TROFSS User's Guide
Contents
1. 150 0 000 0 442 0 558 0 000 10 AI Quality 0 703 0 611 Rel Import AI 0 513 0 150 0 000 0 536 0 464 0 000 11 AI Quality 0 678 0 635 Rel Import AI 0 477 0 150 0 000 0 546 0 403 0 052 12 AI Quality 0 651 0 658 Rel Import AI 0 456 0 150 0 000 0 536 0 347 0 116 13 AI Quality 0 623 0 680 Rel Import AI 0 419 0 150 0 000 0 526 0 283 0 191 14 AI Quality 0 592 0 699 Rel Import AI 0 329 0 150 0 000 0 512 0 199 0 289 15 AI Quality 0 554 0 713 Rel Import AI 0 262 0 150 0 021 0 493 0 162 0 323 16 AI Quality 0 515 0 727 Rel Import AI 0 253 0 150 0 053 0 474 0 157 0 316 17 AI Quality 0 476 0 740 Rel Import AI 0 241 TROFSS program v 2 10 12 2006 8 0 150 0 087 0 454 0 151 0 308 18 AI Quality 0 435 0 752 Rel Import AI 0 222 0 150 0 123 0 432 0 146 0 300 19 AI Quality 0 393 0 763 Rel Import AI 0 192 0 150 0 164 0 407 0 139 0 290 20 AI Quality 0 348 0 772 Rel Import AI 0 136 0 150 0 213 0 378 0 131 0 279 21 AI Quality 0 296 0 777 Rel Import AI 0 000 0 150 0 277 0 339 0 120 0 264 CPU TIME IN SECONDS 2 88 7 Description of Output At present the output provides input for plots of the solution using the R package 8 Acknowledgement When the user reports results obtained by the present program due ref erence should be made to De Corte 2006 and De Corte Lievens amp Sackett 2007 11 References De Corte W 2006 TROFSS User s Guide De Corte W Lievens F amp Sackett P 2007 Combining predictor2. D ssel gt command prompt Now you can execute the program by typing trofss lt minput gt moutput where minput is the name of the input file and moutput is the name of the output file At the end of the execution the PC will return the command prompt D ssel gt You can then inspect the output by editing the output file with either Notepad Wordpad or any other simple editor program 6 Sample Output Program execution starts on 4 9 2006 at 16 59 3 THE PRESENT CODE IS TO BE USED FOR RESEARCH PURPOSES ONLY THE PROGRAM AUTOMATICALLY ABORTS AFTER SOME TIME AND A NEW VERSION OF THE CODE MUST BE DOWNLOADED 4 4 4 44 4 44 TROFSS tttttttttttt Computation of the PARETO SURFACE in SINGLE STAGE PROBATIONARY or NON PROBATIONARY selection decision when the applicant group is a MIXTURE OF MINORITY AND MAJORITY APPLICANTS such that both the objectives of selection quality and adverse impact are of importance Selection quality can refer to TROFSS program v 2 10 12 2006 6 either the globally standardized expected criterion performance or the utility per selected applicant The method of normal boundary intersection is used to determine Pareto points that are evenly spread on the solution surface and for each point the corresponding values of the selection rate in case of a probationary selection decision the global criterion cutoff value and the predictor weights are computed Predictor weights obey a varian
3. for probationary selections e 7 and following For each applicant group K with K 1 2 DIFC K 1 with 1 NC DIFP K I with 1 NPRED The element DIFC K I indicates the effect size value of criterion dimension for applicant group K whereas DIFP K corresponds to the effect size value of predictor for the same candidate group The elements of the first rows of DIFC and DIFP are all zero because the first applicant group is the reference group The elements of the second row pertain to the majority applicant group that is used to determine the adverse impact ratios e 8 WC I with 1 NC Vector of length NC with the pre assigned weights of the criterion dimensions e 9 and following CC I J with both and J 1 NC NC x NC matrix of criterion dimension intercorrelations Only the strict upper triangle of the correla tionmatrix So if NC 1 then CC 1 1 must not be specified e 10 and following PC I J with both and J 1 NPRED Matrix of predictor correlations Only the strict upper triangle of the correlationmatrix e 11 and following PV I J with 1 NC and J 1 NPRED matrix of predictor validities Thus PV I J indicates the validity of predictor J with respect to criterion dimension I e 12 OPTIONAL only if IUTIL 1 The values of NAPPL RETRAN SIY XMUY TFACC TROFSS program v 2 10 12 2006 4 NAPPL Total number of applicants RETRAN RETRAN indicates
4. less or equal to 10 IUTIL If IUTIL 0 the globally standardized expected criterion score of the selected applicants is used as the selection quality criterion If IUTIL 1 selection quality corresponds to the selection utility per selected applicant To obtain the utility in monetary value the utility must be multiplied by the value of TFACC see below If IUTIL 1 then the validity of the composite predictor represents the selection quality objective IBN the number of points used to approximate the Pareto surface Values between 20 and 30 are usually adequate The program always generated a total of IBN 1 points of the Pareto surface If IBN 1 only the two TROFSS program v 2 10 12 2006 3 extreme points of the Pareto surface are determined IBN 0 may only be used in combination with IUTIL 1 e 3 XSEL VALLOW XSEL Required proportion of successfully selected applicants VALLOW Predictor weights must at least be equal to the value of VALLOW Normally VALLOW 0 e 4 OPTIONAL only if IFIB is different from zero The value of XOB XOB indicates the lower bound on the global selection ratio for probationary selections e 5 OPTIONAL only if IFIB is different from zero The value XUP XUP indicates the upper bound on the global selection ratio for probationary selections e 6 and following OPTIONAL only if IFIP is different from zero The value of XOB XOB indicates the global selection ratio
5. sizes selection predictors First group is base Group 1 0 000 0 000 0 000 0 000 Group 2 1 000 0 230 0 090 0 330 TROFSS program v 2 10 12 2006 7 Effect sizes criterion dimensions First group is base Group 1 0 000 0 000 Group 2 0 210 0 130 Fixed cutoff value overall criterion dimension is 7 500 Predictor weights are optimized Computations start from random initialized values DETAILS SELECTED PARETO OPTIMAL TRADE OFFS First line number of Pareto optimal trade off Value AI and Quality and Relative Importance AI Objective Second line Selection ratio and Unit Sum Predictor Weights NOTE In case of probationary selection the AI value corresponds to the adverse impact after the probationary period whereas the selection ratio is before the probationary period 1 AI Quality 0 868 0 350 Rel Import AI 1 000 0 150 0 000 0 000 1 000 0 000 2 AI Quality 0 850 0 380 Rel Import AI 0 628 0 150 0 000 0 056 0 944 0 000 3 AI Quality 0 833 0 410 Rel Import AI 0 627 0 150 0 000 0 110 0 890 0 000 4 AI Quality 0 815 0 439 Rel Import AI 0 626 0 150 0 000 0 162 0 838 0 000 5 AI Quality 0 798 0 468 Rel Import AI 0 624 0 150 0 000 0 213 0 787 0 000 6 AI Quality 0 780 0 498 Rel Import AI 0 620 0 150 0 000 0 264 0 736 0 000 7 AI Quality 0 762 0 527 Rel Import AI 0 614 0 150 0 000 0 318 0 682 0 000 8 AI Quality 0 743 0 556 Rel Import AI 0 604 0 150 0 000 0 375 0 625 0 000 9 AI Quality 0 724 0 584 Rel Import AI 0 583 0
6. TROFSS program v 2 10 12 2006 1 TROFSS User s Guide j 1 Description TROFSS is a FORTRAN77 program that determines a point wise approximation to the PARETO SURFACE in SINGLE STAGE PROBATIONARY or NON PROBATI ONARY selection decision when the applicant group is a MIXTURE OF MINORITY AND MAJORITY APPLICANTS such that both the objectives of selection quality and adverse impact are of importance Selection quality can refer to either the predictor composite validity the globally standardized expected criterion performance or the utility per selected applicant The method of normal boundary intersection is used to determine Pareto points that are evenly spread on the solution surface and for each point the corresponding values of the selection rate in case of a probationary selection decision the global criterion cutoff value and the predictor weights are computed At present the program is limited to problems with no more than 10 selection predic tors a single majority and a single minority group and no more than 3 criterion behaviour dimensions The effect sizes are defined with respect to the minority applicant group i e the first group such that this group has all effect size values equal to zero The computation of the adverse impact ratio assumes that the last subgroup is the majority group The present program computes solutions over the entire set of feasible predictor weights Predictor weights are feasible if a at lea
7. ce constraint At present the program is limited to problems with no more than 10 selection predictors a single majority and a single minority group and no more than 5 criterion behaviour dimensions Program written by Wilfried De Corte Ghent University Belgium The program uses routines from the Slatec library see http www geocities com Athens Olympus 5564 a couple of algorithms from StatLib see http lib stat cmu edu apstat and some adapted code from Genz to evaluate multivariate normal probabilities cf http www math wsu edu math faculty genz homepage PROBLEM SPECIFICATION Problem relates to a non probationary selection Quality Objective is Expected Criterion Score Number of criterion dimensions 2 Number of applicant groups 2 Proportional representation applicant groups 0 250 0 750 Overall proportion of successful selectees 0 150 Number of available predictors 4 Weights used to combine the individual criterion dimensions to the composite criterion are 3 000 1 000 Correlation matrix of the criterion dimensions Criterion 1 1 000 0 170 Criterion 2 0 170 1 000 Correlation matrix of the predictors Predictor 1 1 000 0 240 0 000 0 190 Predictor 2 0 240 1 000 0 120 0 160 Predictor 3 0 000 0 120 1 000 0 510 Predictor 4 0 190 0 160 0 510 1 000 Validities of the predictors columns with respect to the criterion dimensions rows Criterion 1 0 300 0 300 0 180 0 280 Criterion 2 0 160 0 260 0 200 0 250 Effect
8. ll Files in the Save as type box When saving in Wordpad use the Text Document MS DOS Format option in the Save as type box and be aware that Wordpad has the nasty habit of adding the exten sion txt to the file name that you specify Thus with Wordpad if you specify the name of the input file as MINPUT the file will in fact be saved as MINPUT TXT and this is the name that you have to use in the command to run the present programs Here is a sample input file for the trofss program TROFSS program v 2 10 12 2006 5 2 1 0 0 0 25 0 75 4 0O 20 0 15 0 0 00 0 O O O O 0 210 0 130 1 000 0 230 0 090 0 330 3 000 1 000 0 170 0 240 0 000 0 190 0 120 0 160 0 510 0 300 0 300 0 180 0 280 0 160 0 260 0 200 0 250 5 Running the Program Suppose you copied the executable source of the program to the d ssel directory on your machine In that case the input file must also be saved in the d ssel directory Next to run the program you have to open an MS DOS Command window The way to do this varies from one operating system i e Windows 95 98 NT a s o to the other and you should use your local HELP button when in doubt about this feature In the MS DOS Command window you type d followed by RETURN or ENTER and your computer will return the D gt command prompt Next you type cd ssel after the D gt command prompt again followed by RETURN or ENTER and your computer will respond with the
9. s to achieve optimal trade offs between selection quality and adverse impact Journal of Applied Psychology accepted Fong K W Jefferson T H Suyehiro amp Walton L 1993 Guide to the SLATEC common mathematical library http www netlib org slatec
10. st one weight is positive and b all weights are non negative and at least equal to a given non negative value The FORTRAN 77 program to implement the solution uses a routines from the SLATEC FORTRAN77 library Fong et al 1993 b an extension of the algorithm presented by Genz 2001 to compute multivariate probabilities c the algorithm AS249 from the STATLIB software library and d bits of optimization code To implement the program the user must specify a number of input parameter values These are detailed below Among other things the setting of the problem parameters provides the opportunity to address probationary or non probationary selections to con strain the minimum and maximum hiring rate in the probationary period and to choose between either the composite validity the globally standardized expected criterion score of the selected candidates or the selection utility as the selection quality criterion To derive the expected utility the return of the corresponding random selection must be computed first This can be done using the program with certain specific values for some of the input parameters see below 2 Assumptional Basis The calculations are based on the assumption that the predictor and eventually the criterion dimensions have a joint multivariate normal distribution with the same vari TROFSS program v 2 10 12 2006 2 ance covariance matrix but different mean vectors in the different applicant pop
11. the the payoff of the corresponding random selection To obtain the value of RETRAN run the program with values of 1 0 and 0 for IUTIL IBN and RETRAN respectively to compute the payoff of a corresponding selection with a single non valid i e predictor validity is zero for all criteria predictor with zero effect size SIY Money valued standard deviation of the criterion behaviour in the entire applicant group for 1 time period XMUY Money valued mean criterion behaviour in the entire applicant pop ulation for 1 time period TFACC equate TFACC to XMUY e 13 OPTIONAL only if IUTIL 1 The values of RYR TS RYR Correlation between rated aggregate or composite criterion and money valued criterion behaviour TS Number of time periods that a successfully selected employee will remain on the job e 14 OPTIONAL only if IUTIL 1 The values of TRCO SECO TRCO Training costs per selected applicant SECO Separation costs per unsuccessfully selected applicant e 15 OPTIONAL only if IUTIL 1 The values of TECO I with 1 NPRED Vector of length NPRED with the predictor costs per applicant 4 Sample Input File Important in preparing the input file use a simple text editor such as Notepad Wordpad or any other standard ASCII producing editor DO NOT USE TEXT PRO CESSING PROGRAMS SUCH AS MS WORD or WORDPERFECT Also when saving the input file in Notepad use the option A
12. ulations Given this assumption it is without further restrictions understood that the joint dis tribution of the predictors and the criterion dimensions is standard multivariate normal in the reference applicant population i e the minority applicant population 3 Input Observe that all input is in free format Variables or vectores that have a name commencing with the letters I J K L M N get INTEGER values All other variables vectors and matrices get FLOATING POINT values See the example input file e 1 NC IFIXCR IFIB IFIP VMAMI I 1 NGR NC number of criterion dimensions NC lt 3 IFIXCR The value of the composite criterion behaviour cutoff is estimated o 2 IFIXCR 0 or given IFIXCR 1 For probationary selection set IFIXCR 0 For non probationary selection set IFIXCR 1 IFIB Set IFIB 0 in case of a non probationary selection Set IFIB 1 in case of a probationary selection for which the initial hiring rate is bounded from below and above see below IFIP Set IFIP 0 in case of a non probationary selection Set IFIP 1 in case of a probationary selection for which the initial hiring rate is fixed at a given value VMAMI I 1 2 VMAMI I indicates the proportion of the total applicant group that comes from candidate population Observe that VMAMI 1 VMAMI 2 must be equal to 1 NPRED IUTIL IBN NPRED the number of selection predictors NPRED
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