Mplus VERSION 8.7 (Mac) MUTHEN & MUTHEN 10/21/2021 10:49 PM INPUT INSTRUCTIONS TITLE: this is an example of an N=1 time series analysis with a univariate first-order autoregressive AR(1) model for a continuous dependent variable DATA: FILE = ex6.23.dat; VARIABLE: NAMES = y; LAGGED = y(1); ANALYSIS: ESTIMATOR = BAYES; PROCESSORS = 2; BITERATIONS = (2000); MODEL: y ON y&1; OUTPUT: TECH1 TECH8; PLOT: TYPE = PLOT3; INPUT READING TERMINATED NORMALLY this is an example of an N=1 time series analysis with a univariate first-order autoregressive AR(1) model for a continuous dependent variable SUMMARY OF ANALYSIS Number of groups 1 Number of observations 100 Number of dependent variables 1 Number of independent variables 1 Number of continuous latent variables 0 Observed dependent variables Continuous Y Observed independent variables Y&1 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) ex6.23.dat Input data format FREE SUMMARY OF DATA COVARIANCE COVERAGE OF DATA Minimum covariance coverage value 0.100 Number of missing data patterns 2 PROPORTION OF DATA PRESENT Covariance Coverage Y ________ Y 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 0.534 -0.035 -2.006 1.00% -0.372 0.224 0.612 100.000 1.117 -0.429 2.989 1.00% 0.814 1.463 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 3 Information Criteria Deviance (DIC) 298.426 Estimated Number of Parameters (pD) 3.101 MODEL RESULTS Posterior One-Tailed 95% C.I. Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance Y ON Y&1 0.171 0.104 0.058 -0.044 0.363 Intercepts Y 0.449 0.121 0.000 0.203 0.689 * Residual Variances Y 1.137 0.168 0.000 0.877 1.529 * TECHNICAL 1 OUTPUT PARAMETER SPECIFICATION NU Y Y&1 ________ ________ 0 0 LAMBDA Y Y&1 ________ ________ Y 0 0 Y&1 0 0 THETA Y Y&1 ________ ________ Y 0 Y&1 0 0 ALPHA Y Y&1 ________ ________ 1 0 BETA Y Y&1 ________ ________ Y 0 2 Y&1 0 0 PSI Y Y&1 ________ ________ Y 3 Y&1 0 0 STARTING VALUES NU Y Y&1 ________ ________ 0.000 0.000 LAMBDA Y Y&1 ________ ________ Y 1.000 0.000 Y&1 0.000 1.000 THETA Y Y&1 ________ ________ Y 0.000 Y&1 0.000 0.000 ALPHA Y Y&1 ________ ________ 0.534 0.000 BETA Y Y&1 ________ ________ Y 0.000 0.000 Y&1 0.000 0.000 PSI Y Y&1 ________ ________ Y 0.559 Y&1 0.000 0.533 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~IG(-1.000,0.000) 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 1.006 3 200 1.003 3 300 1.000 1 400 1.003 1 500 1.000 1 600 1.000 1 700 1.001 2 800 1.006 2 900 1.003 2 1000 1.001 2 1100 1.000 1 1200 1.000 1 1300 1.000 1 1400 1.000 1 1500 1.000 1 1600 1.001 2 1700 1.000 1 1800 1.000 1 1900 1.000 3 2000 1.000 3 PLOT INFORMATION The following plots are available: Histograms (sample values) Scatterplots (sample values) Time series plots (sample values, ACF, PACF) Bayesian posterior parameter distributions Bayesian posterior parameter trace plots Bayesian autocorrelation plots Beginning Time: 22:49:01 Ending Time: 22:49:01 Elapsed Time: 00:00:00 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