Mplus VERSION 6.11 MUTHEN & MUTHEN 09/27/2011 12:55 PM INPUT INSTRUCTIONS title: Simulating x-m interaction effect on y using a random slope, Step 2: External Monte Carlo analysis data: file = xmreplist.dat; type = montecarlo; variable: names = y m x; usev = y m x xm; define: xm = x*m; analysis: model: [y*1] (beta0); y on x*.4 (beta2); y on xm*.2 (beta3); y on m*.5 (beta1); [m*2] (gamma0); m on x*.5 (gamma1); y*.5; m*1; model constraint: new(tie*.35 pie*.25 de*.8); tie=beta1*gamma1+beta3*gamma1; pie=beta1*gamma1; de=beta2+beta3*gamma0; INPUT READING TERMINATED NORMALLY Simulating x-m interaction effect on y using a random slope, Step 2: External Monte Carlo analysis SUMMARY OF ANALYSIS Number of groups 1 Average number of observations 400 Number of replications Requested 500 Completed 500 Number of dependent variables 2 Number of independent variables 2 Number of continuous latent variables 0 Observed dependent variables Continuous Y M Observed independent variables X XM Estimator ML Information matrix OBSERVED Maximum number of iterations 1000 Convergence criterion 0.500D-04 Maximum number of steepest descent iterations 20 Input data file(s) Multiple data files from xmreplist.dat Input data format FREE SAMPLE STATISTICS NOTE: These are average results over 500 data sets. SAMPLE STATISTICS Means Y M X XM ________ ________ ________ ________ 1 2.579 2.254 0.501 1.253 Covariances Y M X XM ________ ________ ________ ________ Y 1.203 M 0.742 1.058 X 0.288 0.125 0.249 XM 1.069 0.809 0.625 2.061 Correlations Y M X XM ________ ________ ________ ________ Y 1.000 M 0.658 1.000 X 0.526 0.243 1.000 XM 0.679 0.548 0.871 1.000 MODEL FIT INFORMATION Number of Free Parameters 8 Loglikelihood H0 Value Mean -993.100 Std Dev 20.276 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.994 -1040.269 -1039.380 0.980 0.984 -1034.742 -1034.043 0.950 0.960 -1026.453 -1024.967 0.900 0.898 -1019.086 -1019.164 0.800 0.790 -1010.165 -1011.911 0.700 0.682 -1003.733 -1004.382 0.500 0.514 -993.100 -992.722 0.300 0.296 -982.467 -982.822 0.200 0.208 -976.035 -975.721 0.100 0.100 -967.114 -967.464 0.050 0.056 -959.747 -957.950 0.020 0.018 -951.458 -952.296 0.010 0.010 -945.931 -947.433 H1 Value Mean -854.472 Std Dev 26.230 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 -915.492 -920.643 0.980 0.986 -908.341 -904.008 0.950 0.954 -897.618 -897.046 0.900 0.894 -888.089 -889.012 0.800 0.806 -876.547 -876.409 0.700 0.698 -868.227 -868.683 0.500 0.486 -854.472 -855.064 0.300 0.262 -840.717 -842.571 0.200 0.190 -832.396 -833.712 0.100 0.120 -820.855 -818.213 0.050 0.052 -811.325 -810.383 0.020 0.030 -800.602 -799.256 0.010 0.012 -793.452 -792.705 Information Criteria Akaike (AIC) Mean 2002.200 Std Dev 40.553 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 1907.862 1902.795 0.980 0.982 1918.917 1919.146 0.950 0.944 1935.495 1929.914 0.900 0.900 1950.228 1949.391 0.800 0.792 1968.071 1966.422 0.700 0.704 1980.934 1981.296 0.500 0.486 2002.200 2001.306 0.300 0.318 2023.466 2024.640 0.200 0.210 2036.329 2039.411 0.100 0.102 2054.173 2054.173 0.050 0.040 2068.906 2065.806 0.020 0.016 2085.484 2083.017 0.010 0.006 2096.538 2093.014 Bayesian (BIC) Mean 2034.132 Std Dev 40.553 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 1939.794 1934.727 0.980 0.982 1950.848 1951.078 0.950 0.944 1967.426 1961.846 0.900 0.900 1982.159 1981.323 0.800 0.792 2000.003 1998.354 0.700 0.704 2012.866 2013.228 0.500 0.486 2034.132 2033.238 0.300 0.318 2055.398 2056.571 0.200 0.210 2068.261 2071.342 0.100 0.102 2086.104 2086.105 0.050 0.040 2100.837 2097.738 0.020 0.016 2117.415 2114.949 0.010 0.006 2128.470 2124.946 Sample-Size Adjusted BIC (n* = (n + 2) / 24) Mean 2008.747 Std Dev 40.553 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 1914.409 1909.343 0.980 0.982 1925.464 1925.694 0.950 0.944 1942.042 1936.461 0.900 0.900 1956.775 1955.938 0.800 0.792 1974.618 1972.969 0.700 0.704 1987.481 1987.843 0.500 0.486 2008.747 2007.853 0.300 0.318 2030.013 2031.187 0.200 0.210 2042.877 2045.958 0.100 0.102 2060.720 2060.720 0.050 0.040 2075.453 2072.353 0.020 0.016 2092.031 2089.564 0.010 0.006 2103.085 2099.562 Chi-Square Test of Model Fit Degrees of freedom 1 Mean 277.257 Std Dev 34.676 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 1.000 0.000 203.811 0.980 1.000 0.001 209.650 0.950 1.000 0.004 222.051 0.900 1.000 0.016 233.792 0.800 1.000 0.064 249.098 0.700 1.000 0.148 258.985 0.500 1.000 0.455 273.958 0.300 1.000 1.074 293.928 0.200 1.000 1.642 306.718 0.100 1.000 2.706 324.569 0.050 1.000 3.841 340.761 0.020 1.000 5.412 351.723 0.010 1.000 6.635 365.388 RMSEA (Root Mean Square Error Of Approximation) Mean 0.829 Std Dev 0.052 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.996 0.708 0.712 0.980 0.980 0.723 0.722 0.950 0.950 0.744 0.743 0.900 0.904 0.763 0.763 0.800 0.808 0.786 0.788 0.700 0.706 0.802 0.803 0.500 0.472 0.829 0.826 0.300 0.288 0.857 0.856 0.200 0.208 0.873 0.874 0.100 0.114 0.896 0.899 0.050 0.064 0.915 0.922 0.020 0.024 0.936 0.936 0.010 0.014 0.950 0.954 CFI/TLI CFI Mean 0.576 Std Dev 0.039 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.994 0.486 0.494 0.980 0.984 0.497 0.498 0.950 0.938 0.513 0.508 0.900 0.880 0.527 0.522 0.800 0.812 0.544 0.544 0.700 0.710 0.556 0.557 0.500 0.502 0.576 0.576 0.300 0.304 0.596 0.596 0.200 0.196 0.608 0.608 0.100 0.100 0.625 0.624 0.050 0.058 0.639 0.643 0.020 0.024 0.655 0.656 0.010 0.012 0.666 0.668 TLI Mean -1.120 Std Dev 0.193 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.994 -1.568 -1.528 0.980 0.984 -1.516 -1.511 0.950 0.938 -1.437 -1.459 0.900 0.880 -1.367 -1.389 0.800 0.812 -1.282 -1.280 0.700 0.710 -1.221 -1.213 0.500 0.502 -1.120 -1.120 0.300 0.304 -1.019 -1.018 0.200 0.196 -0.958 -0.962 0.100 0.100 -0.873 -0.878 0.050 0.058 -0.803 -0.786 0.020 0.024 -0.724 -0.719 0.010 0.012 -0.672 -0.660 SRMR (Standardized Root Mean Square Residual) Mean 0.105 Std Dev 0.010 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.994 0.082 0.083 0.980 0.988 0.084 0.086 0.950 0.940 0.088 0.088 0.900 0.898 0.092 0.092 0.800 0.800 0.096 0.096 0.700 0.702 0.100 0.100 0.500 0.490 0.105 0.104 0.300 0.298 0.110 0.110 0.200 0.206 0.113 0.114 0.100 0.106 0.118 0.118 0.050 0.040 0.121 0.121 0.020 0.016 0.126 0.124 0.010 0.014 0.128 0.131 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff Y ON X 0.400 0.4011 0.1784 0.1761 0.0318 0.950 0.616 XM 0.200 0.2006 0.0716 0.0711 0.0051 0.958 0.780 M 0.500 0.5006 0.0493 0.0501 0.0024 0.964 1.000 M ON X 0.500 0.5015 0.0981 0.0997 0.0096 0.940 0.998 Intercepts Y 1.000 0.9984 0.1107 0.1122 0.0122 0.954 1.000 M 2.000 2.0032 0.0683 0.0705 0.0047 0.962 1.000 Residual Variances Y 0.500 0.4974 0.0372 0.0352 0.0014 0.936 1.000 M 1.000 0.9933 0.0667 0.0702 0.0045 0.960 1.000 New/Additional Parameters TIE 0.350 0.3518 0.0748 0.0745 0.0056 0.932 0.998 PIE 0.250 0.2509 0.0544 0.0561 0.0029 0.950 0.998 DE 0.800 0.8027 0.0802 0.0766 0.0064 0.936 1.000 QUALITY OF NUMERICAL RESULTS Average Condition Number for the Information Matrix 0.117E-03 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION NU Y M X XM ________ ________ ________ ________ 1 0 0 0 0 LAMBDA Y M X XM ________ ________ ________ ________ Y 0 0 0 0 M 0 0 0 0 X 0 0 0 0 XM 0 0 0 0 THETA Y M X XM ________ ________ ________ ________ Y 0 M 0 0 X 0 0 0 XM 0 0 0 0 ALPHA Y M X XM ________ ________ ________ ________ 1 1 2 0 0 BETA Y M X XM ________ ________ ________ ________ Y 0 3 4 5 M 0 0 6 0 X 0 0 0 0 XM 0 0 0 0 PSI Y M X XM ________ ________ ________ ________ Y 7 M 0 8 X 0 0 0 XM 0 0 0 0 PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS New/Additional Parameters TIE PIE DE ________ ________ ________ 1 9 10 11 STARTING VALUES NU Y M X XM ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 LAMBDA Y M X XM ________ ________ ________ ________ Y 1.000 0.000 0.000 0.000 M 0.000 1.000 0.000 0.000 X 0.000 0.000 1.000 0.000 XM 0.000 0.000 0.000 1.000 THETA Y M X XM ________ ________ ________ ________ Y 0.000 M 0.000 0.000 X 0.000 0.000 0.000 XM 0.000 0.000 0.000 0.000 ALPHA Y M X XM ________ ________ ________ ________ 1 1.000 2.000 0.540 1.357 BETA Y M X XM ________ ________ ________ ________ Y 0.000 0.500 0.400 0.200 M 0.000 0.000 0.500 0.000 X 0.000 0.000 0.000 0.000 XM 0.000 0.000 0.000 0.000 PSI Y M X XM ________ ________ ________ ________ Y 0.500 M 0.000 1.000 X 0.000 0.000 0.248 XM 0.000 0.000 0.624 2.141 STARTING VALUES FOR THE ADDITIONAL PARAMETERS New/Additional Parameters TIE PIE DE ________ ________ ________ 1 0.350 0.250 0.800 Beginning Time: 12:55:30 Ending Time: 12:55:35 Elapsed Time: 00:00:05 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