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 TITLE mean model 1 t test SPECIFICATIONS DATA C G2247 LECTURES LEC12 ESS VARIABLES 7 CASES 100 METHODS ML MATRIX RAW ANALYSIS MOMENT LABELS V1 ID V2 x V3 w V4 w1 V5 w2 V6 w3 V7 y EQUATIONS V2 V999 E2 V7 V999 V2 E7 VARIANCES V999 1 E2 E7 COVARIANCES PRINT effect yes digit 3 linesize 80 fit all END 25 RECORDS OF INPUT MODEL FILE WERE READ DATA IS READ FROM C G2247 LECTURES LEC12 ESS THERE ARE 8 VARIABLES AND 100 CASES IT IS A RAW DATA ESS FILE TITLE mean model 1 t test 04 09 02 PAGE 2 SAMPLE STATISTICS BASED ON COMPLETE CASES UNIVARIATE STATISTICS VARIABLE MEAN SKEWNESS G1 KURTOSIS G2 STANDARD DEV X 0 6100 0 4511 1 7966 0 4902 Y 40 3281 0 2715 0 4601 16 7514 V999 1 0000 0 0000 0 0000 0 0000 MULTIVARIATE KURTOSIS MARDIA S COEFFICIENT G2 P NORMALIZED ESTIMATE 1 4376 1 7970 ELLIPTICAL THEORY KURTOSIS ESTIMATES MARDIA BASED KAPPA TITLE 0 1797 MEAN SCALED UNIVARIATE KURTOSIS mean model 1 t test 04 09 02 PAGE 0 2227 3 Lecture 11 Page 1 MATRIX CONTAINS SPECIAL VARIABLE V999 THE UNIT CONSTANT COVARIANCE MATRIX IS IN UPPER TRIANGLE MEANS ARE IN BOTTOM ROW OF MATRIX COVARIANCE MEAN MATRIX TO BE ANALYZED 2 VARIABLES SELECTED FROM 8 VARIABLES BASED ON 100 CASES X Y V999 X V 2 0 240 3 092 0 610 V 2 V 7 V999 Y V V999 V999 7 280 611 40 328 1 000 BENTLER WEEKS STRUCTURAL REPRESENTATION NUMBER OF DEPENDENT VARIABLES DEPENDENT V S 2 7 2 NUMBER OF INDEPENDENT VARIABLES INDEPENDENT V S 999 INDEPENDENT E S 2 7 3 NUMBER OF FREE PARAMETERS 5 NUMBER OF FIXED NONZERO PARAMETERS 3RD STAGE OF COMPUTATION REQUIRED PROGRAM ALLOCATED 100000 WORDS DETERMINANT OF INPUT MATRIX IS 3 600 WORDS OF MEMORY 0 57874E 02 GOODNESS OF FIT SUMMARY INDEPENDENCE MODEL CHI SQUARE INDEPENDENCE AIC MODEL AIC 13 13136 0 00000 15 131 ON INDEPENDENCE CAIC MODEL CAIC 1 DEGREES OF FREEDOM 9 52619 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 ITERATION 1 2 3 4 5 PARAMETER ABS CHANGE 42 507530 253 484665 57 618114 7 332404 0 000000 ALPHA 1 00000 1 00000 1 00000 1 00000 1 00000 FUNCTION 1 40716 0 32647 0 00958 0 00000 0 00000 Lecture 11 Page 2 TITLE mean model 1 t test MAXIMUM LIKELIHOOD SOLUTION NORMAL DISTRIBUTION THEORY 04 09 02 PAGE 7 MEASUREMENT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS X V2 610 V999 049 12 381 1 000 E2 Y V7 12 865 V2 3 182 4 043 32 480 V999 2 490 13 045 1 000 E7 VARIANCES OF INDEPENDENT VARIABLES E E2 X E7 Y D 240 I 034 I 7 036 I I 240 838 I 34 231 I 7 036 I I I I I I I I I I MAXIMUM LIKELIHOOD SOLUTION NORMAL DISTRIBUTION THEORY STANDARDIZED SOLUTION X Y V2 V7 000 V999 376 V2 R SQUARED 1 000 E2 000 V999 926 E7 000 142 E N D O F M E T H O D 1 Execution begins at 10 31 16 94 Execution ends at 10 31 17 00 Elapsed time 0 06 seconds Lecture 11 Page 3 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 TITLE mean model 2 Ancova SPECIFICATIONS DATA C G2247 LECTURES LEC12 ESS VARIABLES 7 CASES 100 METHODS ML MATRIX RAW ANALYSIS MOMENT LABELS V1 ID V2 x V3 w V4 w1 V5 w2 V6 w3 V7 y EQUATIONS V2 V999 E2 V3 V999 E3 V7 V999 V2 V3 E7 VARIANCES V999 1 E2 E3 E7 COVARIANCES E3 E2 22 RECORDS OF INPUT MODEL FILE WERE READ DATA IS READ FROM C G2247 LECTURES LEC12 ESS THERE ARE 7 VARIABLES AND 100 CASES IT IS A RAW DATA ESS FILE TITLE mean model 2 Ancova EQS EM386 Licensee Quant 04 09 02 PAGE 2 SAMPLE STATISTICS BASED ON COMPLETE CASES UNIVARIATE STATISTICS VARIABLE MEAN SKEWNESS G1 KURTOSIS G2 STANDARD DEV X W 0 6100 0 4511 1 7966 0 4902 Y 11 1662 0 2077 0 2139 5 0448 40 3281 0 2715 0 4601 16 7514 V999 1 0000 0 0000 0 0000 0 0000 MULTIVARIATE KURTOSIS MARDIA S COEFFICIENT G2 P NORMALIZED ESTIMATE 1 9630 1 7920 ELLIPTICAL THEORY KURTOSIS ESTIMATES MARDIA BASED KAPPA 0 1309 MEAN SCALED UNIVARIATE KURTOSIS MARDIA BASED KAPPA IS USED IN COMPUTATION KAPPA 0 1247 0 1309 Lecture 11 Page 4 CASE NUMBERS WITH LARGEST CONTRIBUTION TO NORMALIZED MULTIVARIATE KURTOSIS CASE NUMBER ESTIMATE 8 63 48 2617 40 2043 78 93 99 56 5399 56 0268 45 9762 TITLE mean model 2 Ancova 04 09 02 PAGE EQS EM386 Licensee Quant MATRIX CONTAINS SPECIAL VARIABLE V999 THE UNIT CONSTANT COVARIANCE MATRIX IS IN UPPER TRIANGLE MEANS ARE IN BOTTOM ROW OF MATRIX COVARIANCE MEAN MATRIX TO BE ANALYZED 3 VARIABLES SELECTED FROM 7 VARIABLES BASED ON 100 CASES X W Y V999 V 2 V 3 V 7 V999 X V 2 0 240 0 586 3 092 0 610 W V Y V 3 25 450 61 913 11 166 7 280 611 40 328 3 V999 V999 1 000 BENTLER WEEKS STRUCTURAL REPRESENTATION NUMBER OF DEPENDENT VARIABLES DEPENDENT V S 2 3 NUMBER OF INDEPENDENT VARIABLES INDEPENDENT V S 999 INDEPENDENT E S 2 3 3 7 4 7 NUMBER OF FREE PARAMETERS 9 NUMBER OF FIXED NONZERO PARAMETERS 3RD STAGE OF COMPUTATION REQUIRED PROGRAM ALLOCATED 100000 WORDS DETERMINANT OF INPUT MATRIX IS 4 1009 WORDS OF MEMORY 0 67973E 03 PARAMETER ESTIMATES APPEAR IN ORDER NO SPECIAL PROBLEMS WERE ENCOUNTERED DURING OPTIMIZATION GOODNESS OF FIT SUMMARY INDEPENDENCE MODEL CHI SQUARE INDEPENDENCE AIC MODEL AIC 85 68782 0 00000 91 688 ON INDEPENDENCE CAIC MODEL CAIC 3 DEGREES OF FREEDOM 74 87231 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 Lecture 11 Page 5 MAXIMUM LIKELIHOOD SOLUTION NORMAL DISTRIBUTION THEORY MEASUREMENT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS X V2 610 V999 049 12 381 1 000 E2 W V3 11 166 V999 507 22 023 1 000 E3 Y V7 7 345 V2 2 290 3 207 2 264 V3 223 10 172 10 572 V999 2 769 3 817 1 …