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 first-order autoregressive AR(1)
IRT model with binary factor indicators
DATA: FILE = ex6.27.dat;
VARIABLE: NAMES = u1-u4;
CATEGORICAL = u1-u4;
ANALYSIS: ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (2000);
MODEL: f BY u1-u4*(&1);
f@1;
f ON f&1;
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT3;
INPUT READING TERMINATED NORMALLY
this is an example of an N=1 time series analysis
with a first-order autoregressive AR(1)
IRT model with binary factor indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 200
Number of dependent variables 4
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
Continuous latent variables
F F&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
Link PROBIT
Input data file(s)
ex6.27.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.445 89.000
Category 2 0.555 111.000
U2
Category 1 0.445 89.000
Category 2 0.555 111.000
U3
Category 1 0.485 97.000
Category 2 0.515 103.000
U4
Category 1 0.410 82.000
Category 2 0.590 118.000
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 9
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
F BY
U1 0.973 0.227 0.000 0.605 1.489 *
U2 1.018 0.224 0.000 0.685 1.536 *
U3 1.429 0.326 0.000 0.864 2.162 *
U4 1.076 0.230 0.000 0.687 1.591 *
F ON
F&1 0.249 0.098 0.007 0.054 0.437 *
Thresholds
U1$1 -0.197 0.145 0.083 -0.494 0.077
U2$1 -0.192 0.140 0.082 -0.478 0.063
U3$1 -0.059 0.191 0.367 -0.466 0.274
U4$1 -0.339 0.157 0.004 -0.668 -0.057 *
Residual Variances
F 1.000 0.000 0.000 1.000 1.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
6 7 8 9
NU
U1 U2 U3 U4
________ ________ ________ ________
0 0 0 0
LAMBDA
F F&1
________ ________
U1 1 0
U2 2 0
U3 3 0
U4 4 0
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
ALPHA
F F&1
________ ________
0 0
BETA
F F&1
________ ________
F 0 5
F&1 0 0
PSI
F F&1
________ ________
F 0
F&1 0 0
STARTING VALUES
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
-0.123 -0.123 -0.033 -0.202
NU
U1 U2 U3 U4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
F F&1
________ ________
U1 1.000 0.000
U2 1.000 0.000
U3 1.000 0.000
U4 1.000 0.000
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
ALPHA
F F&1
________ ________
0.000 0.000
BETA
F F&1
________ ________
F 0.000 0.000
F&1 0.000 0.000
PSI
F F&1
________ ________
F 1.000
F&1 0.000 1.000
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 2~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 3~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 4~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 5~N(0.000,infinity) 0.0000 infinity infinity
Parameter 6~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 7~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 8~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 9~N(0.000,5.000) 0.0000 5.0000 2.2361
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
CHAIN BSEED
1 0
2 285380
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.723 9
200 1.371 2
300 1.679 3
400 2.170 3
500 1.389 1
600 1.131 1
700 1.069 1
800 1.011 2
900 1.058 3
1000 1.068 3
1100 1.125 3
1200 1.119 4
1300 1.050 1
1400 1.054 1
1500 1.072 3
1600 1.115 3
1700 1.083 3
1800 1.093 3
1900 1.066 2
2000 1.054 2
PLOT INFORMATION
The following plots are available:
Histograms (sample values)
Scatterplots (sample values)
Time series plots (sample values, ACF, PACF)
Sample proportions and estimated probabilities
Bayesian posterior parameter distributions
Bayesian posterior parameter trace plots
Bayesian autocorrelation plots
Bayesian prior parameter distributions
Beginning Time: 23:12:31
Ending Time: 23:12:31
Elapsed Time: 00:00:00
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