COPOPS User's Guide
Contents
1. 0 183 0 277 3 0 273 4 0 176 9 99 0 577 0 178 0 304 3 0 257 4 0 171 9 99 0 583 0 173 0 334 3 0 237 4 0 166 9 99 0 589 0 168 0 366 3 0 214 4 0 158 9 99 0 593 0 162 0 404 3 0 183 4 0 148 9 97 0 595 0 158 0 265 3 0 327 4 0 136 7 99 0 595 0 154 0 451 3 0 138 4 0 132 9 118 0 598 0 154 0 251 4 0 351 7 0 210 9 97 0 602 0 153 0 274 3 0 309 4 0 157 7 97 0 608 0 147 0 283 3 0 287 4 0 180 7 97 0 614 0 141 0 292 3 0 260 4 0 205 7 COPOPS program 96 0 616 97 0 619 116 0 621 96 0 625 116 0 630 96 0 633 96 0 642 96 0 649 96 0 657 116 0 657 96 0 663 116 0 665 96 0 666 116 0 669 27 08 2010 139 135 133 132 125 125 118 110 103 102 094 092 083 081 O COCCO CC CC ooo O COCO CSC Co 0 oo 311 301 385 310 379 307 303 296 287 343 273 318 247 274 3 3 4 3 4 3 3 3 3 4 3 4 3 4 ooooooooo00o00000 347 223 273 343 301 338 332 322 309 399 289 442 255 498 CONTRIBUTION SUBSETS TO THE PARETO FRONT BASED B SPLINE APPROXIMATION OF THE SUBSET FRONTS SUBSET 116 Diversity 0 0810 0 0897 0 0984 Quality 0 6690 0 6662 0 6604 SUBSET Diversity 0 1008 0 1158 0 1308 Quality 0 6583 0 6439 0 6262 SUBSET Diversity 0 1375 0 1462 0 1548 Quality 0 6177 0 6097 0 5994 SUBSET Diversity 0 0908 0995 9 0820 6688 662. 0 4070 0 4219 0 4235 0 4250 0 4266 0 4281 0 4296 0 4311 0 4326 0 4341 0 4356 0 4370 0 4385 0 4399 0 4413 0 4426 0 4439 0 4452 0 4463 0 4474 0 4483 0 4488 0 4496 0 4530 0 4561 0 4626 0 4644 0 4674 0 4744 0 4788 0 4824 0 4903 0 4981 0 5059 0 5136 0 5212 0 5287 0 5362 0 5435 0 5507 0 5577 0 5646 0 5712 0 5775 0 5833 0 5886 0 5929 0 5948 0 5951 0 5984 0 6018 0 6084 0 6144 0 6158 0 6194 0 6208 0 6246 0 6305 0 6332 0 6415 0 6494 0 6567 0 6574 0 6630 0 6648 0 6664 0 6690 SORTED PARETO OPTIMAL DIVERSITY FOR PLOT USING R 0 2562 0 2536 0 2533 0 2530 0 2527 0 2524 0 2521 0 2518 0 2515 0 2512 0 2509 0 2506 0 2503 0 2499 0 2496 0 2493 0 2489 0 2486 0 2482 0 2478 0 2473 0 2468 0 2404 0 2396 0 2394 0 2383 0 2379 0 2360 0 2354 0 2318 0 2317 0 2279 0 2240 0 2202 0 2163 0 2123 0 2083 0 2043 0 2001 0 1959 0 1916 0 1872 0 1827 0 1779 0 1729 0 1676 0 1616 0 1582 0 1544 0 1539 0 1529 0 1474 0 1415 0 1389 0 1349 0 1329 0 1320 0 1255 0 1251 0 1179 0 1105 0 1026 0 1016 0 0939 0 0925 0 0833 0 0810 SUMMARY TABLE SELECTED PARETO OPTIMAL SYSTEMS AND TRADE OFFS Subset Quality Diversity Predictor weights 4 0 407 0 256 0 407 4 35 0 422 0 254 0 404 4 0 040 9 35 0 423 0 253 0 403 4 0 045 9 COPOPS program 27 08 2010 35 0 425 0 253 0 402 4 0 050 9 35 0 427 0 253 0 400 4 0 056 9 35 0 428 0 252 0 399 4 0 061 9 35 0 430
3. 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 copops program KEY 1 9 0 20 0 10 0 30 100 0 20 0 0 1 008 0 725 0 684 0 162 0 992 1 213 0 797 0 602 0 178 0 598 0 780 0 467 0 596 0 593 0 649 0 430 0 272 0 629 0 694 0 620 0 432 0 516 0 532 0 373 0 475 0 561 0 506 0 622 0 426 0 337 0 413 0 090 0 335 0 456 0 415 0 725 0 642 0 574 0 192 0 757 0 348 0 029 0 398 0 169 0 294 522 0 545 0 561 0 407 0 545 0 529 0 525 0 442 0 341 0 10 20 10 10 15 15 20 25 3 1 ND O 1 1 1 1 1 1 1 5 Running the Program Suppose you copied the executable code of the program to the C ssel directory on your machine In that case the input file must also be saved in the C 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 XP Vista Windows 7 a s o to the other and you should use your local HELP button when in doubt about this feature If the MS DOS Command window does not automatically open with the prompt C gt then you type in the MS DOS Command window C followed by RETURN or COPOP
4. 0 252 0 398 4 0 067 9 35 0 431 0 252 0 396 4 0 072 9 35 0 433 0 252 0 394 4 0 078 9 35 0 434 0 251 0 392 4 0 085 9 35 0 436 0 251 0 390 4 0 091 9 35 0 437 0 251 0 387 4 0 098 9 35 0 438 0 250 0 384 4 0 105 9 35 0 440 0 250 0 381 4 0 113 9 35 0 441 0 250 0 377 4 0 121 9 35 0 443 0 249 0 373 4 0 129 9 35 0 444 0 249 0 368 4 0 138 9 35 0 445 0 249 0 363 4 0 148 9 35 0 446 0 248 0 356 4 0 159 9 35 0 447 0 248 0 348 4 0 172 9 35 0 448 0 247 0 337 4 0 187 9 35 0 449 0 247 0 321 4 0 208 9 119 0 450 0 240 0 398 4 0 040 8 0 066 9 99 0 453 0 240 0 041 3 0 413 4 0 041 9 119 0 456 0 239 0 386 4 0 039 8 0 099 9 119 0 463 0 238 0 361 4 0 036 8 0 150 9 99 0 464 0 238 0 040 3 0 395 4 0 096 9 119 0 467 0 236 0 334 4 0 041 8 0 189 9 99 0 474 0 235 0 039 3 0 348 4 0 181 9 118 0 479 0 232 0 351 4 0 040 7 0 192 9 99 0 482 0 232 0 052 3 0 347 4 0 182 9 99 0 490 0 228 0 066 3 0 346 4 0 184 9 99 0 498 0 224 0 080 3 0 344 4 0 185 9 99 0 506 0 220 0 095 3 0 342 4 0 186 9 99 0 514 0 216 0 111 3 0 339 4 0 186 9 99 0 521 0 212 0 128 3 0 334 4 0 186 9 99 0 529 0 208 0 146 3 0 329 4 0 186 9 99 0 536 0 204 0 165 3 0 323 4 0 186 9 99 0 543 0 200 0 185 3 0 316 4 0 185 9 99 0 551 0 196 0 206 3 0 308 4 0 184 9 99 0 558 0 192 0 228 3 0 298 4 0 182 9 99 0 565 0 187 0 251 3 0 286 4 0 179 9 99 0 571
5. 380 Quality 0 5941 0 5924 0 5893 0 5856 0 5813 0 5764 0 5710 0 5651 0 5589 0 5525 0 5457 0 5387 0 5315 0 5240 0 5163 0 5085 0 5005 0 4924 0 4839 0 4758 0 4641 e e SUBSET 119 Diversitv 0 2381 0 2383 0 2384 0 2386 0 2388 0 2390 0 2392 0 2394 0 2395 0 2397 0 2399 0 2401 0 2403 0 2404 0 2405 Qualitv 0 4638 0 4630 0 4625 0 4615 0 4604 0 4591 0 4579 0 4566 0 4559 0 4546 0 4533 0 4520 0 4507 0 4496 0 4494 SUBSET 35 Diversity 0 2468 0 2473 0 2477 0 2481 0 2485 0 2489 0 2493 0 2496 0 2500 0 2504 0 2508 0 2512 0 2515 0 2519 0 2523 0 2527 0 2530 0 2534 0 2536 Quality 0 4488 0 4484 0 4477 0 4467 0 4455 0 4441 0 4427 0 4413 0 4398 0 4381 0 4363 0 4344 0 4326 0 4309 0 4289 0 4268 0 4250 0 4231 0 4219 SUBSET 4 Diversity 0 2562 0 2562 Quality 0 4070 0 4070 COVERAGE GLOBAL PARETO FRONT BY THE SUBSETS 99 0 4609 96 0 2630 116 0 1694 97 0 1358 35 0 0388 118 0 0222 119 0 0217 34 0 0108 CPU TIME IN SECONDS 34 41 7 Description of Output e COVERAGE GLOBAL PARETO FRONT BY THE SUBSETS proportion of the global Pareto front i e the front over all feasible predictor subsets captured or COPOPS program 27 08 2010 9 approximated very nearly by the predictor subsets Only subsets that contribute at least 001 are mentioned 8 Acknowledgement When the user reports results obtained by the present program due refer ence s
6. 57 6595 1026 1177 1326 6567 6418 6240 1386 1473 1559 6169 6085 5979 9 0831 O 0919 1006 0 e 6685 O 6651 6585 O o 1045 0 1195 1345 0 e 6551 O 6398 6215 0 e 1397 0 1483 1570 0 e 6160 0 6073 5964 0 e 0842 0929 1007 6682 6646 6584 1064 1214 1364 6534 6376 6191 1408 1494 1581 6150 6061 5949 0853 0940 6679 6638 1083 1233 1374 6516 6353 6178 1418 1505 1586 6141 6048 5942 4 4 6 4 6 4 4 4 4 6 4 6 4 6 ON 0864 0 0951 0 6675 0 6631 O 1102 0 1251 0 6497 0 6332 0 1429 0 1516 O 6130 0 6034 0 120 236 246 145 247 172 202 235 273 239 319 231 381 213 OOO OOO OOO ORO 000 0875 0962 6671 6622 1120 1270 6479 6309 1440 1527 6119 6020 6 7 9 6 9 6 6 6 6 9 6 9 6 9 0886 0973 6667 6614 1139 1289 6459 6286 1451 1537 6108 6008 COPOPS program 27 08 2010 8 0 1587 0 1627 0 1668 0 1708 0 1748 0 1788 0 1828 0 1869 0 1909 0 1949 0 1989 0 2029 0 2069 0 2109 0 2149 0 2189 0 2229 0 2269 0 2309 0 2349 0 2
7. COPOPS program 27 08 2010 1 COPOPS User s Guide i 1 Description COPOPS is a FORTRAN77 program that implements a decision aid for obtaining Pareto optimal predictor subsets as described in De Corte Sackett and Lievens 2010 The executable code is offered as is without any guarantee whatsoever Executing the code reguires a key that can be obtained by mailing to the first author The present program is limited to the followed conditions a two selection goals b the total number of feasible predictor subsets may not exceed 500 c only one minority group and only one job performance criterion and d the maximum number of computed trade offs per subset is 50 Observe that the program is computationaly very complex Even with the above limitations the execution time may take several minutes of CPU time depending on the floating point performance of the computer 2 Input Note 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 0 KEY e 1 ITY NP IFWE IBN ITY Controls the metric used to translate the selection guality and the se lection diversity goal ITY 0 quality corresponds to expected job performance and diversity refers to the adverse impact ratio ITY 1 quality corresponds to the composite validity and diversity r
8. S program 27 08 2010 4 ENTER and your computer will return the C gt command prompt Next you type cd ssel after the C gt command prompt again followed by RETURN or ENTER and your computer will respond with the C ssel gt command prompt Now you can execute the program by typing copops 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 C 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 The output corresponds to the above input file Only part of the output is printed Other examples of the input and corresponding output files are available at the URL that contains the executable program DATE 26 08 2010 TIME 11 11 46 THE PRESENT CODE IS FOR DEMONSTRATION PURPOSES ONLY 4 4 4 4 4444 COPOPS COMPUTATION of PARETO OPTIMAL PREDICTOR SUBSETS Program written by W De Corte Ghent University Belgium INPUT DATA AND DESCRIPTION SELECTION SITUATION Quality objective refers to the composite validity Diversity objective refers to the minority hiring rate Number of available predictors 9 Number of applicant groups 2 Proportional representation applicant groups First group is the Minority group 0 200 0 800 Overall selection ratio 0 300 Correlation matrix of the predi
9. ctors Predictor 1 1 000 0 598 0 780 0 467 0 596 0 593 0 649 O Predictor 2 0 598 1 000 0 629 0 694 0 620 0 432 0 516 O Predictor 3 0 780 0 629 1 000 0 475 0 561 0 506 0 622 0 Predictor 4 0 467 0 694 0 475 1 000 0 413 0 090 0 335 O Predictor 5 0 596 0 620 0 561 0 413 1 000 0 725 0 642 0 Predictor 6 0 593 0 432 0 506 0 090 0 725 1 000 0 757 0 Predictor 7 0 649 0 516 0 622 0 335 0 642 0 757 1 000 O Predictor 8 0 430 0 532 0 426 0 456 0 574 0 348 0 398 1 Predictor 9 0 272 0 373 0 337 0 415 0 192 0 029 0 169 O Predictor Validities Criterion 1 0 522 0 545 0 561 0 407 0 545 0 529 0 525 O 430 532 426 456 574 348 398 000 294 442 H 272 373 337 415 192 029 169 294 000 341 COPOPS program 27 08 2010 Effect sizes predictors in Minority group 1 008 0 725 0 684 0 162 0 992 1 213 0 797 0 602 0 178 Effect sizes criterion in Minority group 0 000 Predictor weights are optimized Ratio constraint on the within stage predictor weights Max weight Min weight equals 10 0 Total number of feasible predictor subsets is 129 IDENTITY PREDICTOR SUBSETS Subset 1 Predictors Subset Predictors Subset Predictors Subset Predictors Subset Predictors Subset 6 Predictors LINES DELETED Subset 126 Predictors Subset 127 Predictors Subset 128 Predictors Subset 129 Predictors oF W N Oo 01 PP W N NOD 0 0 0 NN O O O SORTED PARETO OPTIMAL GUALITY FOR PLOT USING R
10. efers to the minority selection rate NP total number of predictors NP lt 10 IFWE IFWE controls the weighting of the predictors when forming compos ites If IFWE O then optimal weighting if IFIWE 1 then regression weighting if IFIWE 2 then unit weighting IBN IBN controls the number of Pareto optimal solutions computed for each feasible predictor subset The value of IBN must be between 10 and 50 Recommended value is 20 COPOPS program 27 08 2010 2 e 2 NRWE WMA Only required if IFIXWE 0 NRWE If NRWE 0 then the predictor weighting when forming predictor composites must obey a ratio constraint No such ratio constraint if NRWE cl WMA The ratio between the largest and the smallest predictor weight when forming composites must be between 1 WMA and WMA If NRWE 1 a value for WMA must be specified but the value is ignored e 3 SELR COLIM PMIN CESMIN SELR Selection ratio of the selection COLIM Maximum total predictor costs PMIN proportion of minority applicants in the total applicant group CESMIN Criterion effect size i e mean difference on the performance cri terion between the minority and the majority applicant populations If the mean criterion performance in the minority population is less than the mean performance in the majority population then CESMIN should have a NEGA TIVE value positive otherwise e 4 PESMIN I 1 NP Vector of l
11. ength NP with the effect sizes of the available predictors all effect sizes are for the minority population relative to the majority population e 5 and following NP 2 lines Set of NP 1 lines specifying CP I J with 1 NP 1 and J 1 1 NP the correlation matrix of the NP predictors Note that the strict upper diagonal part of the correlation matrix must be specified see example e 6 PVAL I 1 NP Vector of length NP with the validities of the available predictors e 7 PCOST I 1 NP Vector of length NP with the predictor cost PER APPLICANT of the available predictors e 3 MIP MAP MIP the minimum number of predictors that must be used in the composite and MAP the maximum number of predictors that can be used in the composite COPOPS program 27 08 2010 3 e 9 ISP I 1 NP Vector of length NP with values of 0 1 or 2 ISP I 0 indicates that predictor can not be used a value equal to 2 indicates that the predictor must be used a code egual to 1 indicates that the predictor can be used 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 All Files in the Save as type box When saving in Wordpad use the Text Document MS DOS Format option in the
12. hould be made to De Corte 2010 and De Corte Sackett and Lievens 2010 11 References De Corte W 2010 COPOSP User s Guide De Corte W Sackett P amp Lievens F 2010 Selecting predictor subsets considering validity and adverse impact International Journal of Selection and Assessment 18 260 270
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