Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
TITLE: this is an example of an N=1
first-order autoregressive AR(1) IRT model
with binary indicators
montecarlo:
names are u1-u4;
nobservations = 200;
nreps = 1;
save = ex6.27.dat;
generate = u1-u4(1);
categorical = u1-u4;
ANALYSIS:
estimator = bayes;
proc = 2;
biter = (2000);
MODEL POPULATION:
f BY u1-u4*1 (&1);
f@1;
! u1-u4*1;
f on f&1*.3;
MODEL:
f BY u1-u4*1(&1);
f@1;
! u1-u4*1;
f on f&1*.3;
output:
tech8;
INPUT READING TERMINATED NORMALLY
this is an example of an N=1
first-order autoregressive AR(1) IRT model
with binary indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 200
Number of replications
Requested 1
Completed 1
Value of seed 0
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
MODEL FIT INFORMATION
Number of Free Parameters 9
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
F BY
U1 1.000 0.9735 0.0000 0.2273 0.0007 1.000 1.000
U2 1.000 1.0179 0.0000 0.2240 0.0003 1.000 1.000
U3 1.000 1.4294 0.0000 0.3255 0.1844 1.000 1.000
U4 1.000 1.0757 0.0000 0.2295 0.0057 1.000 1.000
F ON
F&1 0.300 0.2487 0.0000 0.0984 0.0026 1.000 1.000
Thresholds
U1$1 0.000 -0.1969 0.0000 0.1452 0.0388 1.000 0.000
U2$1 0.000 -0.1924 0.0000 0.1397 0.0370 1.000 0.000
U3$1 0.000 -0.0594 0.0000 0.1910 0.0035 1.000 0.000
U4$1 0.000 -0.3388 0.0000 0.1569 0.1148 0.000 1.000
Residual Variances
F 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
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
________ ________ ________ ________
0.000 0.000 0.000 0.000
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 0.300
F&1 0.000 0.000
PSI
F F&1
________ ________
F 1.000
F&1 0.000 1.000
POPULATION VALUES
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
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 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
ALPHA
F F&1
________ ________
0.000 0.000
BETA
F F&1
________ ________
F 0.000 0.300
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
REPLICATION 1:
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.722 9
200 1.371 2
300 1.679 3
400 2.169 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
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
U4
Save file
ex6.27.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:22
Ending Time: 22:24:23
Elapsed Time: 00:00:01
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