G89 2247 LECTURE 5 HANDOUT 1 EQS A STRUCTURAL EQUATION PROGRAM COPYRIGHT BY P M BENTLER MULTIVARIATE SOFTWARE INC VERSION 5 7b C 1985 1998 PROGRAM CONTROL INFORMATION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 TITLE simulation example lecture 5 SIMULATION POP MOD SEED 1209493 DATA sm1 SAVE SEPARATE REPLICATIONS 1 SPECIFICATIONS VARIABLES 4 CASES 250 METHODS ML MATRIX RAW EQUATIONS V3 0 50 V1 0 30 V4 1E3 V4 0 40 V2 0 40 V3 1E4 VARIANCES V1 1 00 V2 1 00 E3 0 60 E4 0 60 COVARIANCES V2 V1 40 E4 E3 15 PRINT digit 3 linesize 80 fit all 27 RECORDS OF INPUT MODEL FILE WERE READ TITLE simulation example lecture 5 EQS EM386 Licensee Quant 02 23 04 PAGE 2 SIMULATION DEFINITIONS NUMBER OF REPLICATIONS SAMPLE DATA GENERATED FROM SAMPLE SIZE DATA IS NORMAL DATA TO BE CONTAMINATED ORIGINAL SEED DATA FILE TO BE SAVED IN WHICH TYPE 1 MODEL 250 YES NO 1209493 YES SEPARATED PAGE 1 G89 2247 LECTURE 5 HANDOUT UNIVARIATE CHARACTERISTICS OF SIMULATED DATA MEAN V1 V2 E3 E4 IFMT STAND DEV 1 1364 0 4545 0 3409 1 1364 1 IANALY UNIVARIATE TRANSFORMATION 1 0000 1 0000 0 7746 0 7746 NORMAL NORMAL NORMAL NORMAL DISTRIBUTION DISTRIBUTION DISTRIBUTION DISTRIBUTION 0 SIMULATION PROCEED IN REPLICATION nfle 0 knorm 4 nnfle 0 nnorm 10 1 SEED IS 1209493 00 TITLE simulation example lecture 5 EQS EM386 Licensee Quant 02 23 04 PAGE SIMULATION IN REPLICATION 1 SEED IS INPUT DATA FILE NAME IS SM1001 DAT 3 1209493 SAMPLE STATISTICS BASED ON COMPLETE CASES UNIVARIATE STATISTICS VARIABLE MEAN V1 V2 V3 V4 1 1738 0 5268 1 4866 1 9792 SKEWNESS G1 0 0609 0 1734 0 0505 0 0314 KURTOSIS G2 0 2786 0 2390 0 0658 0 2068 STANDARD DEV 1 0224 1 0741 1 0524 1 1416 MULTIVARIATE KURTOSIS MARDIA S COEFFICIENT G2 P NORMALIZED ESTIMATE 0 2905 0 2546 ELLIPTICAL THEORY KURTOSIS ESTIMATES MARDIA BASED KAPPA 0 0106 MEAN SCALED UNIVARIATE KURTOSIS MARDIA BASED KAPPA IS USED IN COMPUTATION KAPPA 0 0194 0 0106 CASE NUMBERS WITH LARGEST CONTRIBUTION TO NORMALIZED MULTIVARIATE KURTOSIS CASE NUMBER ESTIMATE 119 161 198 200 220 122 4944 216 7896 160 0419 232 9937 351 0266 PAGE 2 G89 2247 LECTURE 5 HANDOUT TITLE simulation example lecture 5 02 23 04 PAGE 4 EQS EM386 Licensee Quant COVARIANCE MATRIX TO BE ANALYZED 4 VARIABLES SELECTED FROM 4 VARIABLES BASED ON 250 CASES V1 V2 V3 V4 V V V V 1 2 3 4 V1 V 1 1 045 0 500 0 636 0 520 V2 V3 V 2 V4 V 1 154 0 443 0 683 3 V 1 107 0 726 4 1 303 BENTLER WEEKS STRUCTURAL REPRESENTATION NUMBER OF DEPENDENT VARIABLES DEPENDENT V S 3 4 2 NUMBER OF INDEPENDENT VARIABLES INDEPENDENT V S 1 2 INDEPENDENT E S 3 4 4 NUMBER OF FREE PARAMETERS 10 NUMBER OF FIXED NONZERO PARAMETERS 3RD STAGE OF COMPUTATION REQUIRED PROGRAM ALLOCATED 400000 WORDS DETERMINANT OF INPUT MATRIX IS 2 1486 WORDS OF MEMORY 0 44820E 00 TITLE simulation example lecture 5 02 23 04 PAGE EQS EM386 Licensee Quant MAXIMUM LIKELIHOOD SOLUTION NORMAL DISTRIBUTION THEORY 5 PARAMETER ESTIMATES APPEAR IN ORDER NO SPECIAL PROBLEMS WERE ENCOUNTERED DURING OPTIMIZATION RESIDUAL COVARIANCE MATRIX V1 V2 V3 V4 V V V V 1 2 3 4 V1 V 1 0 000 0 000 0 000 0 000 S SIGMA V2 V 2 0 000 0 000 0 000 AVERAGE ABSOLUTE AVERAGE OFF DIAGONAL ABSOLUTE V3 V V4 3 V 0 000 0 000 COVARIANCE COVARIANCE 4 0 000 RESIDUALS RESIDUALS 0 0000 0 0000 PAGE 3 G89 2247 LECTURE 5 HANDOUT STANDARDIZED RESIDUAL MATRIX V1 V2 V3 V4 V V V V 1 2 3 4 V1 V 1 0 000 0 000 0 000 0 000 V2 V V3 2 V 0 000 0 000 0 000 V4 3 V 0 000 0 000 4 0 000 AVERAGE ABSOLUTE STANDARDIZED RESIDUALS AVERAGE OFF DIAGONAL ABSOLUTE STANDARDIZED RESIDUALS 0 0000 0 0000 TITLE simulation example lecture 5 02 23 04 PAGE EQS EM386 Licensee Quant MAXIMUM LIKELIHOOD SOLUTION NORMAL DISTRIBUTION THEORY 6 LARGEST STANDARDIZED RESIDUALS V 4 V 3 0 000 V 3 V 3 0 000 V 4 V 4 0 000 V 3 V 2 0 000 V 4 V 2 0 000 V 3 V 1 0 000 V 4 V 1 0 000 V 2 V 2 0 000 V 2 V 1 0 000 V 1 V 1 0 000 DISTRIBUTION OF STANDARDIZED RESIDUALS 20 15 10 5 1 2 3 4 5 6 7 8 9 A B C RANGE FREQ PERCENT 1 0 5 0 0 00 2 0 4 0 5 0 0 00 3 0 3 0 4 0 0 00 4 0 2 0 3 0 0 00 5 0 1 0 2 0 0 00 6 0 0 0 1 7 70 00 7 0 1 0 0 3 30 00 8 0 2 0 1 0 0 00 9 0 3 0 2 0 0 00 A 0 4 0 3 0 0 00 B 0 5 0 4 0 0 00 C 0 5 0 0 00 TOTAL 10 100 00 EACH REPRESENTS 1 RESIDUALS PAGE 4 G89 2247 LECTURE 5 HANDOUT TITLE simulation example lecture 5 02 23 04 PAGE EQS EM386 Licensee Quant MAXIMUM LIKELIHOOD SOLUTION NORMAL DISTRIBUTION THEORY 7 GOODNESS OF FIT SUMMARY INDEPENDENCE MODEL CHI SQUARE INDEPENDENCE AIC MODEL AIC 325 84068 0 00000 337 841 ON INDEPENDENCE CAIC MODEL CAIC 6 DEGREES OF FREEDOM 298 71191 0 00000 CHI SQUARE 0 000 BASED ON 0 DEGREES OF FREEDOM NONPOSITIVE DEGREES OF FREEDOM PROBABILITY COMPUTATIONS ARE UNDEFINED BENTLER BONETT NORMED FIT INDEX 1 000 NON NORMED FIT INDEX WILL NOT BE COMPUTED BECAUSE A DEGREES OF FREEDOM IS ZERO ITERATIVE SUMMARY PARAMETER ABS CHANGE 0 064900 0 002898 0 000037 ITERATION 1 2 3 ALPHA 1 00000 1 00000 1 00000 FUNCTION 0 00019 0 00000 0 00000 TITLE simulation example lecture 5 02 23 04 PAGE EQS EM386 Licensee Quant MAXIMUM LIKELIHOOD SOLUTION NORMAL DISTRIBUTION THEORY 8 MEASUREMENT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS V3 V3 321 V4 105 3 049 448 V1 070 6 398 1 000 E3 V4 V4 506 V3 107 4 750 397 V2 063 6 279 1 000 E4 VARIANCES OF INDEPENDENT VARIABLES V V1 V1 V2 V2 F 1 045 I 094 I 11 158 I I 1 154 I 103 I 11 158 I I I I I I I I PAGE 5 G89 2247 LECTURE 5 HANDOUT TITLE simulation example lecture 5 02 23 04 PAGE 10 EQS EM386 Licensee Quant MAXIMUM LIKELIHOOD SOLUTION NORMAL DISTRIBUTION THEORY VARIANCES OF INDEPENDENT VARIABLES E E3 V3 566 I 053 I 10 662 I I E4 V4 670 I 060 I 11 150 I D COVARIANCES AMONG INDEPENDENT VARIABLES V V2 V2 500 I V1 V1 076 I 6 543 I I I I I I I I COVARIANCES AMONG INDEPENDENT …