Mplus VERSION 6.1 MUTHEN & MUTHEN 10/15/2010 12:54 PM INPUT INSTRUCTIONS TITLE: ML MONTECARLO: NAMES ARE y x; NOBS = 500; NREP = 500; NCsizes = 1; csizes = 10 (50); within = x; MODEL POPULATION: %within% x*1; y on x*1; y*2; %between% y*.222; !icc = .222/2.222 = 0.1 ANALYSIS: type = twolevel; estimator = ml; process = 2; MODEL: %within% y on x*1; y*2 (w); %between% y*.222 (b); !icc = .222/2.222 = 0.1 Model constraint: new(icc*.1); icc = b/(w+b); output: tech9; INPUT READING TERMINATED NORMALLY ML SUMMARY OF ANALYSIS Number of groups 1 Number of observations 500 Number of replications Requested 500 Completed 500 Value of seed 0 Number of dependent variables 1 Number of independent variables 1 Number of continuous latent variables 0 Observed dependent variables Continuous Y Observed independent variables X Variables with special functions Within variables X Estimator ML Information matrix OBSERVED Maximum number of iterations 100 Convergence criterion 0.100D-05 Maximum number of EM iterations 500 Convergence criteria for the EM algorithm Loglikelihood change 0.100D-02 Relative loglikelihood change 0.100D-05 Derivative 0.100D-03 Minimum variance 0.100D-03 Maximum number of steepest descent iterations 20 Maximum number of iterations for H1 2000 Convergence criterion for H1 0.100D-03 Optimization algorithm EMA SUMMARY OF DATA FOR THE FIRST REPLICATION Cluster information Size (s) Number of clusters of Size s 50 10 Average cluster size 50.000 Estimated Intraclass Correlations for the Y Variables Intraclass Variable Correlation Y 0.077 SAMPLE STATISTICS FOR THE FIRST REPLICATION NOTE: The sample statistics for within and between refer to the maximum-likelihood estimated within and between covariance matrices, respectively. ESTIMATED SAMPLE STATISTICS FOR WITHIN Means Y X ________ ________ 1 0.000 -0.035 Covariances Y X ________ ________ Y 3.002 X 0.994 0.997 Correlations Y X ________ ________ Y 1.000 X 0.574 1.000 ESTIMATED SAMPLE STATISTICS FOR BETWEEN Means Y X ________ ________ 1 0.020 0.000 Covariances Y X ________ ________ Y 0.251 X 0.000 0.000 Correlations Y X ________ ________ Y 1.000 X 0.000 0.000 MODEL FIT INFORMATION Number of Free Parameters 4 Loglikelihood H0 Value Mean -891.126 Std Dev 15.753 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.988 -927.773 -929.260 0.980 0.972 -923.479 -924.449 0.950 0.938 -917.039 -920.095 0.900 0.908 -911.316 -910.938 0.800 0.836 -904.384 -902.718 0.700 0.722 -899.387 -898.825 0.500 0.478 -891.126 -892.297 0.300 0.286 -882.866 -883.553 0.200 0.204 -877.869 -877.700 0.100 0.114 -870.937 -869.891 0.050 0.046 -865.214 -865.776 0.020 0.024 -858.774 -857.545 0.010 0.014 -854.480 -853.583 H1 Value Mean -891.126 Std Dev 15.753 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.988 -927.773 -929.260 0.980 0.972 -923.479 -924.449 0.950 0.938 -917.039 -920.095 0.900 0.908 -911.316 -910.938 0.800 0.836 -904.384 -902.718 0.700 0.722 -899.387 -898.824 0.500 0.478 -891.126 -892.297 0.300 0.286 -882.865 -883.553 0.200 0.204 -877.868 -877.700 0.100 0.114 -870.937 -869.891 0.050 0.046 -865.214 -865.776 0.020 0.024 -858.774 -857.545 0.010 0.014 -854.480 -853.583 Information Criteria Akaike (AIC) Mean 1790.253 Std Dev 31.506 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.986 1716.960 1715.135 0.980 0.976 1725.549 1722.459 0.950 0.954 1738.428 1739.372 0.900 0.886 1749.875 1747.384 0.800 0.796 1763.737 1763.274 0.700 0.714 1773.731 1774.684 0.500 0.522 1790.253 1791.970 0.300 0.278 1806.775 1805.603 0.200 0.164 1816.769 1813.249 0.100 0.092 1830.631 1828.573 0.050 0.062 1842.078 1848.134 0.020 0.028 1854.957 1855.868 0.010 0.012 1863.546 1863.851 Bayesian (BIC) Mean 1807.111 Std Dev 31.506 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.986 1733.818 1731.993 0.980 0.976 1742.407 1739.317 0.950 0.954 1755.287 1756.231 0.900 0.886 1766.733 1764.243 0.800 0.796 1780.596 1780.132 0.700 0.714 1790.589 1791.542 0.500 0.522 1807.111 1808.828 0.300 0.278 1823.633 1822.461 0.200 0.164 1833.627 1830.107 0.100 0.092 1847.490 1845.432 0.050 0.062 1858.936 1864.992 0.020 0.028 1871.816 1872.727 0.010 0.012 1880.404 1880.710 Sample-Size Adjusted BIC (n* = (n + 2) / 24) Mean 1794.415 Std Dev 31.506 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.986 1721.122 1719.297 0.980 0.976 1729.711 1726.621 0.950 0.954 1742.590 1743.535 0.900 0.886 1754.037 1751.546 0.800 0.796 1767.899 1767.436 0.700 0.714 1777.893 1778.846 0.500 0.522 1794.415 1796.132 0.300 0.278 1810.937 1809.765 0.200 0.164 1820.931 1817.411 0.100 0.092 1834.794 1832.735 0.050 0.062 1846.240 1852.296 0.020 0.028 1859.119 1860.030 0.010 0.012 1867.708 1868.014 Chi-Square Test of Model Fit Degrees of freedom 0 Mean 0.000 Std Dev 0.005 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.378 0.000 0.000 0.980 0.378 0.000 0.000 0.950 0.378 0.000 0.000 0.900 0.378 0.000 0.000 0.800 0.378 0.000 0.000 0.700 0.378 0.000 0.000 0.500 0.378 0.000 0.000 0.300 0.378 0.000 0.000 0.200 0.378 0.000 0.000 0.100 0.378 0.000 0.000 0.050 0.378 0.000 0.000 0.020 0.378 0.000 0.000 0.010 0.378 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) for the WITHIN level 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 0.252 0.000 0.000 0.300 0.116 0.000 0.000 0.200 0.084 0.000 0.000 0.100 0.038 0.000 0.000 0.050 0.022 0.000 0.000 0.020 0.018 0.000 0.000 0.010 0.012 0.000 0.000 SRMR (Standardized Root Mean Square Residual) for the BETWEEN level 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 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff Within Level Y ON X 1.000 0.9957 0.0630 0.0639 0.0040 0.948 1.000 Residual Variances Y 2.000 2.0052 0.1291 0.1281 0.0167 0.946 1.000 Between Level Means Y 0.000 -0.0035 0.1624 0.1485 0.0263 0.892 0.108 Variances Y 0.222 0.1932 0.1155 0.1045 0.0141 0.808 0.180 New/Additional Parameters ICC 0.100 0.0860 0.0458 0.0422 0.0023 0.812 0.498 QUALITY OF NUMERICAL RESULTS Average Condition Number for the Information Matrix 0.316E-02 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION FOR WITHIN NU Y X ________ ________ 1 0 0 LAMBDA Y X ________ ________ Y 0 0 X 0 0 THETA Y X ________ ________ Y 0 X 0 0 ALPHA Y X ________ ________ 1 0 0 BETA Y X ________ ________ Y 0 1 X 0 0 PSI Y X ________ ________ Y 2 X 0 0 PARAMETER SPECIFICATION FOR BETWEEN NU Y X ________ ________ 1 0 0 LAMBDA Y X ________ ________ Y 0 0 X 0 0 THETA Y X ________ ________ Y 0 X 0 0 ALPHA Y X ________ ________ 1 3 0 BETA Y X ________ ________ Y 0 0 X 0 0 PSI Y X ________ ________ Y 4 X 0 0 PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS ICC ________ 1 5 STARTING VALUES FOR WITHIN NU Y X ________ ________ 1 0.000 0.000 LAMBDA Y X ________ ________ Y 1.000 0.000 X 0.000 1.000 THETA Y X ________ ________ Y 0.000 X 0.000 0.000 ALPHA Y X ________ ________ 1 0.000 0.000 BETA Y X ________ ________ Y 0.000 1.000 X 0.000 0.000 PSI Y X ________ ________ Y 2.000 X 0.000 0.500 STARTING VALUES FOR BETWEEN NU Y X ________ ________ 1 0.000 0.000 LAMBDA Y X ________ ________ Y 1.000 0.000 X 0.000 1.000 THETA Y X ________ ________ Y 0.000 X 0.000 0.000 ALPHA Y X ________ ________ 1 0.000 0.000 BETA Y X ________ ________ Y 0.000 0.000 X 0.000 0.000 PSI Y X ________ ________ Y 0.222 X 0.000 0.000 STARTING VALUES FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS ICC ________ 1 0.100 POPULATION VALUES FOR WITHIN NU Y X ________ ________ 1 0.000 0.000 LAMBDA Y X ________ ________ Y 1.000 0.000 X 0.000 1.000 THETA Y X ________ ________ Y 0.000 X 0.000 0.000 ALPHA Y X ________ ________ 1 0.000 0.000 BETA Y X ________ ________ Y 0.000 1.000 X 0.000 0.000 PSI Y X ________ ________ Y 2.000 X 0.000 1.000 POPULATION VALUES FOR BETWEEN NU Y X ________ ________ 1 0.000 0.000 LAMBDA Y X ________ ________ Y 1.000 0.000 X 0.000 1.000 THETA Y X ________ ________ Y 0.000 X 0.000 0.000 ALPHA Y X ________ ________ 1 0.000 0.000 BETA Y X ________ ________ Y 0.000 0.000 X 0.000 0.000 PSI Y X ________ ________ Y 0.222 X 0.000 0.000 TECHNICAL 9 OUTPUT Error messages for each replication (if any) Beginning Time: 12:54:31 Ending Time: 12:54:34 Elapsed Time: 00:00:03 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) 1998-2010 Muthen & Muthen