Mplus VERSION 6.11 MUTHEN & MUTHEN 10/24/2011 9:28 AM INPUT INSTRUCTIONS title: Nominal M, Continuous Y Using a latent class variable to represent M Simulating x-m interaction effect on y by class-varying y on x Step 2: External Monte Carlo analysis data: file = n800xmreplist.dat; type = montecarlo; variable: names = y x m; usev = y x; classes = c(3); knownclass = c(m=1 m=2 m=3); analysis: type = mixture; estimator = ml; model: %overall% [c#1*-1] (gamma01); [c#2*-.5] (gamma02); c#1 on x*.7 (gamma11); c#2 on x*.3 (gamma12); y on x*0; y*.75; %c#1% [y*-2] (beta01); y on x*-.5 (beta11); %c#2% [y*0] (beta02); y on x*-.3 (beta12); %c#3% [y*2] (beta03); y on x*-.2 (beta13); model constraint: new(denom0*1.9744 denom1*2.5595 p10*.1863 p11*.2894 p20*.3072 p21*.3199 p30*.5065 p31*.3907 term11*-.1162 term10*.3538 term01*.2026 term00*.6404 de*-.2866 tie*-.47 total*-.7566 pie*-.4378); ! index is x' for multinomial denominator denom0=exp(gamma01)+exp(gamma02)+1; denom1=exp(gamma01+gamma11)+exp(gamma02+gamma12)+1; ! first index is class, second x' for probabilities p10=exp(gamma01)/denom0; p11=exp(gamma01+gamma11)/denom1; p20=exp(gamma02)/denom0; p21=exp(gamma02+gamma12)/denom1; p30=1/denom0; p31=1/denom1; ! first index is x, second x', summing over class term11=(beta01+beta11)*p11+(beta02+beta12)*p21+(beta03+beta13)*p31; term10=(beta01+beta11)*p10+(beta02+beta12)*p20+(beta03+beta13)*p30; term01=(beta01)*p11+(beta02)*p21+(beta03)*p31; term00=(beta01)*p10+(beta02)*p20+(beta03)*p30; de=term10-term00; tie=term11-term10; total=term11-term00; pie=term01-term00; INPUT READING TERMINATED NORMALLY Nominal M, Continuous Y Using a latent class variable to represent M Simulating x-m interaction effect on y by class-varying y on x Step 2: External Monte Carlo analysis SUMMARY OF ANALYSIS Number of groups 1 Average number of observations 800 Number of replications Requested 500 Completed 500 Number of dependent variables 1 Number of independent variables 1 Number of continuous latent variables 0 Number of categorical latent variables 1 Observed dependent variables Continuous Y Observed independent variables X Categorical latent variables C Knownclass C Estimator ML 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-06 Relative loglikelihood change 0.100D-06 Derivative 0.100D-05 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-05 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-05 Basis for M step termination ITERATION Maximum value for logit thresholds 15 Minimum value for logit thresholds -15 Minimum expected cell size for chi-square 0.100D-01 Optimization algorithm EMA Input data file(s) Multiple data files from n800xmreplist.dat Input data format FREE SAMPLE STATISTICS NOTE: These are average results over 500 data sets. SAMPLE STATISTICS Means Y X ________ ________ 1 0.260 0.500 Covariances Y X ________ ________ Y 3.627 X -0.187 0.250 Correlations Y X ________ ________ Y 1.000 X -0.197 1.000 MODEL FIT INFORMATION Number of Free Parameters 11 Loglikelihood H0 Value Mean -1860.902 Std Dev 20.791 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.992 -1909.268 -1907.743 0.980 0.980 -1903.600 -1904.753 0.950 0.950 -1895.101 -1896.282 0.900 0.900 -1887.548 -1887.949 0.800 0.802 -1878.400 -1878.653 0.700 0.712 -1871.805 -1871.233 0.500 0.502 -1860.902 -1860.896 0.300 0.314 -1849.999 -1849.327 0.200 0.200 -1843.404 -1843.578 0.100 0.092 -1834.256 -1835.095 0.050 0.048 -1826.703 -1827.316 0.020 0.012 -1818.204 -1820.489 0.010 0.010 -1812.536 -1818.004 Information Criteria Akaike (AIC) Mean 3743.804 Std Dev 41.582 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 3647.072 3643.719 0.980 0.988 3658.407 3662.122 0.950 0.952 3675.406 3676.110 0.900 0.908 3690.513 3691.070 0.800 0.800 3708.809 3708.554 0.700 0.686 3721.998 3720.594 0.500 0.498 3743.804 3743.759 0.300 0.288 3765.609 3763.878 0.200 0.198 3778.799 3778.568 0.100 0.100 3797.095 3796.963 0.050 0.050 3812.202 3812.098 0.020 0.020 3829.201 3827.927 0.010 0.008 3840.536 3836.739 Bayesian (BIC) Mean 3795.335 Std Dev 41.582 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 3698.603 3695.249 0.980 0.988 3709.938 3713.653 0.950 0.952 3726.937 3727.641 0.900 0.908 3742.043 3742.601 0.800 0.800 3760.339 3760.085 0.700 0.686 3773.529 3772.125 0.500 0.498 3795.335 3795.290 0.300 0.288 3817.140 3815.409 0.200 0.198 3830.330 3830.099 0.100 0.100 3848.626 3848.493 0.050 0.050 3863.733 3863.629 0.020 0.020 3880.731 3879.457 0.010 0.008 3892.067 3888.270 Sample-Size Adjusted BIC (n* = (n + 2) / 24) Mean 3760.404 Std Dev 41.582 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 3663.672 3660.318 0.980 0.988 3675.007 3678.722 0.950 0.952 3692.006 3692.710 0.900 0.908 3707.112 3707.670 0.800 0.800 3725.408 3725.154 0.700 0.686 3738.598 3737.194 0.500 0.498 3760.404 3760.358 0.300 0.288 3782.209 3780.478 0.200 0.198 3795.399 3795.168 0.100 0.100 3813.695 3813.562 0.050 0.050 3828.802 3828.698 0.020 0.020 3845.800 3844.526 0.010 0.008 3857.135 3853.338 Entropy 1.000 FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES BASED ON THE ESTIMATED MODEL Latent Classes 1 190.73400 0.23842 2 251.46200 0.31433 3 357.80400 0.44726 FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS BASED ON ESTIMATED POSTERIOR PROBABILITIES Latent Classes 1 190.73400 0.23842 2 251.46200 0.31433 3 357.80400 0.44726 CLASSIFICATION QUALITY Entropy 1.000 CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP Class Counts and Proportions Latent Classes 1 191 0.23842 2 251 0.31433 3 358 0.44726 Average Latent Class Probabilities for Most Likely Latent Class Membership (Row) by Latent Class (Column) 1 2 3 1 1.000 0.000 0.000 2 0.000 1.000 0.000 3 0.000 0.000 1.000 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff Latent Class 1 Y ON X -0.500 -0.5045 0.1332 0.1285 0.0177 0.944 0.972 Intercepts Y -2.000 -2.0007 0.1011 0.1001 0.0102 0.958 1.000 Residual Variances Y 0.750 0.7465 0.0360 0.0373 0.0013 0.954 1.000 Latent Class 2 Y ON X -0.300 -0.2976 0.1125 0.1093 0.0126 0.942 0.772 Intercepts Y 0.000 0.0021 0.0799 0.0780 0.0064 0.944 0.056 Residual Variances Y 0.750 0.7465 0.0360 0.0373 0.0013 0.954 1.000 Latent Class 3 Y ON X -0.200 -0.1948 0.0917 0.0923 0.0084 0.954 0.554 Intercepts Y 2.000 2.0002 0.0629 0.0609 0.0039 0.936 1.000 Residual Variances Y 0.750 0.7465 0.0360 0.0373 0.0013 0.954 1.000 Categorical Latent Variables C#1 ON X 0.700 0.6916 0.1667 0.1832 0.0278 0.966 0.982 C#2 ON X 0.300 0.2982 0.1693 0.1656 0.0286 0.946 0.426 Intercepts C#1 -1.000 -0.9920 0.1233 0.1357 0.0152 0.962 1.000 C#2 -0.500 -0.4950 0.1142 0.1146 0.0130 0.966 0.998 New/Additional Parameters DENOM0 1.974 1.9872 0.0950 0.0989 0.0092 0.964 1.000 DENOM1 2.559 2.5729 0.1614 0.1617 0.0262 0.966 1.000 P10 0.186 0.1877 0.0178 0.0195 0.0003 0.970 1.000 P11 0.289 0.2892 0.0216 0.0226 0.0005 0.964 1.000 P20 0.307 0.3080 0.0230 0.0231 0.0005 0.954 1.000 P21 0.320 0.3207 0.0233 0.0233 0.0005 0.960 1.000 P30 0.507 0.5044 0.0240 0.0250 0.0006 0.968 1.000 P31 0.391 0.3902 0.0241 0.0244 0.0006 0.962 1.000 TERM11 -0.116 -0.1148 0.0936 0.0981 0.0088 0.960 0.214 TERM10 0.354 0.3494 0.0944 0.0940 0.0089 0.952 0.956 TERM01 0.203 0.2028 0.0906 0.0934 0.0082 0.956 0.592 TERM00 0.640 0.6340 0.0850 0.0882 0.0072 0.960 1.000 DE -0.287 -0.2846 0.0640 0.0627 0.0041 0.928 0.992 TIE -0.470 -0.4642 0.1114 0.1213 0.0124 0.958 0.974 TOTAL -0.757 -0.7488 0.1196 0.1319 0.0143 0.980 1.000 PIE -0.438 -0.4312 0.1040 0.1131 0.0108 0.966 0.972 QUALITY OF NUMERICAL RESULTS Average Condition Number for the Information Matrix 0.114E-02 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION FOR LATENT CLASS 1 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 1 0 BETA Y X ________ ________ Y 0 2 X 0 0 PSI Y X ________ ________ Y 3 X 0 0 PARAMETER SPECIFICATION FOR LATENT CLASS 2 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 4 0 BETA Y X ________ ________ Y 0 5 X 0 0 PSI Y X ________ ________ Y 3 X 0 0 PARAMETER SPECIFICATION FOR LATENT CLASS 3 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 6 0 BETA Y X ________ ________ Y 0 7 X 0 0 PSI Y X ________ ________ Y 3 X 0 0 PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART ALPHA(C) C#1 C#2 C#3 ________ ________ ________ 1 8 9 0 GAMMA(C) X ________ C#1 10 C#2 11 C#3 0 PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS DENOM0 DENOM1 P10 P11 P20 ________ ________ ________ ________ ________ 1 12 13 14 15 16 NEW/ADDITIONAL PARAMETERS P21 P30 P31 TERM11 TERM10 ________ ________ ________ ________ ________ 1 17 18 19 20 21 NEW/ADDITIONAL PARAMETERS TERM01 TERM00 DE TIE TOTAL ________ ________ ________ ________ ________ 1 22 23 24 25 26 NEW/ADDITIONAL PARAMETERS PIE ________ 1 27 STARTING VALUES FOR LATENT CLASS 1 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 -2.000 0.000 BETA Y X ________ ________ Y 0.000 -0.500 X 0.000 0.000 PSI Y X ________ ________ Y 0.750 X 0.000 0.500 STARTING VALUES FOR LATENT CLASS 2 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 -0.300 X 0.000 0.000 PSI Y X ________ ________ Y 0.750 X 0.000 0.500 STARTING VALUES FOR LATENT CLASS 3 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 2.000 0.000 BETA Y X ________ ________ Y 0.000 -0.200 X 0.000 0.000 PSI Y X ________ ________ Y 0.750 X 0.000 0.500 STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART ALPHA(C) C#1 C#2 C#3 ________ ________ ________ 1 -1.000 -0.500 0.000 GAMMA(C) X ________ C#1 0.700 C#2 0.300 C#3 0.000 STARTING VALUES FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS DENOM0 DENOM1 P10 P11 P20 ________ ________ ________ ________ ________ 1 1.974 2.559 0.186 0.289 0.307 NEW/ADDITIONAL PARAMETERS P21 P30 P31 TERM11 TERM10 ________ ________ ________ ________ ________ 1 0.320 0.507 0.391 -0.116 0.354 NEW/ADDITIONAL PARAMETERS TERM01 TERM00 DE TIE TOTAL ________ ________ ________ ________ ________ 1 0.203 0.640 -0.287 -0.470 -0.757 NEW/ADDITIONAL PARAMETERS PIE ________ 1 -0.438 Beginning Time: 09:28:02 Ending Time: 09:28:18 Elapsed Time: 00:00:16 MUTHEN & 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