Mplus VERSION 8.7 (Mac) MUTHEN & MUTHEN 10/21/2021 11:07 PM INPUT INSTRUCTIONS TITLE: this is an example of a two-level time series analysis with a univariate first-order autoregressive AR(1) model for a continuous dependent variable with a covariate, random intercept, random AR(1) slope, random slope, and random residual variance DATA: FILE = ex9.31.dat; VARIABLE: NAMES = y x w xm subject; WITHIN = x; BETWEEN = w xm; CLUSTER = subject; LAGGED = y(1); DEFINE: CENTER X (GROUPMEAN); ANALYSIS: TYPE = TWOLEVEL RANDOM; ESTIMATOR = BAYES; PROCESSORS = 2; BITERATIONS = (2000); MODEL: %WITHIN% sy | y ON y&1; sx | y ON x; logv | y; %BETWEEN% y ON w xm; sy ON w xm; sx ON w xm; logv ON w xm; y sy sx logv WITH y sy sx logv; OUTPUT: TECH1 TECH8; PLOT: TYPE= PLOT3; INPUT READING TERMINATED NORMALLY this is an example of a two-level time series analysis with a univariate first-order autoregressive AR(1) model for a continuous dependent variable with a covariate, random intercept, random AR(1) slope, random slope, and random residual variance SUMMARY OF ANALYSIS Number of groups 1 Number of observations 5000 Number of dependent variables 1 Number of independent variables 4 Number of continuous latent variables 3 Observed dependent variables Continuous Y Observed independent variables X W XM Y&1 Continuous latent variables SY SX LOGV Variables with special functions Cluster variable SUBJECT Within variables X Y&1 Between variables W XM Centering (GROUPMEAN) X Estimator BAYES Specifications for Bayesian Estimation Point estimate MEDIAN Number of Markov chain Monte Carlo (MCMC) chains 2 Random seed for the first chain 0 Starting value information UNPERTURBED Algorithm used for Markov chain Monte Carlo GIBBS(PX1) Convergence criterion 0.500D-01 Maximum number of iterations 50000 K-th iteration used for thinning 1 Input data file(s) ex9.31.dat Input data format FREE SUMMARY OF DATA Number of clusters 100 Size (s) Cluster ID with Size s 50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 COVARIANCE COVERAGE OF DATA Minimum covariance coverage value 0.100 Number of missing data patterns 2 PROPORTION OF DATA PRESENT Covariance Coverage Y X W XM ________ ________ ________ ________ Y 1.000 X 1.000 1.000 W 1.000 1.000 1.000 XM 1.000 1.000 1.000 1.000 UNIVARIATE SAMPLE STATISTICS UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS Variable/ Mean/ Skewness/ Minimum/ % with Percentiles Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median Y 0.013 0.287 -10.377 0.02% -1.551 -0.526 -0.098 5000.000 4.351 1.600 10.792 0.02% 0.390 1.530 X 0.000 0.017 -3.681 0.02% -0.966 -0.305 0.006 5000.000 1.241 -0.140 4.237 0.02% 0.284 0.952 W -0.055 0.514 -2.098 1.00% -0.760 -0.416 -0.285 100.000 0.744 0.072 2.415 1.00% 0.022 0.682 XM 0.136 -0.054 -2.490 1.00% -0.741 -0.031 0.173 100.000 0.963 0.139 2.544 1.00% 0.418 0.829 THE MODEL ESTIMATION TERMINATED NORMALLY USE THE FBITERATIONS OPTION TO INCREASE THE NUMBER OF ITERATIONS BY A FACTOR OF AT LEAST TWO TO CHECK CONVERGENCE AND THAT THE PSR VALUE DOES NOT INCREASE. MODEL FIT INFORMATION Number of Free Parameters 22 Information Criteria Deviance (DIC) 14729.136 Estimated Number of Parameters (pD) 318.156 MODEL RESULTS Posterior One-Tailed 95% C.I. Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance Within Level Between Level SY ON W 0.120 0.016 0.000 0.090 0.151 * XM 0.054 0.014 0.000 0.027 0.082 * SX ON W 0.289 0.101 0.004 0.090 0.483 * XM 0.343 0.089 0.001 0.174 0.519 * LOGV ON W 0.325 0.046 0.000 0.234 0.412 * XM 0.053 0.041 0.086 -0.024 0.137 Y ON W 0.493 0.092 0.000 0.305 0.666 * XM 0.392 0.082 0.000 0.236 0.556 * Y WITH SY -0.002 0.011 0.401 -0.026 0.020 SX -0.067 0.074 0.157 -0.221 0.070 LOGV -0.006 0.034 0.431 -0.074 0.062 SY WITH SX -0.009 0.012 0.210 -0.034 0.014 LOGV 0.002 0.006 0.352 -0.009 0.014 SX WITH LOGV 0.000 0.035 0.495 -0.068 0.067 Intercepts Y -0.012 0.080 0.444 -0.172 0.145 SY 0.190 0.014 0.000 0.163 0.217 * SX 0.772 0.086 0.000 0.605 0.939 * LOGV 0.053 0.039 0.080 -0.022 0.130 Residual Variances Y 0.592 0.099 0.000 0.433 0.823 * SY 0.008 0.003 0.000 0.004 0.015 * SX 0.697 0.114 0.000 0.520 0.957 * LOGV 0.104 0.023 0.000 0.066 0.155 * TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION FOR WITHIN NU Y X Y&1 ________ ________ ________ 0 0 0 LAMBDA Y X Y&1 ________ ________ ________ Y 0 0 0 X 0 0 0 Y&1 0 0 0 THETA Y X Y&1 ________ ________ ________ Y 0 X 0 0 Y&1 0 0 0 ALPHA Y X Y&1 ________ ________ ________ 0 0 0 BETA Y X Y&1 ________ ________ ________ Y 0 0 0 X 0 0 0 Y&1 0 0 0 PSI Y X Y&1 ________ ________ ________ Y 0 X 0 0 Y&1 0 0 0 PARAMETER SPECIFICATION FOR BETWEEN NU Y W XM ________ ________ ________ 0 0 0 LAMBDA SY SX LOGV Y W ________ ________ ________ ________ ________ Y 0 0 0 0 0 W 0 0 0 0 0 XM 0 0 0 0 0 LAMBDA XM ________ Y 0 W 0 XM 0 THETA Y W XM ________ ________ ________ Y 0 W 0 0 XM 0 0 0 ALPHA SY SX LOGV Y W ________ ________ ________ ________ ________ 1 2 3 4 0 ALPHA XM ________ 0 BETA SY SX LOGV Y W ________ ________ ________ ________ ________ SY 0 0 0 0 5 SX 0 0 0 0 7 LOGV 0 0 0 0 9 Y 0 0 0 0 11 W 0 0 0 0 0 XM 0 0 0 0 0 BETA XM ________ SY 6 SX 8 LOGV 10 Y 12 W 0 XM 0 PSI SY SX LOGV Y W ________ ________ ________ ________ ________ SY 13 SX 14 15 LOGV 16 17 18 Y 19 20 21 22 W 0 0 0 0 0 XM 0 0 0 0 0 PSI XM ________ XM 0 STARTING VALUES FOR WITHIN NU Y X Y&1 ________ ________ ________ 0.000 0.000 0.000 LAMBDA Y X Y&1 ________ ________ ________ Y 1.000 0.000 0.000 X 0.000 1.000 0.000 Y&1 0.000 0.000 1.000 THETA Y X Y&1 ________ ________ ________ Y 0.000 X 0.000 0.000 Y&1 0.000 0.000 0.000 ALPHA Y X Y&1 ________ ________ ________ 0.000 0.000 0.000 BETA Y X Y&1 ________ ________ ________ Y 0.000 0.000 0.000 X 0.000 0.000 0.000 Y&1 0.000 0.000 0.000 PSI Y X Y&1 ________ ________ ________ Y 0.000 X 0.000 0.620 Y&1 0.000 0.000 2.175 STARTING VALUES FOR BETWEEN NU Y W XM ________ ________ ________ 0.000 0.000 0.000 LAMBDA SY SX LOGV Y W ________ ________ ________ ________ ________ Y 0.000 0.000 0.000 1.000 0.000 W 0.000 0.000 0.000 0.000 1.000 XM 0.000 0.000 0.000 0.000 0.000 LAMBDA XM ________ Y 0.000 W 0.000 XM 1.000 THETA Y W XM ________ ________ ________ Y 0.000 W 0.000 0.000 XM 0.000 0.000 0.000 ALPHA SY SX LOGV Y W ________ ________ ________ ________ ________ 0.000 0.000 0.000 0.013 0.000 ALPHA XM ________ 0.000 BETA SY SX LOGV Y W ________ ________ ________ ________ ________ SY 0.000 0.000 0.000 0.000 0.000 SX 0.000 0.000 0.000 0.000 0.000 LOGV 0.000 0.000 0.000 0.000 0.000 Y 0.000 0.000 0.000 0.000 0.000 W 0.000 0.000 0.000 0.000 0.000 XM 0.000 0.000 0.000 0.000 0.000 BETA XM ________ SY 0.000 SX 0.000 LOGV 0.000 Y 0.000 W 0.000 XM 0.000 PSI SY SX LOGV Y W ________ ________ ________ ________ ________ SY 1.000 SX 0.000 1.000 LOGV 0.000 0.000 1.000 Y 0.000 0.000 0.000 2.175 W 0.000 0.000 0.000 0.000 0.372 XM 0.000 0.000 0.000 0.000 0.000 PSI XM ________ XM 0.481 PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV. Parameter 1~N(0.000,infinity) 0.0000 infinity infinity Parameter 2~N(0.000,infinity) 0.0000 infinity infinity Parameter 3~N(0.000,infinity) 0.0000 infinity infinity Parameter 4~N(0.000,infinity) 0.0000 infinity infinity Parameter 5~N(0.000,infinity) 0.0000 infinity infinity Parameter 6~N(0.000,infinity) 0.0000 infinity infinity Parameter 7~N(0.000,infinity) 0.0000 infinity infinity Parameter 8~N(0.000,infinity) 0.0000 infinity infinity Parameter 9~N(0.000,infinity) 0.0000 infinity infinity Parameter 10~N(0.000,infinity) 0.0000 infinity infinity Parameter 11~N(0.000,infinity) 0.0000 infinity infinity Parameter 12~N(0.000,infinity) 0.0000 infinity infinity Parameter 13~IW(0.000,-5) infinity infinity infinity Parameter 14~IW(0.000,-5) infinity infinity infinity Parameter 15~IW(0.000,-5) infinity infinity infinity Parameter 16~IW(0.000,-5) infinity infinity infinity Parameter 17~IW(0.000,-5) infinity infinity infinity Parameter 18~IW(0.000,-5) infinity infinity infinity Parameter 19~IW(0.000,-5) infinity infinity infinity Parameter 20~IW(0.000,-5) infinity infinity infinity Parameter 21~IW(0.000,-5) infinity infinity infinity Parameter 22~IW(0.000,-5) infinity infinity infinity TECHNICAL 8 OUTPUT TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION CHAIN BSEED 1 0 2 285380 POTENTIAL PARAMETER WITH ITERATION SCALE REDUCTION HIGHEST PSR 100 1.221 1 200 1.121 5 300 1.028 10 400 1.018 21 500 1.028 17 600 1.014 21 700 1.008 21 800 1.010 16 900 1.017 21 1000 1.024 21 1100 1.012 16 1200 1.010 21 1300 1.011 21 1400 1.006 21 1500 1.003 17 1600 1.003 9 1700 1.009 9 1800 1.008 9 1900 1.007 10 2000 1.004 9 PLOT INFORMATION The following plots are available: Histograms (sample values) Scatterplots (sample values) Between-level histograms (sample values, sample means/variances) Between-level scatterplots (sample values, sample means/variances) Time series plots (sample values, ACF, PACF) Histogram of subjects per time point Bayesian posterior parameter distributions Bayesian posterior parameter trace plots Bayesian autocorrelation plots Beginning Time: 23:07:24 Ending Time: 23:07:37 Elapsed Time: 00:00:13 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) 1998-2021 Muthen & Muthen