Mplus DEVELOPMENT MUTHEN & MUTHEN 02/21/2006 2:11 PM INPUT INSTRUCTIONS Title: lsay_4.inp LSAY math outcomes Growth mixture model with 4-classes *class specific intercept variance DATA: file is lsay.dat; VARIABLE: Names are lsayid schcode classize urban tracking ntracks mthlvl female mthflg7-mthflg12 mothed fathed mothsei fathsei homeres race expect parapsh parcpsh parmpsh peerapsh peermpsh bas7 basse7 alg7 algse7 geo7 geose7 qlt7 qltse7 mth7 mthse7 mtha7 mthase7 bas8 basse8 alg8 algse8 geo8 geose8 qlt8 qltse8 mth8 mthse8 mtha8 mthase8 bas9 basse9 alg9 algse9 geo9 geose9 qlt9 qltse9 mth9 mthse9 mtha9 mthase9 bas10 basse10 alg10 algse10 geo10 geose10 qlt10 qltse10 mth10 mthse10 mtha10 mthase10 bas11 basse11 alg11 algse11 geo11 geose11 qlt11 qltse11 mth11 mthse11 mtha11 mthase11 bas12 basse12 alg12 algse12 geo12 geose12 qlt12 qltse12 mth12 mthse12 mtha12 mthase12 mthcrs7-mthcrs12 mtrk10-mtrk12 totstud lchfull lchpart parvis mcirr mclub strat mstrat comp mcomp african hispan asian expel arrest dropot self worth other satisf respect failure esteem problem cloctn dloctn eloctn floctn gloctn hloctn iloctn jloctn kloctn lloctn drink runawa suicid alc7 alc10 alc11 alc12 arest7 runa8 runa9 runa10 runa11 run12 suic8 suic9 suic10 suic11 suic12 drop7 drop8 drop9 drop10 drop11 drop12 fdrop8 fdrop9 fdrop10 fdrop11 fdrop12 enj7 good7 und7 useboy7 nerv7 wor7 scar7 use7 logic7 boybet7 job7 often7 enj8 good8 und8 useboy8 nerv8 wor8 scar8 use8 logic8 boybet8 job8 often8 enj9 good9 und9 useboy9 nerv9 wor9 scar9 use9 logic9 boybet9 job9 often9 enj10 good10 und10 useboy10 nerv10 wor10 scar10 use10 logic10 boybet10 job10 often10; Missing are all(9999); Usevar=mth7 mth8 mth9 mth10; classes=c(4); Analysis: Type = mixture missing; starts=70 7; Model: %overall% i s | mth7@0 mth8@1 mth9@2 mth10@3; %c#1% i; i with s; %c#2% i; i with s; %c#3% i; i with s; Output: tech11; Plot: type=plot3; series= mth7-mth10(*); *** WARNING Data set contains cases with missing on all variables. These cases were not included in the analysis. Number of cases with missing on all variables: 14 1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS lsay_4.inp LSAY math outcomes Growth mixture model with 4-classes *class specific intercept variance SUMMARY OF ANALYSIS Number of groups 1 Number of observations 3102 Number of dependent variables 4 Number of independent variables 0 Number of continuous latent variables 2 Number of categorical latent variables 1 Observed dependent variables Continuous MTH7 MTH8 MTH9 MTH10 Continuous latent variables I S 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 Maximum number of iterations for H1 2000 Convergence criterion for H1 0.100D-03 Optimization algorithm EMA Random Starts Specifications Number of initial stage starts 70 Number of final stage starts 7 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 Input data file(s) lsay.dat Input data format FREE SUMMARY OF DATA Number of patterns 15 Number of y patterns 15 Number of u patterns 0 COVARIANCE COVERAGE OF DATA Minimum covariance coverage value 0.100 PROPORTION OF DATA PRESENT FOR Y Covariance Coverage MTH7 MTH8 MTH9 MTH10 ________ ________ ________ ________ MTH7 0.988 MTH8 0.822 0.832 MTH9 0.714 0.657 0.722 MTH10 0.651 0.592 0.587 0.658 RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES Initial stage loglikelihood values, seeds, and initial stage start numbers: -33434.609 341041 34 -33438.625 963053 43 -33455.179 481835 57 -33456.003 415931 10 -33456.296 392418 28 -33460.748 887676 22 -33461.384 915107 54 -33475.133 851945 18 -33476.018 76974 16 -33479.631 399671 13 -33480.718 848163 47 -33484.330 85462 51 -33484.929 645664 39 -33486.143 27071 15 -33486.904 153942 31 -33487.256 966014 37 -33490.241 432148 30 -33490.539 967237 48 -33495.109 462953 7 -33495.257 761633 50 -33495.898 93468 3 -33495.903 551639 55 -33497.433 608496 4 -33497.756 568859 49 -33498.100 467339 66 -33498.855 902278 21 -33500.031 915642 40 -33500.911 830392 35 -33501.018 318230 46 -33501.956 207896 25 -33502.313 253358 2 -33502.723 285380 1 -33504.498 136842 58 -33504.630 372176 23 -33507.065 569131 26 -33509.145 366706 29 -33512.860 626891 32 -33518.005 443917 60 -33519.771 603842 61 -33520.685 939021 8 -33521.555 987090 70 -33522.299 573096 20 -33522.515 260601 36 -33529.144 685657 69 -33530.230 533739 11 -33535.592 650371 14 -33535.937 637345 19 -33538.529 754100 56 -33539.208 903420 5 -33541.458 370466 41 -33545.501 107446 12 -33547.650 364676 27 -33550.592 120506 45 -33550.900 227563 63 -33558.615 127215 9 -33560.614 422103 62 -33564.721 407168 44 -33565.522 405079 68 -33567.248 789985 67 -33568.781 967902 52 -33570.276 195873 6 -33571.261 347515 24 -33574.855 565819 65 -33576.414 259507 53 -33581.536 749453 33 -33592.340 68985 17 -33594.952 804561 59 -33605.056 311214 64 -33626.868 352277 42 -33627.307 246261 38 -33641.558 unperturbed 0 Loglikelihood values at local maxima, seeds, and initial stage start numbers: -33420.993 392418 28 -33420.993 481835 57 -33420.993 887676 22 -33420.993 341041 34 -33420.993 963053 43 -33420.993 915107 54 -33427.631 415931 10 THE MODEL ESTIMATION TERMINATED NORMALLY WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN CLASS 1 IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/ RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE S. WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN CLASS 2 IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/ RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE S. WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN CLASS 3 IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/ RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE S. TESTS OF MODEL FIT Loglikelihood H0 Value -33420.993 H0 Scaling Correction Factor 1.048 for MLR Information Criteria Number of Free Parameters 24 Akaike (AIC) 66889.985 Bayesian (BIC) 67034.940 Sample-Size Adjusted BIC 66958.683 (n* = (n + 2) / 24) Entropy 0.742 FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES BASED ON THE ESTIMATED MODEL Latent Classes 1 176.58392 0.05693 2 135.94338 0.04382 3 534.35524 0.17226 4 2255.11745 0.72699 FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS BASED ON ESTIMATED POSTERIOR PROBABILITIES Latent Classes 1 176.58388 0.05693 2 135.94323 0.04382 3 534.35515 0.17226 4 2255.11773 0.72699 CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP Class Counts and Proportions Latent Classes 1 113 0.03643 2 73 0.02353 3 564 0.18182 4 2352 0.75822 Average Latent Class Probabilities for Most Likely Latent Class Membership (Row) by Latent Class (Column) 1 2 3 4 1 0.802 0.000 0.011 0.187 2 0.000 0.753 0.118 0.129 3 0.022 0.052 0.721 0.205 4 0.031 0.022 0.050 0.897 MODEL RESULTS Estimates S.E. Est./S.E. Latent Class 1 I | MTH7 1.000 0.000 0.000 MTH8 1.000 0.000 0.000 MTH9 1.000 0.000 0.000 MTH10 1.000 0.000 0.000 S | MTH7 0.000 0.000 0.000 MTH8 1.000 0.000 0.000 MTH9 2.000 0.000 0.000 MTH10 3.000 0.000 0.000 S WITH I 4.788 1.642 2.915 Means I 41.912 0.979 42.800 S 9.697 0.496 19.553 Intercepts MTH7 0.000 0.000 0.000 MTH8 0.000 0.000 0.000 MTH9 0.000 0.000 0.000 MTH10 0.000 0.000 0.000 Variances I 29.731 7.109 4.182 S 0.594 0.274 2.167 Residual Variances MTH7 16.122 1.088 14.813 MTH8 18.886 0.898 21.041 MTH9 16.640 0.854 19.484 MTH10 15.479 1.332 11.621 Latent Class 2 I | MTH7 1.000 0.000 0.000 MTH8 1.000 0.000 0.000 MTH9 1.000 0.000 0.000 MTH10 1.000 0.000 0.000 S | MTH7 0.000 0.000 0.000 MTH8 1.000 0.000 0.000 MTH9 2.000 0.000 0.000 MTH10 3.000 0.000 0.000 S WITH I 4.424 3.243 1.364 Means I 50.493 3.999 12.627 S -1.367 0.685 -1.997 Intercepts MTH7 0.000 0.000 0.000 MTH8 0.000 0.000 0.000 MTH9 0.000 0.000 0.000 MTH10 0.000 0.000 0.000 Variances I 21.904 12.321 1.778 S 0.594 0.274 2.167 Residual Variances MTH7 16.122 1.088 14.813 MTH8 18.886 0.898 21.041 MTH9 16.640 0.854 19.484 MTH10 15.479 1.332 11.621 Latent Class 3 I | MTH7 1.000 0.000 0.000 MTH8 1.000 0.000 0.000 MTH9 1.000 0.000 0.000 MTH10 1.000 0.000 0.000 S | MTH7 0.000 0.000 0.000 MTH8 1.000 0.000 0.000 MTH9 2.000 0.000 0.000 MTH10 3.000 0.000 0.000 S WITH I 3.004 1.034 2.906 Means I 39.571 0.749 52.858 S 1.073 0.431 2.488 Intercepts MTH7 0.000 0.000 0.000 MTH8 0.000 0.000 0.000 MTH9 0.000 0.000 0.000 MTH10 0.000 0.000 0.000 Variances I 6.188 2.738 2.260 S 0.594 0.274 2.167 Residual Variances MTH7 16.122 1.088 14.813 MTH8 18.886 0.898 21.041 MTH9 16.640 0.854 19.484 MTH10 15.479 1.332 11.621 Latent Class 4 I | MTH7 1.000 0.000 0.000 MTH8 1.000 0.000 0.000 MTH9 1.000 0.000 0.000 MTH10 1.000 0.000 0.000 S | MTH7 0.000 0.000 0.000 MTH8 1.000 0.000 0.000 MTH9 2.000 0.000 0.000 MTH10 3.000 0.000 0.000 S WITH I 4.020 0.870 4.619 Means I 53.356 0.356 149.908 S 4.500 0.092 48.728 Intercepts MTH7 0.000 0.000 0.000 MTH8 0.000 0.000 0.000 MTH9 0.000 0.000 0.000 MTH10 0.000 0.000 0.000 Variances I 72.370 3.237 22.357 S 0.594 0.274 2.167 Residual Variances MTH7 16.122 1.088 14.813 MTH8 18.886 0.898 21.041 MTH9 16.640 0.854 19.484 MTH10 15.479 1.332 11.621 Categorical Latent Variables Means C#1 -2.547 0.219 -11.631 C#2 -2.809 0.623 -4.507 C#3 -1.440 0.157 -9.194 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.129E-04 (ratio of smallest to largest eigenvalue) TECHNICAL 11 OUTPUT VUONG-LO-MENDELL-RUBIN LIKELIHOOD RATIO TEST FOR 3 (H0) VERSUS 4 CLASSES H0 Loglikelihood Value -33443.938 2 Times the Loglikelihood Difference 45.891 Difference in the Number of Parameters 5 Mean 2.064 Standard Deviation 8.217 P-Value 0.0001 LO-MENDELL-RUBIN ADJUSTED LRT TEST Value 44.777 P-Value 0.0001 PLOT INFORMATION The following plots are available: Histograms (sample values, estimated factor scores, estimated values) Scatterplots (sample values, estimated factor scores, estimated values) Sample means Estimated means Sample and estimated means Observed individual values Estimated individual values Estimated means and observed individual values Estimated means and estimated individual values Mixture distributions Beginning Time: 14:11:09 Ending Time: 14:12:40 Elapsed Time: 00:01:31 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) 1998-2005 Muthen & Muthen