EQS A STRUCTURAL EQUATION PROGRAM COPYRIGHT BY P M BENTLER MULTIVARIATE SOFTWARE INC VERSION 5 7b C 1985 1998 THIS EQS PROGRAM SIMULATES A DATA SET WITH A SIMPLE ONE FACTOR STRUCTURE 1 TITLE 2 SIMULATION TO SHOW CATEGORIZATION EFFECTS 3 SIMULATION 4 POP MOD 5 SEED 1209496 6 DATA CAT 7 SAVE SEPARATE 8 REPLICATIONS 1 9 SPECIFICATIONS 10 VARIABLES 8 CASES 800 11 METHODS ML 12 MATRIX RAW 13 EQUATIONS 14 V1 0 7 F1 1E1 15 V2 0 7 F1 1E2 16 V3 0 7 F1 1E3 17 V4 0 7 F1 1E4 18 V5 0 7 F1 1E5 19 V6 0 7 F1 1E6 20 V7 0 7 F1 1E7 21 V8 0 7 F1 1E8 22 VARIANCES 23 F1 1 0 24 E1 51 25 E2 51 26 E3 51 27 E4 51 28 E5 51 29 E6 51 30 E7 51 31 E8 51 32 PRINT 33 digit 3 34 linesize 80 35 SIMULATION DEFINITIONS NUMBER OF REPLICATIONS 1 SAMPLE DATA GENERATED FROM MODEL SAMPLE SIZE 800 DATA IS NORMAL YES DATA TO BE CONTAMINATED NO ORIGINAL SEED 1209496 UNIVARIATE CHARACTERISTICS OF SIMULATED DATA F1 E1 E2 E3 E4 E5 E6 E7 E8 IFMT MEAN 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 1 IANALY STAND DEV 1 0000 0 7141 0 7141 0 7141 0 7141 0 7141 0 7141 0 7141 0 7141 0 UNIVARIATE TRANSFORMATION NORMAL DISTRIBUTION NORMAL DISTRIBUTION NORMAL DISTRIBUTION NORMAL DISTRIBUTION NORMAL DISTRIBUTION NORMAL DISTRIBUTION NORMAL DISTRIBUTION NORMAL DISTRIBUTION NORMAL DISTRIBUTION SIMULATION IN REPLICATION 1 SEED IS INPUT DATA FILE NAME IS CAT001 DAT 1209496 SAMPLE STATISTICS BASED ON COMPLETE CASES UNIVARIATE STATISTICS VARIABLE MEAN SKEWNESS G1 KURTOSIS G2 STANDARD DEV V1 0 0205 0 0189 0 3653 1 0024 V2 0 0149 0 0378 0 1046 1 0210 V3 0 0299 0 0794 0 0659 1 0018 VARIABLE MEAN SKEWNESS G1 KURTOSIS G2 STANDARD DEV V6 0 0229 0 0001 0 0585 1 0506 V7 0 0157 0 0617 0 0285 1 0627 V8 0 0218 0 0914 0 0219 1 0136 COVARIANCE MATRIX TO BE ANALYZED BASED ON 800 CASES V1 V2 V3 V4 V5 V6 V7 V8 V V V V V V V V 1 2 3 4 5 6 7 8 V1 1 005 0 510 0 491 0 500 0 512 0 558 0 486 0 471 V6 V7 V8 V V V 6 7 8 V6 1 104 0 584 0 492 V4 0 0118 0 0212 0 1283 1 0205 V5 0 0327 0 0514 0 2243 0 9758 8 VARIABLES SELECTED FROM 8 VARIABLES V2 V3 V4 V5 1 042 0 520 0 542 0 475 0 563 0 531 0 530 1 004 0 508 0 482 0 516 0 520 0 526 1 041 0 499 0 569 0 535 0 478 0 952 0 507 0 483 0 458 V7 V8 1 129 0 499 1 027 GOODNESS OF FIT SUMMARY INDEPENDENCE MODEL CHI SQUARE INDEPENDENCE AIC MODEL AIC 2589 86139 14 10027 2645 861 ON INDEPENDENCE CAIC MODEL CAIC 28 DEGREES OF FREEDOM 2430 69226 127 79251 CHI SQUARE 25 900 BASED ON 20 DEGREES OF FREEDOM PROBABILITY VALUE FOR THE CHI SQUARE STATISTIC IS 0 16915 THE NORMAL THEORY RLS CHI SQUARE FOR THIS ML SOLUTION IS BENTLER BONETT NORMED FIT INDEX BENTLER BONETT NONNORMED FIT INDEX COMPARATIVE FIT INDEX CFI 0 990 0 997 0 998 26 173 MAXIMUM LIKELIHOOD SOLUTION NORMAL DISTRIBUTION THEORY MEASUREMENT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS V1 V1 703 F1 032 21 714 1 000 E1 V2 V2 735 F1 033 22 475 1 000 E2 V3 V3 709 F1 032 21 963 1 000 E3 V4 V4 727 F1 033 22 169 1 000 E4 V5 V5 676 F1 032 21 370 1 000 E5 V6 V6 764 F1 034 22 784 1 000 E6 V7 V7 728 F1 035 21 041 1 000 E7 V8 V8 685 F1 033 20 660 1 000 E8 STANDARDIZED SOLUTION V1 V2 V3 V4 V5 V6 V7 V8 V1 V2 V3 V4 V5 V6 V7 V8 702 F1 720 F1 707 F1 712 F1 693 F1 727 F1 685 F1 676 F1 R SQUARED 713 694 707 702 721 687 728 737 E1 E2 E3 E4 E5 E6 E7 E8 492 518 500 507 481 528 469 457 NOW WE BRING THE DATA SET TO SPSS WHERE WE CHECK THE SOLUTION AND THEN CREATE SOME DISCRETIZED BINARY PRESENT ABSENT VERSIONS OF THE VARIABLES DATA LIST FILE C G2247 Lectures Cat001 dat FIXED RECORDS 2 TABLE 1 v1 1 13 v2 14 26 v3 27 39 v4 40 52 v5 53 65 v6 66 78 2 v7 1 13 v8 14 26 FORMATS V1 TO V8 F10 6 EXECUTE FORMATS v1 F10 6 VARIABLE WIDTH v1 10 VARIABLE WIDTH v1 TO V8 10 EXECUTE FACTOR VARIABLES v1 v2 v3 v4 v5 v6 v7 v8 MISSING LISTWISE ANALYSIS v1 v2 v3 v4 v5 v6 v7 v8 PRINT UNIVARIATE CORRELATION EXTRACTION ROTATION PLOT EIGEN CRITERIA MINEIGEN 1 ITERATE 25 EXTRACTION ML CRITERIA ITERATE 25 Factor Analysis Descriptive Statistics Correlation Matrix V1 V2 V3 V4 V5 V6 V7 V8 Correlation V1 1 000 498 489 489 523 530 456 463 V2 498 1 000 508 520 477 525 489 512 V3 489 508 1 000 497 493 491 488 518 V4 489 520 497 1 000 501 531 494 462 V5 523 477 493 501 1 000 494 466 463 V6 530 525 491 531 494 1 000 523 462 V7 456 489 488 494 466 523 1 000 463 V8 463 512 518 462 463 462 463 1 00 Scree Plot 5 4 3 Eigenvalue 2 1 0 1 2 Factor Number 3 4 5 6 7 8 Factor Matrix a Factor 1 V1 702 V2 720 V3 707 V4 712 V5 693 V6 727 V7 685 V8 676 Extraction Method Maximum Likelihood a 1 factors extracted 4 iterations required Goodness of fit Test Chi Square df Sig 25 765 20 174 WE CREATE DISCRETIZED BINARY PRESENT ABSENT VERSIONS OF THE VARIABLES COMPUTE V1 5 0 COMPUTE V2 5 0 COMPUTE V3 5 0 COMPUTE V4 5 0 COMPUTE V5 1 0 COMPUTE V6 1 0 COMPUTE V7 1 0 COMPUTE V8 1 0 IF v1 0 V1 5 1 IF v2 0 V2 5 1 IF v3 0 V3 5 1 IF v4 0 V4 5 1 IF v5 1 28 V5 1 1 IF v6 1 28 V6 1 1 IF v7 1 28 V7 1 1 IF v8 1 28 V8 1 1 FORMATS V1 5 TO V8 1 F3 0 WRITE OUTFILE LEC11B DAT RECORDS 1 1 V1 5 TO V8 1 FACTOR VARIABLES v1 5 TO v8 1 MISSING LISTWISE ANALYSIS v1 5 TO v8 1 PRINT UNIVARIATE CORRELATION EXTRACTION ROTATION PLOT EIGEN EXTRACTION ML Factor Analysis Descriptive Statistics Mean Std Deviation Analysis N V1 5 51 50 800 V2 5 50 50 800 V3 5 51 50 800 V4 5 50 50 800 V5 1 9 25E 02 29 800 V6 1 12 33 800 V7 1 …