Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:12 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 with a covariate
DATA: FILE = ex6.24.dat;
VARIABLE: NAMES ARE y x;
LAGGED = y(1) x(1);
ANALYSIS: ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (1000);
MODEL: y ON y&1 x x&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 with a covariate
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 100
Number of dependent variables 1
Number of independent variables 3
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y
Observed independent variables
X Y&1 X&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)
ex6.24.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 X
________ ________
Y 1.000
X 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 0.109 -0.162 -3.387 1.00% -1.605 -0.196 0.386
100.000 2.697 -0.916 3.235 1.00% 0.610 1.651
X 0.139 -0.455 -2.584 1.00% -0.885 -0.057 0.286
100.000 1.239 -0.383 2.024 1.00% 0.522 1.154
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 5
Information Criteria
Deviance (DIC) 296.229
Estimated Number of Parameters (pD) 5.182
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Y ON
Y&1 -0.022 0.087 0.398 -0.193 0.147
X 0.797 0.106 0.000 0.575 0.980 *
X&1 0.603 0.142 0.000 0.327 0.869 *
Intercepts
Y -0.082 0.101 0.213 -0.259 0.124
Residual Variances
Y 1.083 0.159 0.000 0.827 1.445 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
Y X Y&1 X&1
________ ________ ________ ________
0 0 0 0
LAMBDA
Y X Y&1 X&1
________ ________ ________ ________
Y 0 0 0 0
X 0 0 0 0
Y&1 0 0 0 0
X&1 0 0 0 0
THETA
Y X Y&1 X&1
________ ________ ________ ________
Y 0
X 0 0
Y&1 0 0 0
X&1 0 0 0 0
ALPHA
Y X Y&1 X&1
________ ________ ________ ________
1 0 0 0
BETA
Y X Y&1 X&1
________ ________ ________ ________
Y 0 2 3 4
X 0 0 0 0
Y&1 0 0 0 0
X&1 0 0 0 0
PSI
Y X Y&1 X&1
________ ________ ________ ________
Y 5
X 0 0
Y&1 0 0 0
X&1 0 0 0 0
STARTING VALUES
NU
Y X Y&1 X&1
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
Y X Y&1 X&1
________ ________ ________ ________
Y 1.000 0.000 0.000 0.000
X 0.000 1.000 0.000 0.000
Y&1 0.000 0.000 1.000 0.000
X&1 0.000 0.000 0.000 1.000
THETA
Y X Y&1 X&1
________ ________ ________ ________
Y 0.000
X 0.000 0.000
Y&1 0.000 0.000 0.000
X&1 0.000 0.000 0.000 0.000
ALPHA
Y X Y&1 X&1
________ ________ ________ ________
0.109 0.000 0.000 0.000
BETA
Y X Y&1 X&1
________ ________ ________ ________
Y 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000
Y&1 0.000 0.000 0.000 0.000
X&1 0.000 0.000 0.000 0.000
PSI
Y X Y&1 X&1
________ ________ ________ ________
Y 1.349
X 0.000 0.619
Y&1 0.000 0.000 1.362
X&1 0.000 0.000 0.000 0.625
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~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 1.080 2
200 1.007 4
300 1.004 4
400 1.007 5
500 1.007 5
600 1.000 3
700 1.002 1
800 1.001 1
900 1.003 1
1000 1.003 1
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: 23:12:28
Ending Time: 23:12:29
Elapsed Time: 00:00:01
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