Mplus VERSION 6.11 MUTHEN & MUTHEN 10/24/2011 9:40 AM INPUT INSTRUCTIONS title: Generate as M on X, Y on M and X Analyze as M on X, Y on X Using Imai formulas with rho=0, so same as regular mediation run montecarlo: names = y m x; nobs = 400; nreps = 500; cutpoints = x(0); model population: x@1; [y*1]; ! beta0 y on m*.5 ! beta1 x*.4; ! beta2 [m*2]; ! gamma0 m on x*.5; ! gamma1 y*.5; ! sig1 m*1; ! sig2 analysis: model: [y] (kappa0); y on x (kappa1); [m*2] (gamma0); m on x*.5 (gamma1); y*.75 (sig); m*1 (sig2); y with m*.5 (cov); model constraint: new(rhocurl*.5774 beta1*.5 beta2*.4 beta0*1 sig1*.5 ind*.25 de*.4); rhocurl=cov/(sqrt(sig)*sqrt(sig2)); ! derive the data-generating model parameters ! from the analysis model parameters: beta1=rhocurl*sqrt(sig)/sqrt(sig2); beta2=kappa1-beta1*gamma1; beta0=kappa0-beta1*gamma0; sig1=sig-beta1*beta1*sig2; ! express the effects in terms of the data-generating ! parameters: ind=beta1*gamma1; de=beta2; INPUT READING TERMINATED NORMALLY Generate as M on X, Y on M and X Analyze as M on X, Y on X Using Imai formulas with rho=0, so same as regular mediation run SUMMARY OF ANALYSIS Number of groups 1 Number of observations 400 Number of replications Requested 500 Completed 500 Value of seed 0 Number of dependent variables 2 Number of independent variables 1 Number of continuous latent variables 0 Observed dependent variables Continuous Y M Observed independent variables X Estimator ML Information matrix OBSERVED Maximum number of iterations 1000 Convergence criterion 0.500D-04 Maximum number of steepest descent iterations 20 SAMPLE STATISTICS FOR THE FIRST REPLICATION SAMPLE STATISTICS Means Y M X ________ ________ ________ 1 2.350 2.277 0.487 Covariances Y M X ________ ________ ________ Y 0.854 M 0.614 1.117 X 0.179 0.120 0.250 Correlations Y M X ________ ________ ________ Y 1.000 M 0.629 1.000 X 0.387 0.226 1.000 MODEL FIT INFORMATION Number of Free Parameters 7 Loglikelihood H0 Value Mean -994.016 Std Dev 18.926 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.992 -1038.044 -1037.742 0.980 0.982 -1032.885 -1032.090 0.950 0.958 -1025.148 -1023.712 0.900 0.904 -1018.272 -1018.192 0.800 0.796 -1009.944 -1010.489 0.700 0.706 -1003.941 -1003.694 0.500 0.496 -994.016 -994.400 0.300 0.290 -984.091 -984.892 0.200 0.202 -978.088 -978.027 0.100 0.096 -969.760 -969.907 0.050 0.060 -962.884 -961.612 0.020 0.024 -955.147 -953.255 0.010 0.010 -949.988 -950.129 H1 Value Mean -994.016 Std Dev 18.926 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.992 -1038.044 -1037.742 0.980 0.982 -1032.885 -1032.090 0.950 0.958 -1025.148 -1023.712 0.900 0.904 -1018.272 -1018.192 0.800 0.796 -1009.944 -1010.489 0.700 0.706 -1003.941 -1003.694 0.500 0.496 -994.016 -994.400 0.300 0.290 -984.091 -984.892 0.200 0.202 -978.088 -978.027 0.100 0.096 -969.760 -969.907 0.050 0.060 -962.884 -961.612 0.020 0.024 -955.147 -953.255 0.010 0.010 -949.988 -950.129 Information Criteria Akaike (AIC) Mean 2002.032 Std Dev 37.852 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 1913.976 1911.820 0.980 0.976 1924.295 1920.462 0.950 0.940 1939.769 1934.892 0.900 0.904 1953.520 1953.536 0.800 0.798 1970.175 1969.093 0.700 0.710 1982.182 1983.568 0.500 0.504 2002.032 2002.698 0.300 0.294 2021.882 2021.076 0.200 0.204 2033.888 2034.873 0.100 0.096 2050.544 2049.959 0.050 0.042 2064.295 2060.946 0.020 0.018 2079.769 2077.847 0.010 0.008 2090.088 2083.382 Bayesian (BIC) Mean 2029.972 Std Dev 37.852 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 1941.916 1939.760 0.980 0.976 1952.235 1948.402 0.950 0.940 1967.709 1962.832 0.900 0.904 1981.461 1981.477 0.800 0.798 1998.116 1997.033 0.700 0.710 2010.122 2011.508 0.500 0.504 2029.972 2030.638 0.300 0.294 2049.822 2049.016 0.200 0.204 2061.829 2062.813 0.100 0.096 2078.484 2077.900 0.050 0.042 2092.236 2088.886 0.020 0.018 2107.710 2105.787 0.010 0.008 2118.028 2111.322 Sample-Size Adjusted BIC (n* = (n + 2) / 24) Mean 2007.761 Std Dev 37.852 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 1919.705 1917.548 0.980 0.976 1930.023 1926.191 0.950 0.940 1945.497 1940.620 0.900 0.904 1959.249 1959.265 0.800 0.798 1975.904 1974.822 0.700 0.710 1987.911 1989.297 0.500 0.504 2007.761 2008.427 0.300 0.294 2027.611 2026.805 0.200 0.204 2039.617 2040.602 0.100 0.096 2056.272 2055.688 0.050 0.042 2070.024 2066.674 0.020 0.018 2085.498 2083.576 0.010 0.008 2095.817 2089.111 Chi-Square Test of Model Fit Degrees of freedom 0 Mean 0.000 Std Dev 0.000 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 1.000 0.000 0.000 0.980 1.000 0.000 0.000 0.950 1.000 0.000 0.000 0.900 1.000 0.000 0.000 0.800 1.000 0.000 0.000 0.700 1.000 0.000 0.000 0.500 1.000 0.000 0.000 0.300 1.000 0.000 0.000 0.200 1.000 0.000 0.000 0.100 1.000 0.000 0.000 0.050 1.000 0.000 0.000 0.020 1.000 0.000 0.000 0.010 1.000 0.000 0.000 RMSEA (Root Mean Square Error Of Approximation) Mean 0.000 Std Dev 0.000 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.000 0.000 0.000 0.980 0.000 0.000 0.000 0.950 0.000 0.000 0.000 0.900 0.000 0.000 0.000 0.800 0.000 0.000 0.000 0.700 0.000 0.000 0.000 0.500 0.000 0.000 0.000 0.300 0.000 0.000 0.000 0.200 0.000 0.000 0.000 0.100 0.000 0.000 0.000 0.050 0.000 0.000 0.000 0.020 0.000 0.000 0.000 0.010 0.000 0.000 0.000 SRMR (Standardized Root Mean Square Residual) Mean 0.000 Std Dev 0.000 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 1.000 0.000 0.000 0.980 0.840 0.000 0.000 0.950 0.832 0.000 0.000 0.900 0.832 0.000 0.000 0.800 0.830 0.000 0.000 0.700 0.826 0.000 0.000 0.500 0.796 0.000 0.000 0.300 0.268 0.000 0.000 0.200 0.052 0.000 0.000 0.100 0.012 0.000 0.000 0.050 0.010 0.000 0.000 0.020 0.002 0.000 0.000 0.010 0.000 0.000 0.000 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff Y ON X 0.000 0.6545 0.0877 0.0866 0.4360 0.000 1.000 M ON X 0.500 0.4995 0.1033 0.0998 0.0107 0.952 1.000 Y WITH M 0.500 0.4978 0.0512 0.0498 0.0026 0.942 1.000 Intercepts Y 0.000 2.0014 0.0637 0.0611 4.0098 0.000 1.000 M 2.000 2.0000 0.0751 0.0705 0.0056 0.942 1.000 Residual Variances Y 0.750 0.7486 0.0515 0.0529 0.0027 0.952 1.000 M 1.000 0.9956 0.0714 0.0704 0.0051 0.952 1.000 New/Additional Parameters RHOCURL 0.577 0.5760 0.0345 0.0334 0.0012 0.938 1.000 BETA1 0.500 0.5000 0.0366 0.0354 0.0013 0.928 1.000 BETA2 0.400 0.4049 0.0730 0.0729 0.0053 0.938 1.000 BETA0 1.000 1.0014 0.0897 0.0867 0.0080 0.940 1.000 SIG1 0.500 0.4984 0.0338 0.0352 0.0011 0.950 1.000 IND 0.250 0.2495 0.0543 0.0531 0.0029 0.952 1.000 DE 0.400 0.4049 0.0730 0.0729 0.0053 0.938 1.000 QUALITY OF NUMERICAL RESULTS Average Condition Number for the Information Matrix 0.445E-03 (ratio of smallest to largest eigenvalue) TECHNICAL OUTPUT PARAMETER SPECIFICATION NU Y M X ________ ________ ________ 1 0 0 0 LAMBDA Y M X ________ ________ ________ Y 0 0 0 M 0 0 0 X 0 0 0 THETA Y M X ________ ________ ________ Y 0 M 0 0 X 0 0 0 ALPHA Y M X ________ ________ ________ 1 1 2 0 BETA Y M X ________ ________ ________ Y 0 0 3 M 0 0 4 X 0 0 0 PSI Y M X ________ ________ ________ Y 5 M 6 7 X 0 0 0 PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS New/Additional Parameters RHOCURL BETA1 BETA2 BETA0 SIG1 ________ ________ ________ ________ ________ 1 8 9 10 11 12 New/Additional Parameters IND DE ________ ________ 1 13 14 STARTING VALUES NU Y M X ________ ________ ________ 1 0.000 0.000 0.000 LAMBDA Y M X ________ ________ ________ Y 1.000 0.000 0.000 M 0.000 1.000 0.000 X 0.000 0.000 1.000 THETA Y M X ________ ________ ________ Y 0.000 M 0.000 0.000 X 0.000 0.000 0.000 ALPHA Y M X ________ ________ ________ 1 0.000 2.000 0.487 BETA Y M X ________ ________ ________ Y 0.000 0.000 0.000 M 0.000 0.000 0.500 X 0.000 0.000 0.000 PSI Y M X ________ ________ ________ Y 0.750 M 0.500 1.000 X 0.000 0.000 0.250 STARTING VALUES FOR THE ADDITIONAL PARAMETERS New/Additional Parameters RHOCURL BETA1 BETA2 BETA0 SIG1 ________ ________ ________ ________ ________ 1 0.577 0.500 0.400 1.000 0.500 New/Additional Parameters IND DE ________ ________ 1 0.250 0.400 POPULATION VALUES NU Y M X ________ ________ ________ 1 0.000 0.000 0.000 LAMBDA Y M X ________ ________ ________ Y 1.000 0.000 0.000 M 0.000 1.000 0.000 X 0.000 0.000 1.000 THETA Y M X ________ ________ ________ Y 0.000 M 0.000 0.000 X 0.000 0.000 0.000 ALPHA Y M X ________ ________ ________ 1 1.000 2.000 0.000 BETA Y M X ________ ________ ________ Y 0.000 0.500 0.400 M 0.000 0.000 0.500 X 0.000 0.000 0.000 PSI Y M X ________ ________ ________ Y 0.500 M 0.000 1.000 X 0.000 0.000 1.000 Beginning Time: 09:40:21 Ending Time: 09:40:27 Elapsed Time: 00:00:06 MUTHEN & MUTHEN 3463 Stoner Ave. Los Angeles, CA 90066 Tel: (310) 391-9971 Fax: (310) 391-8971 Web: www.StatModel.com Support: Support@StatModel.com Copyright (c) 1998-2011 Muthen & Muthen