Mplus DEVELOPMENT (inDev 2/4/2008) MUTHEN & MUTHEN 02/08/2008 8:33 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); 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; estimator = wlsm; process = 4; 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; [sw*.5]; %BETWEEN% w@1; ib | u1@1 u2@1 u3@1 u4@1; [u1$1-u4$1*0]; ib ON w*.5; [ib@0]; ib*.5; u1-u4@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; [sw*.5]; %BETWEEN% ib | u1@1 u2@1 u3@1 u4@1; [u1$1-u4$1*0] (1); ib ON w*.5; [ib@0]; ib*.5; u1-u4@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 486 Value of seed 58459 Number of dependent variables 4 Number of independent variables 2 Number of continuous latent variables 3 Observed dependent variables Binary and ordered categorical (ordinal) U1 U2 U3 U4 Observed independent variables X W Continuous latent variables IW SW IB Variables with special functions Within variables X Between variables W Estimator WLSM Optimization Specifications for the Quasi-Newton Algorithm for Continuous Outcomes Maximum number of iterations 1000 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 FS Integration Specifications Type STANDARD Number of integration points 7 Dimensions of numerical integration 2 Adaptive quadrature ON Random Starts Specifications Number of random starts 10 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. ESTIMATED SAMPLE STATISTICS MEANS/INTERCEPTS/THRESHOLDS U1$1 U2$1 U3$1 U4$1 ________ ________ ________ ________ 1 -0.081 -0.377 -0.454 -0.530 SLOPES X W ________ ________ U1 0.699 0.448 U2 0.708 0.433 U3 0.629 0.260 U4 0.504 0.325 WITHIN LEVEL VARIANCE/COVARIANCE U1 U2 U3 U4 ________ ________ ________ ________ U1 1.000 U2 0.372 1.000 U3 0.325 0.556 1.000 U4 0.329 0.609 0.781 1.000 WITHIN LEVEL CORRELATION U1 U2 U3 U4 ________ ________ ________ ________ U1 1.000 U2 0.372 1.000 U3 0.325 0.556 1.000 U4 0.329 0.609 0.781 1.000 BETWEEN LEVEL VARIANCE/COVARIANCE U1 U2 U3 U4 ________ ________ ________ ________ U1 0.319 U2 0.229 0.165 U3 0.176 0.127 0.100 U4 0.139 0.118 0.080 0.089 BETWEEN LEVEL CORRELATION U1 U2 U3 U4 ________ ________ ________ ________ U1 1.000 U2 0.997 1.000 U3 0.987 0.987 1.000 U4 0.823 0.969 0.851 1.000 TESTS OF MODEL FIT Number of Free Parameters 9 Chi-Square Test of Model Fit Degrees of freedom 19 Mean 16.546 Std Dev 7.630 Number of successful computations 486 Proportions Percentiles Expected Observed Expected Observed 0.990 0.905 7.633 3.935 0.980 0.860 8.567 4.942 0.950 0.794 10.117 6.638 0.900 0.698 11.651 7.757 0.800 0.597 13.716 9.826 0.700 0.498 15.352 11.618 0.500 0.350 18.338 15.252 0.300 0.230 21.689 19.713 0.200 0.169 23.900 23.042 0.100 0.088 27.204 26.398 0.050 0.051 30.144 30.026 0.020 0.027 33.687 36.076 0.010 0.021 36.191 37.918 RMSEA (Root Mean Square Error Of Approximation) Mean 0.008 Std Dev 0.013 Number of successful computations 486 Proportions Percentiles Expected Observed Expected Observed 0.990 1.000 -0.022 0.000 0.980 1.000 -0.018 0.000 0.950 1.000 -0.013 0.000 0.900 1.000 -0.009 0.000 0.800 1.000 -0.003 0.000 0.700 0.319 0.001 0.000 0.500 0.307 0.008 0.000 0.300 0.251 0.014 0.009 0.200 0.222 0.018 0.021 0.100 0.148 0.024 0.028 0.050 0.097 0.029 0.034 0.020 0.056 0.034 0.042 0.010 0.031 0.037 0.045 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 1.0269 0.1328 0.1390 0.0183 0.959 1.000 SW ON X 0.200 0.2223 0.0927 0.0898 0.0091 0.942 0.718 SW WITH IW 0.000 0.0058 0.1568 0.1481 0.0246 0.926 0.074 Intercepts SW 0.500 0.5226 0.0828 0.0772 0.0074 0.934 1.000 Residual Variances IW 1.000 1.1428 0.4312 0.4216 0.2060 0.951 0.891 SW 0.500 0.5690 0.1735 0.1666 0.0348 0.953 0.998 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 IB ON W 0.500 0.5204 0.1431 0.1439 0.0208 0.951 0.961 Intercepts IB 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 Thresholds U1$1 0.000 -0.0071 0.1395 0.1377 0.0195 0.938 0.062 U2$1 0.000 -0.0071 0.1395 0.1377 0.0195 0.938 0.062 U3$1 0.000 -0.0071 0.1395 0.1377 0.0195 0.938 0.062 U4$1 0.000 -0.0071 0.1395 0.1377 0.0195 0.938 0.062 Residual Variances U1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 U2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 U3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 U4 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000 IB 0.500 0.4206 0.1950 0.1866 0.0443 0.827 0.712 QUALITY OF NUMERICAL RESULTS Average Condition Number for the Information Matrix 0.641E-02 (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 X W ________ ________ ________ ________ ________ 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 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 X W ________ ________ ________ ________ ________ 1 0 1 0 0 0 BETA IW SW IB X W ________ ________ ________ ________ ________ IW 0 0 0 2 0 SW 0 0 0 3 0 IB 0 0 0 0 0 X 0 0 0 0 0 W 0 0 0 0 0 PSI IW SW IB X W ________ ________ ________ ________ ________ IW 4 SW 5 6 IB 0 0 0 X 0 0 0 0 W 0 0 0 0 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 X W ________ ________ ________ ________ ________ 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 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 X W ________ ________ ________ ________ ________ 1 0 0 0 0 0 BETA IW SW IB X W ________ ________ ________ ________ ________ IW 0 0 0 0 0 SW 0 0 0 0 0 IB 0 0 0 0 7 X 0 0 0 0 0 W 0 0 0 0 0 PSI IW SW IB X W ________ ________ ________ ________ ________ IW 0 SW 0 0 IB 0 0 8 X 0 0 0 0 W 0 0 0 0 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 X W ________ ________ ________ ________ ________ 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 1.000 0.000 W 0.000 0.000 0.000 0.000 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 X W ________ ________ ________ ________ ________ 1 0.000 0.500 0.000 0.000 0.000 BETA IW SW IB X W ________ ________ ________ ________ ________ IW 0.000 0.000 0.000 1.000 0.000 SW 0.000 0.000 0.000 0.200 0.000 IB 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 PSI IW SW IB X W ________ ________ ________ ________ ________ IW 1.000 SW 0.000 0.500 IB 0.000 0.000 0.000 X 0.000 0.000 0.000 0.500 W 0.000 0.000 0.000 0.000 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 X W ________ ________ ________ ________ ________ U1 0.000 0.000 1.000 0.000 0.000 U2 0.000 0.000 1.000 0.000 0.000 U3 0.000 0.000 1.000 0.000 0.000 U4 0.000 0.000 1.000 0.000 0.000 X 0.000 0.000 0.000 1.000 0.000 W 0.000 0.000 0.000 0.000 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 X W ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 BETA IW SW IB X W ________ ________ ________ ________ ________ 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 0.500 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 PSI IW SW IB X W ________ ________ ________ ________ ________ IW 0.000 SW 0.000 0.000 IB 0.000 0.000 0.500 X 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 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 X W ________ ________ ________ ________ ________ 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 1.000 0.000 W 0.000 0.000 0.000 0.000 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 X W ________ ________ ________ ________ ________ 1 0.000 0.500 0.000 0.000 0.000 BETA IW SW IB X W ________ ________ ________ ________ ________ IW 0.000 0.000 0.000 1.000 0.000 SW 0.000 0.000 0.000 0.200 0.000 IB 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 PSI IW SW IB X W ________ ________ ________ ________ ________ IW 1.000 SW 0.000 0.500 IB 0.000 0.000 0.000 X 0.000 0.000 0.000 1.000 W 0.000 0.000 0.000 0.000 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 X W ________ ________ ________ ________ ________ U1 0.000 0.000 1.000 0.000 0.000 U2 0.000 0.000 1.000 0.000 0.000 U3 0.000 0.000 1.000 0.000 0.000 U4 0.000 0.000 1.000 0.000 0.000 X 0.000 0.000 0.000 1.000 0.000 W 0.000 0.000 0.000 0.000 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 X W ________ ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 0.000 BETA IW SW IB X W ________ ________ ________ ________ ________ 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 0.500 X 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 PSI IW SW IB X W ________ ________ ________ ________ ________ IW 0.000 SW 0.000 0.000 IB 0.000 0.000 0.500 X 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 1.000 TECHNICAL 9 OUTPUT Error messages for each replication (if any) REPLICATION 23: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U3. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 77: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U3. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 90: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U2. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 147: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U3. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 176: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U3. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 189: CONVERGENCE PROBLEMS OCCURED IN THE BIVARIATE ESTIMATION OF VARIABLES U1 AND U3. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 219: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U4. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 279: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U4. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 323: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U4. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 344: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U4. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 368: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U4. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 396: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U3. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 417: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U4. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. REPLICATION 499: CONVERGENCE PROBLEMS OCCURED IN THE UNIVARIATE ESTIMATION OF VARIABLE U4. THE SAMPLE STATISTICS COULD NOT BE COMPUTED. Beginning Time: 20:33:09 Ending Time: 06:30:16 Elapsed Time: 14:02:53 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) 1998-2007 Muthen & Muthen