Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:21 PM
INPUT INSTRUCTIONS
TITLE: this is an example of IRT analysis with
random binary items
DATA: FILE = ex9.26.dat;
VARIABLE: NAMES = u level2a level2b;
CATEGORICAL = u;
CLUSTER = level2b level2a;
ANALYSIS: TYPE = CROSSCLASSIFIED RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
MODEL: %WITHIN%
! variation across subjects:
%BETWEEN level2a%
s | f BY u;
f@1;
u@0;
! variation across items:
%BETWEEN level2b%
u; [u$1];
s; [s*1];
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of IRT analysis with
random binary items
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 5000
Number of dependent variables 1
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Binary and ordered categorical (ordinal)
U
Continuous latent variables
F S
Variables with special functions
Cluster variables LEVEL2B LEVEL2A
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)
ex9.26.dat
Input data format FREE
SUMMARY OF DATA
Cluster information for LEVEL2A
Number of clusters 100
Size (s) Cluster ID with Size s
50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
94 95 96 97 98 99 100
Cluster information for LEVEL2B
Number of clusters 50
Size (s) Cluster ID with Size s
100 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49 50
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U
Category 1 0.418 2092.000
Category 2 0.582 2908.000
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 4
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
Between LEVEL2A Level
Variances
F 1.000 0.000 0.000 1.000 1.000
Residual Variances
U 0.000 0.000 0.000 0.000 0.000
Between LEVEL2B Level
Means
S 1.142 0.107 0.000 0.961 1.373 *
Thresholds
U$1 -0.305 0.218 0.080 -0.736 0.141
Variances
U 1.834 0.441 0.000 1.204 2.897 *
S 0.258 0.092 0.000 0.152 0.513 *
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U$1
________
0
NU
U
________
0
THETA
U
________
U 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A
TAU
U$1
________
0
NU
U
________
0
LAMBDA
F
________
U 0
THETA
U
________
U 0
ALPHA
F
________
0
BETA
F
________
F 0
PSI
F
________
F 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B
TAU
U$1
________
4
NU
U
________
0
LAMBDA
S
________
U 0
THETA
U
________
U 1
ALPHA
S
________
2
BETA
S
________
S 0
PSI
S
________
S 3
STARTING VALUES FOR WITHIN
TAU
U$1
________
0.000
NU
U
________
0.000
THETA
U
________
U 1.000
STARTING VALUES FOR BETWEEN LEVEL2A
TAU
U$1
________
0.000
NU
U
________
0.000
LAMBDA
F
________
U 0.000
THETA
U
________
U 0.000
ALPHA
F
________
0.000
BETA
F
________
F 0.000
PSI
F
________
F 1.000
STARTING VALUES FOR BETWEEN LEVEL2B
TAU
U$1
________
-0.183
NU
U
________
0.000
LAMBDA
S
________
U 0.000
THETA
U
________
U 1.000
ALPHA
S
________
1.000
BETA
S
________
S 0.000
PSI
S
________
S 1.000
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~IG(-1.000,0.000) infinity infinity infinity
Parameter 2~N(0.000,infinity) 0.0000 infinity infinity
Parameter 3~IG(-1.000,0.000) infinity infinity infinity
Parameter 4~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 1.845 2
200 1.334 4
300 1.123 4
400 1.136 2
500 1.037 3
Beginning Time: 23:21:02
Ending Time: 23:21:04
Elapsed Time: 00:00:02
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