Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:31 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level random
first-order autoregressive AR(1) IRT model
with binary indicators, random indicator thresholds,
random residual factor variance, and a between-level factor
montecarlo:
names are u1-u4;
NOBS = 20000;
NREP = 1;
NCSIZES = 1;
CSIZES = 200(100);
generate = u1-u4(1);
categorical = u1-u4;
save = ex9.35part2.dat;
ANALYSIS:
TYPE = TWOLEVEL RANDOM;
estimator=bayes;
biter=(2000);
proc=2;
model population:
%within%
f by u1-u4*1(&1);
! y1-y4*.5;
logvf | f;
s | f on f&1;
%between%
fb BY u1-u4*1;
fb*.2;
u1-u4*.3;
[logvf@0]; logvf*.1;
[s*0.3]; s*.02;
model:
%within%
f by u1-u4*1(&1 1-4);
! y1-y4*.5;
logvf | f;
s | f on f&1;
%between%
fb BY u1-u4*1 (1-4);
fb*.2;
u1-u4*.3;
[logvf@0]; logvf*.1;
[s*0.3]; s*.02;
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level random
first-order autoregressive AR(1) IRT model
with binary indicators, random indicator thresholds,
random residual factor variance, and a between-level factor
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 20000
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 5
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
Continuous latent variables
F F&1 FB LOGVF S
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
SUMMARY OF DATA FOR THE FIRST REPLICATION
Cluster information
Size (s) Number of clusters of Size s
100 200
MODEL FIT INFORMATION
Number of Free Parameters 16
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
F BY
U1 1.000 0.9670 0.0000 0.0278 0.0011 1.000 1.000
U2 1.000 0.9978 0.0000 0.0265 0.0000 1.000 1.000
U3 1.000 1.0119 0.0000 0.0278 0.0001 1.000 1.000
U4 1.000 0.9791 0.0000 0.0256 0.0004 1.000 1.000
Between Level
FB BY
U1 1.000 0.9670 0.0000 0.0278 0.0011 1.000 1.000
U2 1.000 0.9978 0.0000 0.0265 0.0000 1.000 1.000
U3 1.000 1.0119 0.0000 0.0278 0.0001 1.000 1.000
U4 1.000 0.9791 0.0000 0.0256 0.0004 1.000 1.000
Means
LOGVF 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S 0.300 0.2976 0.0000 0.0144 0.0000 1.000 1.000
Thresholds
U1$1 0.000 -0.0656 0.0000 0.0509 0.0043 1.000 0.000
U2$1 0.000 -0.0422 0.0000 0.0515 0.0018 1.000 0.000
U3$1 0.000 -0.0170 0.0000 0.0543 0.0003 1.000 0.000
U4$1 0.000 0.0384 0.0000 0.0504 0.0015 1.000 0.000
Variances
FB 0.200 0.1642 0.0000 0.0271 0.0013 1.000 1.000
LOGVF 0.100 0.1098 0.0000 0.0234 0.0001 1.000 1.000
S 0.020 0.0177 0.0000 0.0036 0.0000 1.000 1.000
Residual Variances
U1 0.300 0.2772 0.0000 0.0396 0.0005 1.000 1.000
U2 0.300 0.3236 0.0000 0.0440 0.0006 1.000 1.000
U3 0.300 0.3367 0.0000 0.0463 0.0013 1.000 1.000
U4 0.300 0.2877 0.0000 0.0391 0.0002 1.000 1.000
CORRELATIONS AND MEAN SQUARE ERROR OF THE TRUE FACTOR VALUES AND THE FACTOR SCORES
CORRELATIONS MEAN SQUARE ERROR
Average Std. Dev. Average Std. Dev.
FB 0.762 0.000 0.264 0.000
LOGVF 0.712 0.000 0.228 0.000
S 0.647 0.000 0.106 0.000
U1 0.949 0.000 0.210 0.000
U2 0.954 0.000 0.207 0.000
U3 0.954 0.000 0.205 0.000
U4 0.954 0.000 0.202 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0 0 0 0
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 0
F&1 0 0
PSI
F F&1
________ ________
F 0
F&1 0 0
PARAMETER SPECIFICATION FOR BETWEEN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
13 14 15 16
NU
U1 U2 U3 U4
________ ________ ________ ________
0 0 0 0
LAMBDA
FB LOGVF S
________ ________ ________
U1 1 0 0
U2 2 0 0
U3 3 0 0
U4 4 0 0
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 5
U2 0 6
U3 0 0 7
U4 0 0 0 8
ALPHA
FB LOGVF S
________ ________ ________
0 0 9
BETA
FB LOGVF S
________ ________ ________
FB 0 0 0
LOGVF 0 0 0
S 0 0 0
PSI
FB LOGVF S
________ ________ ________
FB 10
LOGVF 0 11
S 0 0 12
STARTING VALUES FOR WITHIN
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 0.000
F&1 0.000 0.000
PSI
F F&1
________ ________
F 0.000
F&1 0.000 1.000
STARTING VALUES FOR BETWEEN
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
FB LOGVF S
________ ________ ________
U1 1.000 0.000 0.000
U2 1.000 0.000 0.000
U3 1.000 0.000 0.000
U4 1.000 0.000 0.000
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 0.300
U2 0.000 0.300
U3 0.000 0.000 0.300
U4 0.000 0.000 0.000 0.300
ALPHA
FB LOGVF S
________ ________ ________
0.000 0.000 0.300
BETA
FB LOGVF S
________ ________ ________
FB 0.000 0.000 0.000
LOGVF 0.000 0.000 0.000
S 0.000 0.000 0.000
PSI
FB LOGVF S
________ ________ ________
FB 0.200
LOGVF 0.000 0.100
S 0.000 0.000 0.020
POPULATION VALUES FOR WITHIN
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 0.000
F&1 0.000 0.000
PSI
F F&1
________ ________
F 0.000
F&1 0.000 1.000
POPULATION VALUES FOR BETWEEN
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
FB LOGVF S
________ ________ ________
U1 1.000 0.000 0.000
U2 1.000 0.000 0.000
U3 1.000 0.000 0.000
U4 1.000 0.000 0.000
THETA
U1 U2 U3 U4
________ ________ ________ ________
U1 0.300
U2 0.000 0.300
U3 0.000 0.000 0.300
U4 0.000 0.000 0.000 0.300
ALPHA
FB LOGVF S
________ ________ ________
0.000 0.000 0.300
BETA
FB LOGVF S
________ ________ ________
FB 0.000 0.000 0.000
LOGVF 0.000 0.000 0.000
S 0.000 0.000 0.000
PSI
FB LOGVF S
________ ________ ________
FB 0.200
LOGVF 0.000 0.100
S 0.000 0.000 0.020
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~IG(-1.000,0.000) infinity infinity infinity
Parameter 6~IG(-1.000,0.000) infinity infinity infinity
Parameter 7~IG(-1.000,0.000) infinity infinity infinity
Parameter 8~IG(-1.000,0.000) infinity infinity infinity
Parameter 9~N(0.000,infinity) 0.0000 infinity infinity
Parameter 10~IG(-1.000,0.000) infinity infinity infinity
Parameter 11~IG(-1.000,0.000) infinity infinity infinity
Parameter 12~IG(-1.000,0.000) infinity infinity infinity
Parameter 13~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 14~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 15~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 16~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 1.263 3
200 1.797 3
300 1.612 3
400 1.059 3
500 1.062 4
600 1.091 11
700 1.156 11
800 1.200 11
900 1.127 2
1000 1.101 2
1100 1.056 2
1200 1.019 2
1300 1.036 11
1400 1.021 8
1500 1.066 2
1600 1.081 2
1700 1.069 2
1800 1.031 2
1900 1.057 1
2000 1.091 1
2100 1.101 1
2200 1.120 1
2300 1.061 1
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
U4
CLUSTER
Save file
ex9.35part2.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:31:59
Ending Time: 22:32:51
Elapsed Time: 00:00:52
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