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
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: 23:12:28
Ending Time: 23:12:28
Elapsed Time: 00:00:00
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