 lt function nreps nbl 10 10 blue marbles in Urn 1 53 nl lt 18 number of marbles in Urn 1 at 1st pick n2 lt 13 number of marbles in Urn 2 at 2nd pick count lt 0 for i in l nreps nb2 6 6 blue marbles orig in Urn 2
90. rve fromx 1 2tox 1 4 gt f lt function x return 1l exp x gt curve f 0 2 gt polygon c 1 2 1 4 1 4 1 2 c 0 0 1 3 f 1 3 col gray In the call to polygon here the first argument is the set of X coordinates for the rectangle while the second argument specifies the Y coordinates The third argument specifies that the rectangle should be shaded in gray instead we could have for instance used the density argument for striping 23 13 Smoothing Points the lowess Function Just plotting a cloud of points whether connected or not may turn out to be just an uninformative mess In many cases it is better to smooth out the data by fitting a nonparametric regression estimator nonparametric meaning that it is not necessarily in the form of a straigh line such as lowess plot lowess x y The call lowess x y returns the pairs of points on the regression curve and then plot plots them Of course we could get both the cloud and the smoothed curve plot x y lines lowess x y 23 14 Graphing Explicit Functions Say you wanted to plot the function g t t 1 for t between 0 and 5 You could use the following R code g lt function t return t 2 1 0 5 define g x lt seq 0 5 length 10000 x 0 0004 0 0008 0 0012 5 y lt g x y g 0 0004 g 0 0008 g 0 0012 g 5 plot x y type 1 74 But even better you could use the curve function gt
91. ry In this manner we get a uniform interface to different classes So when someone develops a new R class for others to use we can try to apply say summary and reasonably expect it to work This of course means that the person who wrote the class knowing the R idiom would have had the foresight of writing such a function in the class knowing that people would expect one The functions above are known as generic functions The actual function executed will be determined by the class of the object on which you are calling the function For example let s look at a simple regression analysis details in Section 36 1 x lt c 1 2 3 y lt o 1 3 8 lmout lt lm y x lmout call lm formula y x Coefficients Intercept x 3 0 Bad 60 Note that we printed out the object Imout Remember by simply typing the name of an object in interactive mode the object is printed What happened then was that the R interpreter saw that Imout was an object of class Im the quotation marks are part of the class name and thus instead of calling print it called print Im a special print method in the Im class In fact we can take a look at that method gt print Im function x digits max 3 getOption digits 3 cat nCall n deparse x call n n sep if length coef x cat Coefficients n print default format coef x digits digits print gap 2 quote FALSE els
92. ry and elsewhere 29 3 1 Using install package One way to install a package is not surprisingly to use the install packages function As an example suppose you wish to use the mvtnorm package which computes multivariate normal cdf s and other quantities Choose a directory in which you wish to install the package and maybe others in the future say a b c Then at the R prompt type gt install packages mvtnorm a b c This will cause R to automatically go to CRAN download the package compile it and load it into a new directory a b c mvtnorm You do have to tell R where to find that package though which you can do via the libPaths function This is one of the very few differences between R and S In S packages are called libraries and many of the functions which deal with them are different from those in R 83 gt libPaths a b c This will add that new directory to the ones R was already using If you use that directory often enough you may wish to add that call to libPaths in your Rprofile startup file in your home directory A call to libPaths without an argument will show you a list of all the places R will currently look at for loading a package when requested 29 3 2 Using R CMD INSTALL Sometimes one needs to install by hand to do modifications needed to make a particular R package work on your system The following example will show how I did so in one particular
93. s prdids delone lt function delrow dm resp prdids get all indices except delrow therest lt abl 1 delrow nrow dm fit the model lmout lt glm dm therest resp dm therest prdids family binomial predict the deleted row cf lt as numeric lmoutScoef predvalue lt logit dm delrow prdids cf if predvalue gt 0 5 predvalue lt 1 else predvalue lt 0 return abs dm delrow resp predvalue allbutone returns c a a 1 b 1 b 1 Cc abl lt function a b c if a b return b 1 c if b c return a b 1 return c a b 1 b 1 c finds the value of the logistic function at a given x for a given set of coefficients b logit lt function x b lin lt c 1 x b return 1 1 exp lin 32 2 7 To Learn More about snow I recommend the following Web pages e http cran cnr berkeley edu web packages snow index html CRAN page for snow the package and the manual are here 92 e http www bepress com cgi viewcontent cgi article 1016 context uwbiostat A research paper e http www cs uiowa edu luke R cluster cluster html Brief intro by the author e http www sfu ca sblay R snow html clusterCall Examples short but useful 33 Using R from Python Python is an elegant and powerful language but lacks built in facilities for statistical and data manipulation two areas in which R excels Thus an interface between the two
94. s ulx lt NULL gt ulx 1 2 5 7 4 Accessing List Elements The symbol is used to designate named elements of a list but also works for referencing a single element and works for a group of them gt j Sname Joe Ssalary 55000 Sunion TRUE gt 3 1 1 Joe gt 3 2 3 Ssalary 55000 Sunion TRUE Note that returns a value while returns a sublist 7 5 Adding Deleting List Elements One can dynamically add and delete elements gt z lt list a abc b 12 gt z Sa 1 Haber b 11 12 gt z8c 1 gt z Sa 1 abe b IT La Sc 1 1 28 gt z 1 lt NULL delete element 1 Az b 12 c T2 gt if is null z d print it s not there testing existence it s not there gt y 2 lt 8 can skip elements 7 6 Indexing of Lists To do indexing of a list use instead of Z 23 3 c Her T 2 1 1 2 Names of list elements can be abbreviated to whatever extent is possible without causing ambiguity e g gt jSsal 1 55000 One common use is to package return values for functions that return more than one piece of information Say for instance the function f returns a matrix m and a vector v Then one could write return list mat m vec v at the end of the function and then have the caller access these items like this 1 lt m lt 1 mat v lt l vec Thi
95. s is typical form for functions in the R library 29 7 7 Size of a List You can obtain the number of elements in a list via length gt length j 41413 7 8 Recursive Lists Lists can be recursive i e you can have lists within lists For instance lt list u lt list 5 v 12 we lt list b c 13 VV VV SRE paaao Su 5 Sv 1 12 gt length a So a is now a two element list with each element itself being a list 8 Data Frames On an intuitive level a data frame is like a matrix with a rows and columns structure However it differs from a matrix in that each column may have a different mode For instance one column may be numbers and another column might be character strings On a technical level a data frame is a list of vectors See Section 8 2 for more on this 8 1 A Second R Example Session For example consider an employee dataset Each row of our data frame would correspond to one employee The first column might be the employee s name thus of character i e string mode with the second column being salary thus of numeric mode and with the third column being a boolean i e logical mode indicating whether the employee is in a union As my sample data set I have created a file named exams consisting of grades for the three exams in a certain course two midterm exams and a final exam The first few lines in the file are 30 Examl Exam2 Exam3 62 70 60 74
96. sent excerpts of my preparation code here First I read in the data file al12006 lt read csv 2006 csv header T as is T The function read csv is essentially identical to read table except that the input data are in the Comma Separated Value format exported by spreadsheets which is the way the dataset was prepared by the Depart ment of Labor DOL We now have a data frame all2006 consisting of all the data for the year 2006 Some wages in the dataset were reported in hourly rather than yearly terms This indicates possible part time job status which I wanted to exclude A look at the documentation for the dataset showed that column 17 was the pay period i e yearly hourly etc while columns 15 and 19 contained the actual salary and prevailing wage So I did some filtering al12006 lt al12006 a112006 17 Year al12006 lt al12006 a112006 15 gt 20000 al12006 lt al12006 a112006 19 gt 200 I also needed to create a new column for the ratio between actual wage and prevailing wage al12006 lt cbind al12006 a112006 15 1 a112006 19 This new variable is in column 25 Since I knew I would be calculating the median in this column for many subsets of the data I defined a function to do this work medrat lt function dataframe return median dataframe 25 na rm T Note the need to exclude NA values which are common in government datasets In addition I wanted to analyze the talen
97. sing Values 11 Functional Programming Features ght se hte ae aA Hane Pee ahs So a Tage a aa te a SB ohh Ses 11 1 1 Vectorized Functions ee ee 11 1 2 The Case of Vector Valued Functions o e e e MR A ORE we oa eke Bde a AE hh ey ed ee a a ek ete 11 2 1 On Vectors oe Se a be ee a ee eS 11 2 2 On Matrices and DataFrames 0 0 0 00000000 0G 11 3 Combining Elementwise Operations and Filtering with the ifelseQ Function 11 4 Applying the Same Function to All Elements of a Matrix Data Frame and Even Morel 30 30 31 32 32 32 32 32 33 34 35 36 38 39 39 39 40 40 41 42 42 y db 11 4 2 Applying the Same Function to All Elements of a List oh a e a dd o id Da e akg aes Bam Gor Ge do e 12 R Programming Structures 12 1 Use of Braces for Block Definition 000000000000 004 IA A da 4 doa ed ew Dae Pa eared a eS de Pad oe Pare d 12 3 Basic Structure 12 3 1 Looping Over Nonvector Sets o e e 12 4 Return Values 12 5 If Else 12 6 Local and Global Variables a e ds pais Eds ee eee eee cee eee kas nes ae oe ane Se pe ao be a a ees a ee 13 Writing Fast R Code 14 Simulation Programming in R 14 1 The Basics 14 2 Achieving Better Speed 14 3 Built In Random Variate Generators 14 3 1 Obtaining the Same Random Stream in Repeated Runs 15 Input Output 15 1 Rea
98. sults See Section 32 2 11 4 2 Applying the Same Function to All Elements of a List The analog of apply for lists is lapplyQ It applies the given function to all elements of the specified list For example gt lapply list 1 3 25 27 median 111 In this example the list was created only as a temporary measure so we should convert back to numeric gt as numeric lapply list 1 3 25 27 median IT 226 11 4 3 Applying the Same Function to a Vector If your function is vectorized then you can simply call it on the vector as in Section Otherwise you can still avoid writing a loop e g writing lv lt length v outvec lt vector length 1v for i in 1l lv outvec i lt f v i as follows outvec lt apply as matrix v 1 f The call to as matrix will return a matrix whose sole column is v This may not save you much time if you are running R on just one machine but if you are using for instance the snow package see Section 32 2 with parApply instead of apply it could be well worth doing 11 5 Functions Are First Class Objects Functions can be used as arguments assigned etc For instance 45 fl lt function a b return a b f2 lt function a b return a b f lt f1 f 3 2 LD f lt 2 gt 3 2 1 1 g lt function h a b h a b gt g f 1 3 2 ES gt g 2 3 2 1 v MN NENE v Since you can view any object when in R s i
99. t 12 the first command and the second will be rejected but gt y lt vector length 2 gt y 1 lt 5 gt y 2 lt 12 works as does gt y lt c 5 12 The latter is OK because the right hand side is a vector type so we are binding y to an already existent vector 6 2 Generating Useful Vectors with seq and rep Note the operator ZV vV Suen 4321 Beware of the operator precedence gt i lt 2 gt I i 1 ii 9 1 gt Ie tell py a The seq sequence generates an arithmetic sequence e g gt seg 5 8 1 567 8 gt seg 12 30 3 1 12 15 18 21 24 27 30 gt seq 1 1 2 length 10 EJ dad AZ AS 1 4 DS Dee L 7 1 8 19200 Though it may seem innocuous the seq function provides foundation for many R operations See examples in Sections 14 and 23 14 The rep Crepeat function allows us to conveniently put the same constant into long vectors The call form is rep z k which creates a vector of k length z elements each equal to z For example 17 gt x lt rep 8 4 gt Xx 11 8 8 8 8 gt rep 1 3 2 ITT 22 3 32 3 6 3 Vector Arithmetic and Logical Operations You can add vectors e g Pe Se el 2449 gt x 0 5 0 1 kJ 6 223 You may surprised at what happens when we multiply them gt Xx 6 5 0 1 1 5 0 4 As you can see the multiplication was elementwise This is due to the functional programming nature of R The any a
100. t ade bak ee ee a aes eai A pa o Do doe PRG a Paced Chk Hie td BGA toa hos BO ed de 23 15Graphical Devices and Saving Graphs to Files o o o 23 163 Dimensional Plots o 23 17 The Rest of the Story o 24 The Innocuous c Function 25 The Versatile attach Function 26 Debugging A A EA oe ee aes ee eee eee es ote eee eee aes Lee ba ee reir di eii ida A A eee vere 26 4 The debug Package 2 ee 26 4 1 Installation 2 2 ee 26 4 2 Path Issues a 26 43 Sade sae dwg a Od Oe be da a aa ade do A fared 70 70 71 71 71 72 72 73 73 73 73 74 74 74 74 75 76 76 76 77 26 5 Ensuring Consistency with the set seed Function o oo 26 6 Syntax and Runtime ErTOrS ee 27 Startup Files 28 Session Data 29 Packages Libraries 29 1 B stc Notions iio os E a eG dee ee ee da ad o apa 29 3 Downloading a Package from the Web o o oo o e 29 3 1 Using install packageQ o o e ee A oboe GR a i GR whe a Sa Seas a Bite PASC cae ep Sener ote po A nO en AED eye Bee 29 5 Built in Data Sets oog a ee ee 30 Handy Miscellaneous Features 30 1 Scrolling through the Command History 2 2 0 0 2 eee eee 30 2 he Pager sil ale de he he wa ee dbs eS BS a ae Sw Sal ae deh A 30 3 Calculating Run Time ee 31 Writing C C Functions to be Called
101. t and slope of the line For instance the call abline c 2 1 would draw the line y 1 r 2 on whatever graph we ve built up so far But actually even abline is a generic function and since we are invoking it on the output of Im this version of the function knows that the slope and intercept it needs will be in Imout coefficients and it plots that line Note again that it superimposes this line onto the current graph the one which currently graphs the three points In other words the new graph will show both the points and the line 23 3 Starting a New Graph While Keeping the Old Ones Each time you call plot directly or indirectly the current graph window will be replaced by the new one If you don t want that to happen you can on Linux systems call X11 There are similar calls for other platforms 23 4 The lines Function Though there are many options the two basic arguments to lines are a vector of X values and a vector of Y values These are interpreted as X Y pairs representing points to be added to the current graph with lines connecting the points For instance if x and y are the vectors 1 5 2 5 and 3 then the call gt lines c 1 5 2 5 c 3 3 71 would add a line from 1 5 3 to 2 5 3 to the present graph If you want the lines connecting the dots but don t want the dots themselves include type in your call to lines or to plot gt plot x y type 1 23 5 Ano
102. t for row selection e g gt d lt data frame cbind c 0 5 12 13 x gt d V1 x 1 0 xyz 68 5 yabc 12 abe 13 lt NA gt dabc lt d grep ab d 21 1 dabc v1 x 5 yabc 12 abe VV BWD W N 21 1 3 Example of strsplit gt 85 Strsplita pr gt s a p gt s 1 Maz mat gt s 1 L Tan Myyn gt s 1 1 gr 22 Sorting Ordinary numerical sorting of a vector can be done via sort gt REC 13351255 gt sort x LER S S 12 ES If one wants the inverse use order For example gt order x Bh 2 DEA Here is what order s output means The 2 means that x 2 is the smallest in x the 4 means that x 4 is the second smallest etc You can use order together with indexing to sort data frames For instance gt y lt read table y gt y v1 V2 1 def 2 2 ab 5 3 ZzZZZ A gt r lt order y V2 gt gt gt ila ae ae z lt ylr Z v1 V2 ZZZzzz 1 1 def 2 2 ab 5 69 What happened here We called order on the second column of y yielding a vector telling us which numbers from that column should go before which if we were to sort them The 3 in this vector tells us that x 3 2 is the smallest number the 1 tells us that x 1 2 is the second smallest and the 2 tells us that x 2 2 1s the third smallest We then used indexing Section 8 3 3 to produce the frame sorted by column 2 storing it in z 23 Graphics R has a very rich s
103. t patterns at particular companies using the company name stored in column 7 makecorp lt function corpname t lt al12006 a112006 7 corpname 3N Matloff New Insights from the Dept of Labor PERM Labor Certification Database Sloan Foundation West Coast Program on Science and Engineering Workers conference January 18 2008 35 return t goog2006 lt makecorp GOOGLE INC medrat goog2006 ms2006 lt makecorp MICROSOFT CORPORATION medrat ms2006 I also wanted to analyze by occupation DOL has a code number for each job title stored in column 14 which I used to create the corresponding subsets of the original dataset makeocce lt function df lowerbd upperbd return df df 14 gt 1lowerbd df 14 lt upperba for 2007 data prg2007 lt makeocc a112007 15 1021 00 15 1052 00 programmers se2007 lt makeocc al112007 15 1030 00 15 1039 00 s w engineers engr2007 lt makeocc al12007 17 2000 00 17 2999 00 other engineers One more example I wanted to analyze by nationality which is in column 24 Note my use of looping over a vector of mode character mainnatnames lt c CHINA INDIA CANADA GERMANY UNITED KINGDOM natwithindf lt function natlist df for nat in natlist tmpdf lt df df 24 nat mr lt medrat tmpdf cat nat mr n natwithindf mainnatnames prg2007 natwithindf mainnatnames se2007 9 Fa
104. the various columns begin For the above case ix would be c 1 2 4 meaning that column 1 begins at mat 1 column 2 begins at mat 2 and column 3 begins at mat 4 The function below creates an instance of this class Its argument inmat is in full matrix format i e includ ing the Os ut lt function inmat nr lt nrow inmat rtrn lt list class rtrn lt ut rtrn mat lt vector length sumltoi nr rtrn ix lt sumltoi 0 nr 1 1 toro un len A ixi lt rtrn ix i copy the i th column of inmat to mat rtrnSmat ixi ixi i 1 lt inmat 1 i i return rtrn returns 1 i sumltoi lt function i return ix i 1 2 Much of the R library still uses the S3 approach but in the next section we will describe the newer system S4 16 3 2 New Style Classes Here one creates the class by calling setClass Continuing our employee example we could write gt setClass employee representation name Character salary numeric union logical we 1 employee Now let s create an instance of this class for Joe using new gt joe lt new employee name Joe salary 55000 union T gt joe An object of class employee 63 un lot name 1 Joe n lot salary 1 55000 un lot union 1 TRUE Note that the member variables are called slots We reference them via the symbol e g v joe salary LI 55000 The slot functi
105. ther Example Let s plot nonparametric density estimates these are basically smoothed histograms for Exams 1 and 2 from our exams file in Section 8 1 in the same graph We use the function density to generate the estimates Here are the commands we issue dl density testscores Examl from 0 to 100 d2 density testscoresSExam2 from 0 to 100 plot d2 main xlab lines d1 Here s what we did First we computed nonparametric density estimates from the two variables saving them in objects d1 and d2 for later use We then called plot to draw the curve for Exam2 The internal structure of d2 contains vectors of X and Y coordinates needed by plot to draw the figure We then called lines to add Exam1 s curve to the graph Note that we asked R to have blank labels for the figure as a whole and for the X axis otherwise R would have gotten such labels from d2 which would have been specific to Exam 2 The call to plot both initiates the plot and draws the first curve Without specifying type I only the points would have been plotted The call to lines then adds the second curve You can use the lty parameter in plot to specify the type of line e g solid dashed etc Type gt help par to see the various types and their codes 23 6 Adding Points the points Function The points function adds a set of x y points with labels for each to the currently displayed graph For instance in our first
106. through MPI You may prefer to use MPI for this as it provides more flexibility since one s code could include calls to both snow functions and MPI i e Rmpi functions However you may not want to bother with MPI if snow itself is enough In the examples here I used SOCK on machines named pc48 and pc49 setting up the cluster this way gt cls lt makeCluster type SOCK c pc48 pc49 For MPI or PVM one specifies the number of nodes to create rather than specifying the nodes themselves Note that the above R code sets up worker nodes at the machines named pc48 and pc49 these are in addition to the master node which is the machine on which that R code is executed There are various other optional arguments One you may find useful is outfile which records the result of the call in the file outfile This can be helpful if the call fails 88 32 2 3 Overview of Available Functions Let s look at a simple example of multiplication of a vector by a matrix We set up a test matrix gt a lt matrix c 1 2 3 4 5 6 7 8 9 10 11 12 nrow 6 oa 1 2 1 1 1 7 2 2 8 3 3 9 4 4 10 5 5 LI 6 6 12 We will multiply the vector 1 1 T meaning transpose by our matrix a by defining a dot product func tion gt dot lt function x y return x Sy Let s test it using the ordinary applyQ gt apply a 1 dot c 1 1 1 8 10 12 14 16 18 To review your R note that this applies t
107. tistic function to dolm lt function fulldata i bootdata lt fulldatal i lmout lt lm bootdata 1 bootdata 2 return lmout coef I ve put in some extra steps for clarity Our call to boot could then be for instance gt boot d dolm R 500 39 To Learn More There is a plethora of resources one can drawn upon to learn more about R 39 1 R s Internal Help Facilities 39 1 1 The help and example Functions For online help invoke help For example to get information on the seq function type gt help seq or better gt seq Each of the help entries comes with examples One really nice feature is that the example function will actually run thus examples for you For instance seq gt example seq seq gt seq 0 1 length 11 1 0 0 O42 0 2 0 3 0 4 0 5 0 56 0 7 0 8 0 9 1 0 seq gt seq rnorm 20 1 1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 20 100 seq gt seq 1 9 by 2 match 2 13579 seq gt seq 1 9 by pi stay below 1 1 000000 4 141593 7 283185 seq gt seq 1 6 by 3 1 1 4 Imagine how useful this is for graphics To get a quick and very nice example the reader is urged to run the following RIGHT NOW gt example persp 39 1 2 If You Don t Know Quite What You re Looking for You can use the function help search to do a Google style search through R s documentation in order to determine which function will pla
108. ulation code including bootstrapping you need to make sure that the random number streams at each cluster node are independent Indeed just think of what would happen if you just take the default random number seed you ll get identical results at all the nodes which certainly would defeat the purpose of parallel operation The careful way to do this is to install the R package rlecuyer Then before running a simulation call clusterSetupRNG which in its simplest form consists simply of 91 clusterSetupRNG cl for the cluster cl 32 2 6 Example Here we estimate the prediction error rate using leaving one out cross validation in logistic regression working on the cluster cls find prediction error rate for the data matrix dm with the response variable having index resp and the predictors having indices prdids prerr lt function cls dm resp prdids set up an artificial matrix for parApply nr lt nrow dm loopmat lt matrix 1l nr nrow nr parcel out the rows of loopmat to the various members of the cluster cls for each row they will apply delone with arguments being that row dm resp and prdids the return vector consists of 1s and Os 1 meaning that our prediction was wrong errs lt parApply cls loopmat 1 delone dm resp prdids return sum errs nr temporarily delete row delrow from the data matrix dm with the response variable having index resp and the predictors having indice
109. ut it clearly has some powerful features for those who wish to put in a bit of time to learn the package As described in the R FAQ ESS offers R users R support contains code for editing R source code syntactic indentation and highlighting of source code partial evaluations of code loading and error checking of code and source code re vision maintenance and documentation syntactic indentation and highlighting of source code sending examples to running ESS process and previewing interacting with an inferior R pro cess from within Emacs command line editing searchable command history command line completion of R object and file names quick access to object and search lists transcript record ing and an interface to the help system and transcript manipulation recording and saving transcript files manipulating and editing saved transcripts and re evaluating commands from transcript files 34 2 GUIs for R As seen above one submits commands to R via text rather than mouse clicks in a Graphical User Interface GUD If you can t live without GUIs you should consider using one of the free GUIs that have been de veloped for R e g R Commander http socserv mcmaster ca jfox Misc Remdr JGR http stats math uni augsburg de JGR or the Eclipse plug in StatEt http 3gr markushelbig org JGR html 35 Inference on Simple Means and Proportions The function t test provides Student t confidence intervals and hypothesis
110. v off 99 99 The paste function concatenates the string q with the string form of i For example when i 2 the variable fname will be q 2 But that wouldn t quite work as it would give me filenames like q 2 pdf On Linux systems filenames with embedded spaces create headaches One solution would be to use the sep argument for Gin 1 5 fname lt paste q i pdf sep pdf fname hist rnorm 100 sd i dev off Here we used an empty string for the separator Or we could use a function borrowed from C for 1 tn 12 5 fname lt sprintf q td pdf 1i pdf fname hist rnorm 100 sd i dev off Since even many C programmers are unaware of the sprintf function some explanation is needed This function works just like printf except that it prints to a string not to the screen Here we are printing to the string fname What are we printing The function says to first print q then print the character version of i then print pdf When i 2 for instance we print z2 pdf to fname For floating point quantities note also the difference between f and g formats gt sprintf abc sfdef 1 5 1 abc1 500000def gt sprintf abcsgdef 1 5 1 abc1 5def 21 1 2 Example of grep Note that grep searches for a given string in a vector of strings returning the indices of the strings in which the pattern is found That makes it perfec
111. w Quite What You re Looking for 39 2 Help on the Web ee 39 2 1 General Introductions 00 000 a A A EN A dad eta cada oe ota aba E aaa ca bend laci n 93 95 95 95 95 95 96 97 97 98 98 98 98 99 99 99 A Installing Updating R AT Installation i ooo ah o e is ae ls Sb is de dia dle ido Ge dl a AZ Updating otr it NE A A dE A a Prerequisites The only real prerequisite is that you have some programming experience you need not be an expert pro grammer though experts should find the material suitable for their level too Occasionally there will be some remarks aimed at professional programmers say about object oriented programming or Python but these remarks will not make the treatment inaccessible to those having only a moderate background in programming 10 1 What Is R R is a scripting language for statistical data manipulation and analysis It was inspired by and is mostly compatible with the statistical language S developed by AT amp T The name S obviously standing for statis tics was an allusion to another programming language developed at AT amp T with a one letter name C S later was sold to a small firm which added a GUI interface and named the result S Plus R has become more popular than S S Plus both because it s free and because more people are contributing to 1t R is sometimes called GNU S 2 Why Use R for Your Statistical Work
112. we use to write comments gt y print out y IT 2333333 These of course are especially useful when writing programs but they are useful for interactive use too since R does record your commands see Section 28 The comments then help you remember what you were doing when you later read that record As the last example in this quick introduction to R let s work with one of R s internal datasets which it uses for demos You can get a list of these datasets by typing gt datasets One of the datasets is Nile containing data on the flow of the Nile River Let s again find the mean and standard deviation gt mean Nile 1 919 35 gt sd Nile 1 169 2275 14 Histogram of Nile 25 20 15 Frequency 10 T 400 600 800 1000 1200 1400 Nile Figure 1 Nile data and also plot a histogram of the data gt hist Nile A window pops up with the histogram in it as seen in Figure I This one is bare bones simple but R has all kinds of bells and whistles you can use optionally For instance you can change the number of bins by specifying the breaks variable hist z breaks 12 would draw a histogram of the data z with 12 bins You can make nicer labels etc When you become more familiar with R you ll be able to construct complex color graphics of striking beauty Well that s the end of this first 5 minute introduction We leave by cal
113. within a function has the same name as a global Then it will be treated as local except that its initial value will be that of the global Subsequent assignment to it within the function will ordinarily see exception in Section 12 8 not change the value of the global For example gt u 1 1 y 1 E function x y lt u y lt y E3 u lt x return x y u v 2 or object y not found 12 7 Function Arguments Don t Change Yet another influence of the functional programming philosophy is that functions do not change their argu ments i e there are no side effects unless the result is re assigned to the argument Consider for instance this gt x lt 0 4 1 3 gt y lt sort x gt y 49 The point is that x didn t change Again if you want the value of an argument to change the best way to accomplish this is to reassign the return value of the function to the argument 12 8 Writing to Globals Using the Superassignment Operator If you do want to write to global variables or more precisely to variables one level higher than the current scope you can use the superassignment operator gt gt For example gt two lt function u u lt lt 2xu y lt lt 2xy E Zz lt 2xz gt x lt 1 gt y lt 2 A AS gt two x gt x Ea a A Y 1 4 gt oz 1 73 12 9 Arithmetic and Boolean Operators and Values y addition y subtraction y multiplic
114. y a desired role For instance in Section 29 above we needed a function to generate random variates from multivariate normal distributions To determine what function if any does this we could type gt help search multivariate normal getting a response which contains this excerpt mvrnorm MASS Simulate from a Multivariate Normal Distribution This tells us that the function mvrnorm will do the job and it is in the package MASS You can also go to the place in your R directory tree where the base or other package is stored For Linux for instance that is likely usr lib R library base or some similar location The file CONTENTS in that directory gives brief descriptions of each entity 39 2 Help on the Web 39 2 1 General Introductions ttp cran r project org doc manuals R intro html is the R Project s own in ttp personality project org r r guide html by Prof Wm Revelle of the Dept of Psychology of Northwestern University especially good for material on multivariate statis tics and structural equation modeling elhttp www math csi cuny edu Statistics R simpleR index html arough form of John Verzani s book simpleR nice coverage of various statistical procedures 101 e http zoonek2 free fr UNIX 48_R all html A large general reference by Vincent Zoonekynd really excellent with as wide a statistics coverage as I ve seen anywhere ttp wwwmaths anu edu au johnm r usingR p
115. your source code gives you the ability to easily set breakpoints etc It requires another package mvbutils and the Tcl Tk scripting and graphics system The latter is commonly included in Linux distributions and is freely downloadable for all the major platforms It suffers from a less than perfect display but is definitely worthwhile much better than R s built in debugging tools 26 4 1 Installation Choose an installation directory say MyR Then install mvbutils and debug gt install packages mvbutils MyR gt install packages debug MyR For R version 2 5 0 I found that a bug in R caused the debug package to fail I then installed the patched version of 2 5 0 and debug worked fine On one machine I encountered a Tcl Tk problem when I tried to load debug I fixed that I was on a Linux system by setting the environment variable in my case by typing setenv TCL_LIBRARY usr share tcl8 4 26 4 2 Path Issues Each time you wish to use debug load it by executing gt libPaths MyR gt library debug Or place these in an R startup file say Rprofile in the directory in which you want these commands to run automatically Or create a file Renviron in your home directory consisting of the line R_LIBS MyR 26 4 3 Usage Now you are ready to debug Here are the main points e Breakpoints are first set at the function level Say you have a function f at which you wish to break Then type

R for Programmers - matloff - University of California, Davis

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