Mplus VERSION 6.11 MUTHEN & MUTHEN 10/24/2011 9:29 AM INPUT INSTRUCTIONS title: Nominal M, Binary Y Using a latent class variable to represent M data: file = nombin.dat; variable: names = x m y w; freqweight = w; usev = y x; categorical = y; classes = c(3); knownclass = c(m=1 m=2 m=3); analysis: type = mixture; estimator = ml; model: %overall% [c#1] (gamma01); [c#2] (gamma02); c#1 on x (gamma11); c#2 on x (gamma12); y on x; %c#1% [y\$1] (beta01); y on x (beta11); %c#2% [y\$1] (beta02); y on x (beta12); %c#3% [y\$1] (beta03); y on x (beta13); model constraint: new(denom0 denom1 p10 p11 p20 p21 p30 p31 term11 term10 term01 term00 de tie total pie orde ortie orpie); ! 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=(1/(1+exp(beta01-beta11)))*p11+(1/(1+exp(beta02-beta12)))*p21 +(1/(1+exp(beta03-beta13)))*p31; term10=(1/(1+exp(beta01-beta11)))*p10+(1/(1+exp(beta02-beta12)))*p20 +(1/(1+exp(beta03-beta13)))*p30; term01=(1/(1+exp(beta01)))*p11+(1/(1+exp(beta02)))*p21 +(1/(1+exp(beta03)))*p31; term00=(1/(1+exp(beta01)))*p10+(1/(1+exp(beta02)))*p20 +(1/(1+exp(beta03)))*p30; de=term10-term00; tie=term11-term10; total=term11-term00; pie=term01-term00; orde=(term10/(1-term10))/(term00/(1-term00)); ortie=(term11/(1-term11))/(term10/(1-term10)); orpie=(term01/(1-term01))/(term00/(1-term00)); output: tech1 tech8; INPUT READING TERMINATED NORMALLY Nominal M, Binary Y Using a latent class variable to represent M SUMMARY OF ANALYSIS Number of groups 1 Number of observations 480 Number of patterns 12 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 Binary and ordered categorical (ordinal) Y Observed independent variables X Categorical latent variables C Knownclass C Variables with special functions Weight variable W 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 Link LOGIT Input data file(s) nombin.dat Input data format FREE UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES Y Category 1 0.375 180.000 Category 2 0.625 300.000 THE MODEL ESTIMATION TERMINATED NORMALLY MODEL FIT INFORMATION Number of Free Parameters 10 Loglikelihood H0 Value -812.260 Information Criteria Akaike (AIC) 1644.520 Bayesian (BIC) 1686.258 Sample-Size Adjusted BIC 1654.519 (n* = (n + 2) / 24) FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES BASED ON THE ESTIMATED MODEL Latent Classes 1 140.00000 0.29167 2 180.00000 0.37500 3 160.00000 0.33333 FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS BASED ON ESTIMATED POSTERIOR PROBABILITIES Latent Classes 1 140.00000 0.29167 2 180.00000 0.37500 3 160.00000 0.33333 CLASSIFICATION QUALITY Entropy 1.000 CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP Class Counts and Proportions Latent Classes 1 140 0.29167 2 180 0.37500 3 160 0.33333 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 Two-Tailed Estimate S.E. Est./S.E. P-Value Latent Class 1 Y ON X -0.511 0.346 -1.475 0.140 Thresholds Y\$1 0.000 0.258 0.000 1.000 Latent Class 2 Y ON X -0.693 0.329 -2.106 0.035 Thresholds Y\$1 -1.099 0.258 -4.255 0.000 Latent Class 3 Y ON X -0.693 0.371 -1.869 0.062 Thresholds Y\$1 -1.386 0.250 -5.545 0.000 Categorical Latent Variables C#1 ON X 0.799 0.236 3.379 0.001 C#2 ON X 0.734 0.222 3.310 0.001 Intercepts C#1 -0.511 0.163 -3.128 0.002 C#2 -0.223 0.150 -1.488 0.137 New/Additional Parameters DENOM0 2.400 0.183 13.093 0.000 DENOM1 4.000 0.447 8.944 0.000 P10 0.250 0.028 8.944 0.000 P11 0.333 0.030 10.954 0.000 P20 0.333 0.030 10.954 0.000 P21 0.417 0.032 13.093 0.000 P30 0.417 0.032 13.093 0.000 P31 0.250 0.028 8.944 0.000 TERM11 0.542 0.032 16.842 0.000 TERM10 0.572 0.034 16.855 0.000 TERM01 0.679 0.032 21.077 0.000 TERM00 0.708 0.029 24.142 0.000 DE -0.137 0.043 -3.145 0.002 TIE -0.030 0.016 -1.860 0.063 TOTAL -0.167 0.044 -3.828 0.000 PIE -0.029 0.015 -1.965 0.049 ORDE 0.549 0.106 5.199 0.000 ORTIE 0.886 0.058 15.306 0.000 ORPIE 0.872 0.060 14.517 0.000 LOGISTIC REGRESSION ODDS RATIO RESULTS Latent Class 1 Y ON X 0.600 Latent Class 2 Y ON X 0.500 Latent Class 3 Y ON X 0.500 Categorical Latent Variables C#1 ON X 2.222 C#2 ON X 2.083 ALTERNATIVE PARAMETERIZATIONS FOR THE CATEGORICAL LATENT VARIABLE REGRESSION Parameterization using Reference Class 1 C#2 ON X -0.065 0.057 -1.123 0.261 C#3 ON X -0.799 0.058 -13.794 0.000 Intercepts C#2 0.288 0.107 2.679 0.007 C#3 0.511 0.015 34.411 0.000 Parameterization using Reference Class 2 C#1 ON X 0.065 0.057 1.123 0.261 C#3 ON X -0.734 0.060 -12.224 0.000 Intercepts C#1 -0.288 0.107 -2.679 0.007 C#3 0.223 0.106 2.112 0.035 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.170E-03 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION FOR LATENT CLASS 1 NU X ________ 1 0 LAMBDA X ________ X 0 THETA X ________ X 0 ALPHA X ________ 1 0 BETA X ________ X 0 PSI X ________ X 0 PARAMETER SPECIFICATION FOR LATENT CLASS 2 NU X ________ 1 0 LAMBDA X ________ X 0 THETA X ________ X 0 ALPHA X ________ 1 0 BETA X ________ X 0 PSI X ________ X 0 PARAMETER SPECIFICATION FOR LATENT CLASS 3 NU X ________ 1 0 LAMBDA X ________ X 0 THETA X ________ X 0 ALPHA X ________ 1 0 BETA X ________ X 0 PSI X ________ X 0 PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART TAU(U) FOR LATENT CLASS 1 Y\$1 ________ 1 1 TAU(U) FOR LATENT CLASS 2 Y\$1 ________ 1 3 TAU(U) FOR LATENT CLASS 3 Y\$1 ________ 1 5 PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART ALPHA(C) C#1 C#2 C#3 ________ ________ ________ 1 7 8 0 GAMMA(C) X ________ C#1 9 C#2 10 C#3 0 PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR GROWTH MODEL PART LAMBDA(F) FOR LATENT CLASS 1 Y ________ Y 0 ALPHA(F) FOR LATENT CLASS 1 Y ________ 1 0 GAMMA(F) FOR LATENT CLASS 1 X ________ Y 2 LAMBDA(F) FOR LATENT CLASS 2 Y ________ Y 0 ALPHA(F) FOR LATENT CLASS 2 Y ________ 1 0 GAMMA(F) FOR LATENT CLASS 2 X ________ Y 4 LAMBDA(F) FOR LATENT CLASS 3 Y ________ Y 0 ALPHA(F) FOR LATENT CLASS 3 Y ________ 1 0 GAMMA(F) FOR LATENT CLASS 3 X ________ Y 6 PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS DENOM0 DENOM1 P10 P11 P20 ________ ________ ________ ________ ________ 1 11 12 13 14 15 NEW/ADDITIONAL PARAMETERS P21 P30 P31 TERM11 TERM10 ________ ________ ________ ________ ________ 1 16 17 18 19 20 NEW/ADDITIONAL PARAMETERS TERM01 TERM00 DE TIE TOTAL ________ ________ ________ ________ ________ 1 21 22 23 24 25 NEW/ADDITIONAL PARAMETERS PIE ORDE ORTIE ORPIE ________ ________ ________ ________ 1 26 27 28 29 STARTING VALUES FOR LATENT CLASS 1 NU X ________ 1 0.000 LAMBDA X ________ X 1.000 THETA X ________ X 0.000 ALPHA X ________ 1 0.000 BETA X ________ X 0.000 PSI X ________ X 0.125 STARTING VALUES FOR LATENT CLASS 2 NU X ________ 1 0.000 LAMBDA X ________ X 1.000 THETA X ________ X 0.000 ALPHA X ________ 1 0.000 BETA X ________ X 0.000 PSI X ________ X 0.125 STARTING VALUES FOR LATENT CLASS 3 NU X ________ 1 0.000 LAMBDA X ________ X 1.000 THETA X ________ X 0.000 ALPHA X ________ 1 0.000 BETA X ________ X 0.000 PSI X ________ X 0.125 STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART TAU(U) FOR LATENT CLASS 1 Y\$1 ________ 1 -1.511 TAU(U) FOR LATENT CLASS 2 Y\$1 ________ 1 -0.511 TAU(U) FOR LATENT CLASS 3 Y\$1 ________ 1 0.489 STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART ALPHA(C) C#1 C#2 C#3 ________ ________ ________ 1 0.000 0.000 0.000 GAMMA(C) X ________ C#1 0.000 C#2 0.000 C#3 0.000 STARTING VALUES FOR LATENT CLASS INDICATOR GROWTH MODEL PART LAMBDA(F) FOR CLASS LATENT CLASS 1 Y ________ Y 1.000 ALPHA(F) FOR LATENT CLASS 1 Y ________ 1 0.000 GAMMA(F) FOR LATENT CLASS 1 X ________ Y 0.000 LAMBDA(F) FOR CLASS LATENT CLASS 2 Y ________ Y 1.000 ALPHA(F) FOR LATENT CLASS 2 Y ________ 1 0.000 GAMMA(F) FOR LATENT CLASS 2 X ________ Y 0.000 LAMBDA(F) FOR CLASS LATENT CLASS 3 Y ________ Y 1.000 ALPHA(F) FOR LATENT CLASS 3 Y ________ 1 0.000 GAMMA(F) FOR LATENT CLASS 3 X ________ Y 0.000 STARTING VALUES FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS DENOM0 DENOM1 P10 P11 P20 ________ ________ ________ ________ ________ 1 0.500 0.500 0.500 0.500 0.500 NEW/ADDITIONAL PARAMETERS P21 P30 P31 TERM11 TERM10 ________ ________ ________ ________ ________ 1 0.500 0.500 0.500 0.500 0.500 NEW/ADDITIONAL PARAMETERS TERM01 TERM00 DE TIE TOTAL ________ ________ ________ ________ ________ 1 0.500 0.500 0.500 0.500 0.500 NEW/ADDITIONAL PARAMETERS PIE ORDE ORTIE ORPIE ________ ________ ________ ________ 1 0.500 0.500 0.500 0.500 TECHNICAL 8 OUTPUT ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM 1 -0.92658212D+03 0.0000000 0.0000000 140.000 180.000 EM 160.000 2 -0.82347811D+03 103.1040090 0.1112735 140.000 180.000 EM 160.000 3 -0.81309319D+03 10.3849248 0.0126111 140.000 180.000 EM 160.000 4 -0.81226040D+03 0.8327860 0.0010242 140.000 180.000 EM 160.000 5 -0.81226000D+03 0.0004054 0.0000005 140.000 180.000 EM 160.000 6 -0.81226000D+03 0.0000000 0.0000000 140.000 180.000 EM 160.000 Beginning Time: 09:29:16 Ending Time: 09:29:17 Elapsed Time: 00:00:01 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