Mplus DEVELOPMENT (inDev 1/29/2008) MUTHEN & MUTHEN 02/09/2008 2:38 PM INPUT INSTRUCTIONS TITLE: this is an example of a two-level growth model for a categorical outcome (three-level analysis). montecarlo: names are u1-u4 x w; generate = u1-u4(1 p); categorical = u1-u4; nobservations = 500; ncsizes = 1; csizes = 50(10); seed = 58459; nreps = 500; within = x; between = w; ! save = ex9.13.dat; ANALYSIS: TYPE = TWOLEVEL; ! integration = 7; process = 4; link = probit; MODEL POPULATION: %WITHIN% x@1; iw sw | u1@0 u2@1 u3@2 u4@3; iw ON x*1; sw ON x*.2; iw*1; sw*.5; %BETWEEN% w@1; ib sb | u1@0 u2@1 u3@2 u4@3; [u1$1-u4$1*0]; ib ON w*.5; [ib@0]; ib*.5; [sb*.5]; sb@0; MODEL: %WITHIN% iw sw | u1@0 u2@1 u3@2 u4@3; iw ON x*1; sw ON x*.2; iw*1; sw*.5; %BETWEEN% ib sb | u1@0 u2@1 u3@2 u4@3; [u1$1-u4$1*0] (1); ib ON w*.5; [ib@0]; ib*.5; [sb*.5]; sb@0; output: tech9; INPUT READING TERMINATED NORMALLY this is an example of a two-level growth model for a categorical outcome (three-level analysis). SUMMARY OF ANALYSIS Number of groups 1 Number of observations 500 Number of replications Requested 500 Completed 500 Value of seed 58459 Number of dependent variables 4 Number of independent variables 2 Number of continuous latent variables 4 Observed dependent variables Binary and ordered categorical (ordinal) U1 U2 U3 U4 Observed independent variables X W Continuous latent variables IW SW IB SB Variables with special functions Within variables X Between variables W Estimator MLR Information matrix OBSERVED Optimization Specifications for the Quasi-Newton Algorithm for Continuous Outcomes Maximum number of iterations 100 Convergence criterion 0.100D-05 Optimization Specifications for the EM Algorithm Maximum number of iterations 500 Convergence criteria Loglikelihood change 0.100D-02 Relative loglikelihood change 0.100D-05 Derivative 0.100D-02 Optimization Specifications for the M step of the EM Algorithm for Categorical Latent variables Number of M step iterations 1 M step convergence criterion 0.100D-02 Basis for M step termination ITERATION Optimization Specifications for the M step of the EM Algorithm for Censored, Binary or Ordered Categorical (Ordinal), Unordered Categorical (Nominal) and Count Outcomes Number of M step iterations 1 M step convergence criterion 0.100D-02 Basis for M step termination ITERATION Maximum value for logit thresholds 10 Minimum value for logit thresholds -10 Minimum expected cell size for chi-square 0.100D-01 Optimization algorithm EMA Integration Specifications Type STANDARD Number of integration points 15 Dimensions of numerical integration 3 Adaptive quadrature ON Link PROBIT Cholesky ON SUMMARY OF DATA FOR THE FIRST REPLICATION Cluster information Size (s) Number of clusters of Size s 10 50 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. SAMPLE STATISTICS Means X W ________ ________ 1 0.044 0.196 Covariances X W ________ ________ X 1.043 W 0.009 0.794 Correlations X W ________ ________ X 1.000 W 0.010 1.000 TESTS OF MODEL FIT Number of Free Parameters 9 Loglikelihood H0 Value Mean -919.139 Std Dev 33.419 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 -996.881 -1001.917 0.980 0.982 -987.771 -987.588 0.950 0.950 -974.110 -975.202 0.900 0.896 -961.969 -963.236 0.800 0.802 -947.264 -947.378 0.700 0.704 -936.664 -936.367 0.500 0.484 -919.139 -920.499 0.300 0.296 -901.614 -901.924 0.200 0.214 -891.014 -889.350 0.100 0.106 -876.310 -875.322 0.050 0.044 -864.169 -865.019 0.020 0.022 -850.507 -848.825 0.010 0.014 -841.397 -839.181 Information Criteria Akaike (AIC) Mean 1856.278 Std Dev 66.838 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.986 1700.794 1693.495 0.980 0.978 1719.014 1708.989 0.950 0.956 1746.337 1747.933 0.900 0.894 1770.619 1767.596 0.800 0.786 1800.028 1795.940 0.700 0.704 1821.229 1821.568 0.500 0.516 1856.278 1858.603 0.300 0.296 1891.328 1889.932 0.200 0.198 1912.529 1911.239 0.100 0.104 1941.937 1943.467 0.050 0.050 1966.219 1965.949 0.020 0.018 1993.542 1989.742 0.010 0.010 2011.762 2007.276 Bayesian (BIC) Mean 1894.210 Std Dev 66.838 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.986 1738.725 1731.427 0.980 0.978 1756.945 1746.921 0.950 0.956 1784.269 1785.864 0.900 0.894 1808.551 1805.528 0.800 0.786 1837.959 1833.872 0.700 0.704 1859.160 1859.499 0.500 0.516 1894.210 1896.534 0.300 0.296 1929.259 1927.864 0.200 0.198 1950.460 1949.171 0.100 0.104 1979.869 1981.398 0.050 0.050 2004.151 2003.880 0.020 0.018 2031.474 2027.673 0.010 0.010 2049.694 2045.207 Sample-Size Adjusted BIC (n* = (n + 2) / 24) Mean 1865.643 Std Dev 66.838 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.986 1710.159 1702.860 0.980 0.978 1728.379 1718.354 0.950 0.956 1755.702 1757.298 0.900 0.894 1779.984 1776.961 0.800 0.786 1809.393 1805.305 0.700 0.704 1830.593 1830.933 0.500 0.516 1865.643 1867.968 0.300 0.296 1900.693 1899.297 0.200 0.198 1921.894 1920.604 0.100 0.104 1951.302 1952.832 0.050 0.050 1975.584 1975.314 0.020 0.018 2002.907 1999.107 0.010 0.010 2021.127 2016.641 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff Within Level IW | U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 U3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 U4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 SW | U1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 U3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000 U4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000 IW ON X 1.000 1.0045 0.1230 0.1206 0.0151 0.924 1.000 SW ON X 0.200 0.1964 0.0769 0.0749 0.0059 0.940 0.746 SW WITH IW 0.000 -0.0074 0.1322 0.1315 0.0175 0.930 0.070 Residual Variances IW 1.000 1.0227 0.3463 0.3588 0.1202 0.944 0.948 SW 0.500 0.5048 0.1426 0.1362 0.0203 0.918 1.000 Between Level IB | U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 U3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 U4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 SB | U1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000 U3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000 U4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000 IB ON W 0.500 0.5026 0.1334 0.1256 0.0178 0.924 0.968 Means SB 0.500 0.4988 0.0691 0.0669 0.0048 0.946 1.000 Intercepts IB 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Thresholds U1$1 0.000 -0.0031 0.1306 0.1270 0.0170 0.946 0.054 U2$1 0.000 -0.0031 0.1306 0.1270 0.0170 0.946 0.054 U3$1 0.000 -0.0031 0.1306 0.1270 0.0170 0.946 0.054 U4$1 0.000 -0.0031 0.1306 0.1270 0.0170 0.946 0.054 Variances SB 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Residual Variances IB 0.500 0.4555 0.1681 0.1584 0.0302 0.866 0.958 QUALITY OF NUMERICAL RESULTS Average Condition Number for the Information Matrix 0.255E-01 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION FOR WITHIN TAU U1$1 U2$1 U3$1 U4$1 ________ ________ ________ ________ 1 0 0 0 0 NU U1 U2 U3 U4 X ________ ________ ________ ________ ________ 1 0 0 0 0 0 NU W ________ 1 0 LAMBDA IW SW IB SB X ________ ________ ________ ________ ________ U1 0 0 0 0 0 U2 0 0 0 0 0 U3 0 0 0 0 0 U4 0 0 0 0 0 X 0 0 0 0 0 W 0 0 0 0 0 LAMBDA W ________ U1 0 U2 0 U3 0 U4 0 X 0 W 0 THETA U1 U2 U3 U4 X ________ ________ ________ ________ ________ U1 0 U2 0 0 U3 0 0 0 U4 0 0 0 0 X 0 0 0 0 0 W 0 0 0 0 0 THETA W ________ W 0 ALPHA IW SW IB SB X ________ ________ ________ ________ ________ 1 0 0 0 0 0 ALPHA W ________ 1 0 BETA IW SW IB SB X ________ ________ ________ ________ ________ IW 0 0 0 0 1 SW 0 0 0 0 2 IB 0 0 0 0 0 SB 0 0 0 0 0 X 0 0 0 0 0 W 0 0 0 0 0 BETA W ________ IW 0 SW 0 IB 0 SB 0 X 0 W 0 PSI IW SW IB SB X ________ ________ ________ ________ ________ IW 3 SW 4 5 IB 0 0 0 SB 0 0 0 0 X 0 0 0 0 0 W 0 0 0 0 0 PSI W ________ W 0 PARAMETER SPECIFICATION FOR BETWEEN TAU U1$1 U2$1 U3$1 U4$1 ________ ________ ________ ________ 1 9 9 9 9 NU U1 U2 U3 U4 X ________ ________ ________ ________ ________ 1 0 0 0 0 0 NU W ________ 1 0 LAMBDA IW SW IB SB X ________ ________ ________ ________ ________ U1 0 0 0 0 0 U2 0 0 0 0 0 U3 0 0 0 0 0 U4 0 0 0 0 0 X 0 0 0 0 0 W 0 0 0 0 0 LAMBDA W ________ U1 0 U2 0 U3 0 U4 0 X 0 W 0 THETA U1 U2 U3 U4 X ________ ________ ________ ________ ________ U1 0 U2 0 0 U3 0 0 0 U4 0 0 0 0 X 0 0 0 0 0 W 0 0 0 0 0 THETA W ________ W 0 ALPHA IW SW IB SB X ________ ________ ________ ________ ________ 1 0 0 0 6 0 ALPHA W ________ 1 0 BETA IW SW IB SB X ________ ________ ________ ________ ________ IW 0 0 0 0 0 SW 0 0 0 0 0 IB 0 0 0 0 0 SB 0 0 0 0 0 X 0 0 0 0 0 W 0 0 0 0 0 BETA W ________ IW 0 SW 0 IB 7 SB 0 X 0 W 0 PSI IW SW IB SB X ________ ________ ________ ________ ________ IW 0 SW 0 0 IB 0 0 8 SB 0 0 0 0 X 0 0 0 0 0 W 0 0 0 0 0 PSI W ________ W 0 STARTING VALUES FOR WITHIN TAU U1$1 U2$1 U3$1 U4$1 ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 NU U1 U2 U3 U4 X ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU W ________ 1 0.000 LAMBDA IW SW IB SB X ________ ________ ________ ________ ________ U1 1.000 0.000 0.000 0.000 0.000 U2 1.000 1.000 0.000 0.000 0.000 U3 1.000 2.000 0.000 0.000 0.000 U4 1.000 3.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 1.000 W 0.000 0.000 0.000 0.000 0.000 LAMBDA W ________ U1 0.000 U2 0.000 U3 0.000 U4 0.000 X 0.000 W 1.000 THETA U1 U2 U3 U4 X ________ ________ ________ ________ ________ U1 1.000 U2 0.000 1.000 U3 0.000 0.000 1.000 U4 0.000 0.000 0.000 1.000 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 THETA W ________ W 0.000 ALPHA IW SW IB SB X ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 ALPHA W ________ 1 0.000 BETA IW SW IB SB X ________ ________ ________ ________ ________ IW 0.000 0.000 0.000 0.000 1.000 SW 0.000 0.000 0.000 0.000 0.200 IB 0.000 0.000 0.000 0.000 0.000 SB 0.000 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 BETA W ________ IW 0.000 SW 0.000 IB 0.000 SB 0.000 X 0.000 W 0.000 PSI IW SW IB SB X ________ ________ ________ ________ ________ IW 1.000 SW 0.000 0.500 IB 0.000 0.000 0.000 SB 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.500 W 0.000 0.000 0.000 0.000 0.000 PSI W ________ W 0.000 STARTING VALUES FOR BETWEEN TAU U1$1 U2$1 U3$1 U4$1 ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 NU U1 U2 U3 U4 X ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU W ________ 1 0.000 LAMBDA IW SW IB SB X ________ ________ ________ ________ ________ U1 0.000 0.000 1.000 0.000 0.000 U2 0.000 0.000 1.000 1.000 0.000 U3 0.000 0.000 1.000 2.000 0.000 U4 0.000 0.000 1.000 3.000 0.000 X 0.000 0.000 0.000 0.000 1.000 W 0.000 0.000 0.000 0.000 0.000 LAMBDA W ________ U1 0.000 U2 0.000 U3 0.000 U4 0.000 X 0.000 W 1.000 THETA U1 U2 U3 U4 X ________ ________ ________ ________ ________ U1 0.000 U2 0.000 0.000 U3 0.000 0.000 0.000 U4 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 THETA W ________ W 0.000 ALPHA IW SW IB SB X ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.500 0.000 ALPHA W ________ 1 0.000 BETA IW SW IB SB X ________ ________ ________ ________ ________ IW 0.000 0.000 0.000 0.000 0.000 SW 0.000 0.000 0.000 0.000 0.000 IB 0.000 0.000 0.000 0.000 0.000 SB 0.000 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 BETA W ________ IW 0.000 SW 0.000 IB 0.500 SB 0.000 X 0.000 W 0.000 PSI IW SW IB SB X ________ ________ ________ ________ ________ IW 0.000 SW 0.000 0.000 IB 0.000 0.000 0.500 SB 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 PSI W ________ W 0.500 POPULATION VALUES FOR WITHIN TAU U1$1 U2$1 U3$1 U4$1 ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 NU U1 U2 U3 U4 X ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU W ________ 1 0.000 LAMBDA IW SW IB SB X ________ ________ ________ ________ ________ U1 1.000 0.000 0.000 0.000 0.000 U2 1.000 1.000 0.000 0.000 0.000 U3 1.000 2.000 0.000 0.000 0.000 U4 1.000 3.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 1.000 W 0.000 0.000 0.000 0.000 0.000 LAMBDA W ________ U1 0.000 U2 0.000 U3 0.000 U4 0.000 X 0.000 W 1.000 THETA U1 U2 U3 U4 X ________ ________ ________ ________ ________ U1 0.000 U2 0.000 0.000 U3 0.000 0.000 0.000 U4 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 THETA W ________ W 0.000 ALPHA IW SW IB SB X ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 ALPHA W ________ 1 0.000 BETA IW SW IB SB X ________ ________ ________ ________ ________ IW 0.000 0.000 0.000 0.000 1.000 SW 0.000 0.000 0.000 0.000 0.200 IB 0.000 0.000 0.000 0.000 0.000 SB 0.000 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 BETA W ________ IW 0.000 SW 0.000 IB 0.000 SB 0.000 X 0.000 W 0.000 PSI IW SW IB SB X ________ ________ ________ ________ ________ IW 1.000 SW 0.000 0.500 IB 0.000 0.000 0.000 SB 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 1.000 W 0.000 0.000 0.000 0.000 0.000 PSI W ________ W 0.000 POPULATION VALUES FOR BETWEEN TAU U1$1 U2$1 U3$1 U4$1 ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 NU U1 U2 U3 U4 X ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 NU W ________ 1 0.000 LAMBDA IW SW IB SB X ________ ________ ________ ________ ________ U1 0.000 0.000 1.000 0.000 0.000 U2 0.000 0.000 1.000 1.000 0.000 U3 0.000 0.000 1.000 2.000 0.000 U4 0.000 0.000 1.000 3.000 0.000 X 0.000 0.000 0.000 0.000 1.000 W 0.000 0.000 0.000 0.000 0.000 LAMBDA W ________ U1 0.000 U2 0.000 U3 0.000 U4 0.000 X 0.000 W 1.000 THETA U1 U2 U3 U4 X ________ ________ ________ ________ ________ U1 0.000 U2 0.000 0.000 U3 0.000 0.000 0.000 U4 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 THETA W ________ W 0.000 ALPHA IW SW IB SB X ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.500 0.000 ALPHA W ________ 1 0.000 BETA IW SW IB SB X ________ ________ ________ ________ ________ IW 0.000 0.000 0.000 0.000 0.000 SW 0.000 0.000 0.000 0.000 0.000 IB 0.000 0.000 0.000 0.000 0.000 SB 0.000 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 BETA W ________ IW 0.000 SW 0.000 IB 0.500 SB 0.000 X 0.000 W 0.000 PSI IW SW IB SB X ________ ________ ________ ________ ________ IW 0.000 SW 0.000 0.000 IB 0.000 0.000 0.500 SB 0.000 0.000 0.000 0.000 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 PSI W ________ W 1.000 TECHNICAL 9 OUTPUT Error messages for each replication (if any) Beginning Time: 14:38:11 Ending Time: 20:08:24 Elapsed Time: 05:30:13 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) 1998-2008 Muthen & Muthen