Mplus VERSION 4.0 MUTHEN & MUTHEN 02/28/2006 11:58 AM INPUT INSTRUCTIONS Title: Fictitous Latent Class Analysis. Data: File is lca1.dat ; Variable: names = id item1 item2 item3 item4 item5 item6 item7 item8 item9; usevariables = item1 item2 item3 item4 item5 item6 item7 item8 item9; categorical = item1 item2 item3 item4 item5 item6 item7 item8 item9; classes = c(3); Analysis: Type=mixture; Plot: type is plot3; series is item1 (1) item2 (2) item3 (3) item4 (4) item5 (5) item6 (6) item7 (7) item8 (8) item9 (9); Savedata: file is lca1_save.txt ; save is cprob; format is free; Output: tech11 tech14; INPUT READING TERMINATED NORMALLY Fictitous Latent Class Analysis. SUMMARY OF ANALYSIS Number of groups 1 Number of observations 1000 Number of dependent variables 9 Number of independent variables 0 Number of continuous latent variables 0 Number of categorical latent variables 1 Observed dependent variables Binary and ordered categorical (ordinal) ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ITEM6 ITEM7 ITEM8 ITEM9 Categorical latent variables C Estimator MLR Information matrix OBSERVED 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-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 Random Starts Specifications Number of initial stage starts 10 Number of final stage starts 2 Number of initial stage iterations 10 Initial stage convergence criterion 0.100D+01 Random starts scale 0.500D+01 Random seed for generating random starts 0 Link LOGIT Input data file(s) lca1.dat Input data format FREE SUMMARY OF CATEGORICAL DATA PROPORTIONS ITEM1 Category 1 0.307 Category 2 0.693 ITEM2 Category 1 0.709 Category 2 0.291 ITEM3 Category 1 0.916 Category 2 0.084 ITEM4 Category 1 0.910 Category 2 0.090 ITEM5 Category 1 0.801 Category 2 0.199 ITEM6 Category 1 0.718 Category 2 0.282 ITEM7 Category 1 0.861 Category 2 0.139 ITEM8 Category 1 0.833 Category 2 0.167 ITEM9 Category 1 0.723 Category 2 0.277 RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES Initial stage loglikelihood values, seeds, and initial stage start numbers: -4237.703 903420 5 -4237.728 253358 2 -4241.797 unperturbed 0 -4241.863 285380 1 -4243.325 93468 3 -4245.050 462953 7 -4248.075 415931 10 -4248.391 195873 6 -4270.671 608496 4 -4272.645 127215 9 -4282.838 939021 8 Loglikelihood values at local maxima, seeds, and initial stage start numbers: -4231.696 253358 2 -4231.696 903420 5 WARNING: WHEN ESTIMATING A MODEL WITH MORE THAN TWO CLASSES, IT MAY BE NECESSARY TO INCREASE THE NUMBER OF RANDOM STARTS USING THE STARTS OPTION TO AVOID LOCAL MAXIMA. THE MODEL ESTIMATION TERMINATED NORMALLY TESTS OF MODEL FIT Loglikelihood H0 Value -4231.696 H0 Scaling Correction Factor 1.106 for MLR Information Criteria Number of Free Parameters 29 Akaike (AIC) 8521.392 Bayesian (BIC) 8663.716 Sample-Size Adjusted BIC 8571.611 (n* = (n + 2) / 24) Entropy 0.548 Chi-Square Test of Model Fit for the Binary and Ordered Categorical (Ordinal) Outcomes Pearson Chi-Square Value 488.509 Degrees of Freedom 482 P-Value 0.4090 Likelihood Ratio Chi-Square Value 319.955 Degrees of Freedom 482 P-Value 1.0000 FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES BASED ON THE ESTIMATED MODEL Latent Classes 1 557.56838 0.55757 2 363.13982 0.36314 3 79.29180 0.07929 FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS BASED ON ESTIMATED POSTERIOR PROBABILITIES Latent Classes 1 557.56836 0.55757 2 363.13989 0.36314 3 79.29175 0.07929 CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP Class Counts and Proportions Latent Classes 1 646 0.64600 2 288 0.28800 3 66 0.06600 Average Latent Class Probabilities for Most Likely Latent Class Membership (Row) by Latent Class (Column) 1 2 3 1 0.777 0.182 0.040 2 0.148 0.848 0.003 3 0.195 0.013 0.792 MODEL RESULTS Estimates S.E. Est./S.E. Latent Class 1 Thresholds ITEM1$1 -2.293 1.542 -1.487 ITEM2$1 0.675 0.411 1.642 ITEM3$1 2.638 0.323 8.160 ITEM4$1 2.658 0.428 6.216 ITEM5$1 1.271 0.472 2.694 ITEM6$1 0.755 0.297 2.546 ITEM7$1 2.062 0.249 8.279 ITEM8$1 1.816 0.330 5.505 ITEM9$1 0.731 0.250 2.926 Latent Class 2 Thresholds ITEM1$1 0.790 1.516 0.521 ITEM2$1 1.629 0.375 4.338 ITEM3$1 3.295 0.538 6.121 ITEM4$1 2.824 0.332 8.517 ITEM5$1 3.070 1.244 2.467 ITEM6$1 1.497 0.416 3.597 ITEM7$1 2.223 0.263 8.454 ITEM8$1 2.092 0.255 8.204 ITEM9$1 1.464 0.342 4.283 Latent Class 3 Thresholds ITEM1$1 -2.488 0.695 -3.580 ITEM2$1 -0.185 0.371 -0.499 ITEM3$1 0.297 0.580 0.511 ITEM4$1 0.331 0.332 0.997 ITEM5$1 -1.183 0.707 -1.673 ITEM6$1 0.116 0.357 0.325 ITEM7$1 -0.050 0.459 -0.108 ITEM8$1 -0.486 0.652 -0.746 ITEM9$1 0.624 0.318 1.964 Categorical Latent Variables Means C#1 1.950 0.420 4.645 C#2 1.522 1.152 1.321 RESULTS IN PROBABILITY SCALE Latent Class 1 ITEM1 Category 1 0.092 0.128 0.714 Category 2 0.908 0.128 7.069 ITEM2 Category 1 0.663 0.092 7.209 Category 2 0.337 0.092 3.671 ITEM3 Category 1 0.933 0.020 46.346 Category 2 0.067 0.020 3.315 ITEM4 Category 1 0.935 0.026 35.708 Category 2 0.065 0.026 2.502 ITEM5 Category 1 0.781 0.081 9.675 Category 2 0.219 0.081 2.715 ITEM6 Category 1 0.680 0.065 10.546 Category 2 0.320 0.065 4.954 ITEM7 Category 1 0.887 0.025 35.584 Category 2 0.113 0.025 4.525 ITEM8 Category 1 0.860 0.040 21.669 Category 2 0.140 0.040 3.524 ITEM9 Category 1 0.675 0.055 12.314 Category 2 0.325 0.055 5.926 Latent Class 2 ITEM1 Category 1 0.688 0.325 2.113 Category 2 0.312 0.325 0.959 ITEM2 Category 1 0.836 0.051 16.240 Category 2 0.164 0.051 3.186 ITEM3 Category 1 0.964 0.019 51.982 Category 2 0.036 0.019 1.926 ITEM4 Category 1 0.944 0.018 53.818 Category 2 0.056 0.018 3.195 ITEM5 Category 1 0.956 0.053 18.115 Category 2 0.044 0.053 0.841 ITEM6 Category 1 0.817 0.062 13.139 Category 2 0.183 0.062 2.942 ITEM7 Category 1 0.902 0.023 38.929 Category 2 0.098 0.023 4.214 ITEM8 Category 1 0.890 0.025 35.690 Category 2 0.110 0.025 4.406 ITEM9 Category 1 0.812 0.052 15.573 Category 2 0.188 0.052 3.601 Latent Class 3 ITEM1 Category 1 0.077 0.049 1.558 Category 2 0.923 0.049 18.756 ITEM2 Category 1 0.454 0.092 4.934 Category 2 0.546 0.092 5.937 ITEM3 Category 1 0.574 0.142 4.041 Category 2 0.426 0.142 3.004 ITEM4 Category 1 0.582 0.081 7.201 Category 2 0.418 0.081 5.170 ITEM5 Category 1 0.235 0.127 1.847 Category 2 0.765 0.127 6.029 ITEM6 Category 1 0.529 0.089 5.949 Category 2 0.471 0.089 5.297 ITEM7 Category 1 0.488 0.115 4.257 Category 2 0.512 0.115 4.473 ITEM8 Category 1 0.381 0.154 2.479 Category 2 0.619 0.154 4.031 ITEM9 Category 1 0.651 0.072 9.019 Category 2 0.349 0.072 4.831 LATENT CLASS ODDS RATIO RESULTS Latent Class 1 Compared to Latent Class 2 ITEM1 Category > 1 21.817 24.930 0.875 ITEM2 Category > 1 2.595 1.090 2.380 ITEM3 Category > 1 1.930 1.143 1.689 ITEM4 Category > 1 1.180 0.751 1.572 ITEM5 Category > 1 6.046 5.643 1.071 ITEM6 Category > 1 2.098 0.879 2.388 ITEM7 Category > 1 1.175 0.473 2.484 ITEM8 Category > 1 1.318 0.685 1.924 ITEM9 Category > 1 2.081 0.634 3.282 Latent Class 1 Compared to Latent Class 3 ITEM1 Category > 1 0.823 1.630 0.505 ITEM2 Category > 1 0.423 0.294 1.438 ITEM3 Category > 1 0.096 0.050 1.928 ITEM4 Category > 1 0.098 0.047 2.096 ITEM5 Category > 1 0.086 0.053 1.610 ITEM6 Category > 1 0.528 0.304 1.735 ITEM7 Category > 1 0.121 0.054 2.239 ITEM8 Category > 1 0.100 0.058 1.734 ITEM9 Category > 1 0.898 0.386 2.328 Latent Class 2 Compared to Latent Class 3 ITEM1 Category > 1 0.038 0.073 0.518 ITEM2 Category > 1 0.163 0.095 1.720 ITEM3 Category > 1 0.050 0.032 1.541 ITEM4 Category > 1 0.083 0.039 2.125 ITEM5 Category > 1 0.014 0.017 0.846 ITEM6 Category > 1 0.251 0.150 1.676 ITEM7 Category > 1 0.103 0.050 2.062 ITEM8 Category > 1 0.076 0.057 1.338 ITEM9 Category > 1 0.432 0.197 2.186 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.147E-02 (ratio of smallest to largest eigenvalue) TECHNICAL 11 OUTPUT VUONG-LO-MENDELL-RUBIN LIKELIHOOD RATIO TEST FOR 2 (H0) VERSUS 3 CLASSES H0 Loglikelihood Value -4251.208 2 Times the Loglikelihood Difference 39.025 Difference in the Number of Parameters 10 Mean 20.255 Standard Deviation 22.224 P-Value 0.1457 LO-MENDELL-RUBIN ADJUSTED LRT TEST Value 38.468 P-Value 0.1500 TECHNICAL 14 OUTPUT BOOTSTRAPPED PARAMETRIC LIKELIHOOD RATIO TEST FOR 2 (H0) VERSUS 3 CLASSES H0 Loglikelihood Value -4251.208 2 Times the Loglikelihood Difference 39.025 Difference in the Number of Parameters 10 Approximate P-Value 0.0000 PLOT INFORMATION The following plots are available: Histograms (sample values) Scatterplots (sample values) Sample proportions Estimated probabilities SAVEDATA INFORMATION Order of variables ITEM1 ITEM2 ITEM3 ITEM4 ITEM5 ITEM6 ITEM7 ITEM8 ITEM9 CPROB1 CPROB2 CPROB3 C Save file lca1_save.txt Save file format Free Save file record length 1000 Beginning Time: 11:58:16 Ending Time: 11:58:58 Elapsed Time: 00:00:42 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) 1998-2006 Muthen & Muthen