Mplus DEVELOPMENT (Dev 10/23/2011) MUTHEN & MUTHEN 10/23/2011 3:29 PM INPUT INSTRUCTIONS title: Pearl (2011) artificial example, Prevention Science Probit. Step 2 data: file = binbinprobreplist.dat; type = montecarlo; variable: names = y m x; !x: tx/ctrl, m: mediator, y: outcome categorical = y m; usev = y m x xm; define: xm=x*m; analysis: estimator = ml; link = probit; model: [m\$1*.254] (fm0); ! Negative intercept. P(m=1 | x=0)=0.40 m on x*.929 (fm1); ! P(m=1 | x=1)=0.75 [y\$1*.84] (fy00); ! Negative intercept. P(y=1 | x=0,m=0)=0.20 y on x*.586 (fy10); ! direct effect of x on y. P(y=1 |x=1,m=0)=0.40 y on m*.315 (fy01); ! main effect of m on y. P(y=1 | x=0,m=1)=0.30 y on xm*.779 (fy11); ! interaction between x and m in their influence on y !P(y=1 | x=1,m=1)=0.80 model constraint: new(de*.32 tie*.14 pie*.035 te*.46 tiete*.304 piete*.07 dete*.696 compdete*.304 pfm0*.4 pfm1*.75 pfy00*.2 pfy10*.4 pfy01*.3 pfy11*.8 numde*.56 dende*.24 orde*4.0303 numind*.7 denind*.56 orind*1.8333); pfm0=phi(-fm0); pfm1=phi(-fm0+fm1); pfy00=phi(-fy00); pfy10=phi(-fy00+fy10); pfy01=phi(-fy00+fy01); pfy11=phi(-fy00+fy10+fy01+fy11); de=(pfy10-pfy00)*(1-pfm0)+(pfy11-pfy01)*pfm0; tie=(pfy11-pfy10)*(pfm1-pfm0); pie=(pfy01-pfy00)*(pfm1-pfm0); te=pfy11*pfm1+pfy10*(1-pfm1) -(pfy01*pfm0+pfy00*(1-pfm0)); tiete=tie/te; piete=pie/te; dete=de/te; compdete=1-de/te; numde=pfy10*(1-pfm0)+pfy11*pfm0; dende=pfy00*(1-pfm0)+pfy01*pfm0; orde=(numde/(1-numde))/(dende/(1-dende)); numind=pfy10*(1-pfm1)+pfy11*pfm1; denind=pfy10*(1-pfm0)+pfy11*pfm0; orind=(numind/(1-numind))/(denind/(1-denind)); INPUT READING TERMINATED NORMALLY Pearl (2011) artificial example, Prevention Science Probit. Step 2 SUMMARY OF ANALYSIS Number of groups 1 Average number of observations 400 Number of replications Requested 500 Completed 500 Number of dependent variables 2 Number of independent variables 2 Number of continuous latent variables 0 Observed dependent variables Binary and ordered categorical (ordinal) Y M Observed independent variables X XM 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-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 EMA Integration Specifications Type STANDARD Number of integration points 15 Dimensions of numerical integration 0 Adaptive quadrature ON Link PROBIT Cholesky OFF Input data file(s) Multiple data files from binbinprobreplist.dat Input data format FREE UNIVARIATE PROPORTIONS FOR CATEGORICAL VARIABLES NOTE: These are average results over 500 data sets. Y Category 1 0.520 Category 2 0.480 M Category 1 0.375 Category 2 0.625 SAMPLE STATISTICS NOTE: These are average results over 500 data sets. SAMPLE STATISTICS Means X XM ________ ________ 1 0.500 0.374 Covariances X XM ________ ________ X 0.250 XM 0.187 0.234 Correlations X XM ________ ________ X 1.000 XM 0.774 1.000 MODEL FIT INFORMATION Number of Free Parameters 6 Loglikelihood H0 Value Mean -461.596 Std Dev 13.183 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.992 -492.263 -491.242 0.980 0.982 -488.669 -488.484 0.950 0.960 -483.280 -482.876 0.900 0.902 -478.491 -478.517 0.800 0.804 -472.690 -472.591 0.700 0.676 -468.509 -469.157 0.500 0.496 -461.596 -461.962 0.300 0.288 -454.683 -455.338 0.200 0.202 -450.501 -450.467 0.100 0.104 -444.701 -444.666 0.050 0.060 -439.911 -439.121 0.020 0.020 -434.522 -434.942 0.010 0.010 -430.929 -431.034 Information Criteria Akaike (AIC) Mean 935.192 Std Dev 26.366 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 873.857 872.102 0.980 0.980 881.045 880.821 0.950 0.940 891.823 889.708 0.900 0.896 901.402 900.357 0.800 0.798 913.002 912.130 0.700 0.712 921.366 922.180 0.500 0.504 935.192 935.881 0.300 0.324 949.018 950.310 0.200 0.196 957.381 956.944 0.100 0.098 968.982 968.284 0.050 0.040 978.560 977.628 0.020 0.018 989.339 987.037 0.010 0.008 996.526 993.398 Bayesian (BIC) Mean 959.140 Std Dev 26.366 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 897.806 896.051 0.980 0.980 904.993 904.770 0.950 0.940 915.772 913.656 0.900 0.896 925.350 924.306 0.800 0.798 936.951 936.079 0.700 0.712 945.314 946.129 0.500 0.504 959.140 959.830 0.300 0.324 972.967 974.258 0.200 0.196 981.330 980.893 0.100 0.098 992.931 992.233 0.050 0.040 1002.509 1001.577 0.020 0.018 1013.287 1010.986 0.010 0.008 1020.475 1017.347 Sample-Size Adjusted BIC (n* = (n + 2) / 24) Mean 940.102 Std Dev 26.366 Number of successful computations 500 Proportions Percentiles Expected Observed Expected Observed 0.990 0.990 878.768 877.013 0.980 0.980 885.955 885.732 0.950 0.940 896.733 894.618 0.900 0.896 906.312 905.267 0.800 0.798 917.913 917.041 0.700 0.712 926.276 927.090 0.500 0.504 940.102 940.792 0.300 0.324 953.928 955.220 0.200 0.196 962.291 961.855 0.100 0.098 973.892 973.195 0.050 0.040 983.471 982.539 0.020 0.018 994.249 991.947 0.010 0.008 1001.436 998.309 MODEL RESULTS ESTIMATES S. E. M. S. E. 95% % Sig Population Average Std. Dev. Average Cover Coeff M ON X 0.929 0.9341 0.1321 0.1321 0.0174 0.962 1.000 Y ON X 0.586 0.5973 0.2242 0.2244 0.0503 0.958 0.766 M 0.315 0.3148 0.2008 0.1990 0.0402 0.952 0.336 XM 0.779 0.7866 0.2857 0.2943 0.0815 0.968 0.794 Thresholds Y\$1 0.840 0.8506 0.1339 0.1315 0.0180 0.956 1.000 M\$1 0.254 0.2588 0.0883 0.0899 0.0078 0.946 0.824 New/Additional Parameters DE 0.320 0.3216 0.0543 0.0539 0.0029 0.946 1.000 TIE 0.140 0.1399 0.0329 0.0329 0.0011 0.938 1.000 PIE 0.035 0.0347 0.0229 0.0227 0.0005 0.950 0.294 TE 0.460 0.4615 0.0434 0.0442 0.0019 0.950 1.000 TIETE 0.304 0.3060 0.0780 0.0764 0.0061 0.942 1.000 PIETE 0.070 0.0758 0.0501 0.0506 0.0025 0.964 0.272 DETE 0.696 0.6940 0.0780 0.0764 0.0061 0.942 1.000 COMPDETE 0.304 0.3060 0.0780 0.0764 0.0061 0.942 1.000 PFM0 0.400 0.3983 0.0339 0.0345 0.0011 0.940 1.000 PFM1 0.750 0.7492 0.0319 0.0306 0.0010 0.938 1.000 PFY00 0.200 0.1996 0.0364 0.0363 0.0013 0.950 1.000 PFY10 0.400 0.4017 0.0692 0.0690 0.0048 0.954 1.000 PFY01 0.300 0.2980 0.0488 0.0511 0.0024 0.956 1.000 PFY11 0.800 0.8003 0.0312 0.0326 0.0010 0.956 1.000 NUMDE 0.560 0.5604 0.0465 0.0458 0.0022 0.942 1.000 DENDE 0.240 0.2389 0.0289 0.0301 0.0008 0.954 1.000 ORDE 4.030 4.2234 1.0455 1.0490 1.1282 0.946 1.000 NUMIND 0.700 0.7003 0.0320 0.0323 0.0010 0.944 1.000 DENIND 0.560 0.5604 0.0465 0.0458 0.0022 0.942 1.000 ORIND 1.833 1.8552 0.2616 0.2566 0.0688 0.954 1.000 QUALITY OF NUMERICAL RESULTS Average Condition Number for the Information Matrix 0.221E-02 (ratio of smallest to largest eigenvalue) TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION TAU Y\$1 M\$1 ________ ________ 1 5 6 NU Y M X XM ________ ________ ________ ________ 1 0 0 0 0 LAMBDA Y M X XM ________ ________ ________ ________ Y 0 0 0 0 M 0 0 0 0 X 0 0 0 0 XM 0 0 0 0 THETA Y M X XM ________ ________ ________ ________ Y 0 M 0 0 X 0 0 0 XM 0 0 0 0 ALPHA Y M X XM ________ ________ ________ ________ 1 0 0 0 0 BETA Y M X XM ________ ________ ________ ________ Y 0 1 2 3 M 0 0 4 0 X 0 0 0 0 XM 0 0 0 0 PSI Y M X XM ________ ________ ________ ________ Y 0 M 0 0 X 0 0 0 XM 0 0 0 0 PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS DE TIE PIE TE TIETE ________ ________ ________ ________ ________ 1 7 8 9 10 11 NEW/ADDITIONAL PARAMETERS PIETE DETE COMPDETE PFM0 PFM1 ________ ________ ________ ________ ________ 1 12 13 14 15 16 NEW/ADDITIONAL PARAMETERS PFY00 PFY10 PFY01 PFY11 NUMDE ________ ________ ________ ________ ________ 1 17 18 19 20 21 NEW/ADDITIONAL PARAMETERS DENDE ORDE NUMIND DENIND ORIND ________ ________ ________ ________ ________ 1 22 23 24 25 26 STARTING VALUES TAU Y\$1 M\$1 ________ ________ 1 0.840 0.254 NU Y M X XM ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 LAMBDA Y M X XM ________ ________ ________ ________ Y 1.000 0.000 0.000 0.000 M 0.000 1.000 0.000 0.000 X 0.000 0.000 1.000 0.000 XM 0.000 0.000 0.000 1.000 THETA Y M X XM ________ ________ ________ ________ Y 0.000 M 0.000 0.000 X 0.000 0.000 0.000 XM 0.000 0.000 0.000 0.000 ALPHA Y M X XM ________ ________ ________ ________ 1 0.000 0.000 0.000 0.000 BETA Y M X XM ________ ________ ________ ________ Y 0.000 0.315 0.586 0.779 M 0.000 0.000 0.929 0.000 X 0.000 0.000 0.000 0.000 XM 0.000 0.000 0.000 0.000 PSI Y M X XM ________ ________ ________ ________ Y 1.000 M 0.000 1.000 X 0.000 0.000 0.500 XM 0.000 0.000 0.000 0.500 STARTING VALUES FOR THE ADDITIONAL PARAMETERS NEW/ADDITIONAL PARAMETERS DE TIE PIE TE TIETE ________ ________ ________ ________ ________ 1 0.320 0.140 0.035 0.460 0.304 NEW/ADDITIONAL PARAMETERS PIETE DETE COMPDETE PFM0 PFM1 ________ ________ ________ ________ ________ 1 0.070 0.696 0.304 0.400 0.750 NEW/ADDITIONAL PARAMETERS PFY00 PFY10 PFY01 PFY11 NUMDE ________ ________ ________ ________ ________ 1 0.200 0.400 0.300 0.800 0.560 NEW/ADDITIONAL PARAMETERS DENDE ORDE NUMIND DENIND ORIND ________ ________ ________ ________ ________ 1 0.240 4.030 0.700 0.560 1.833 Beginning Time: 15:29:06 Ending Time: 15:29:15 Elapsed Time: 00:00:09 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