Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:27 PM
INPUT INSTRUCTIONS
TITLE: this is an example of regression with cross-
classified data
montecarlo:
names = y x1 x2 w z;
within = x1 x2;
between = (level2a) w (level2b) z;
nobs = 3000;
nreps =1;
csizes = 50[30(2)];
ncsizes = 1[1];
save = ex9.24.dat;
analysis:
type = crossclassified random;
estimator = bayes;
processors = 2;
biter = (2000);
model population:
%within%
x1-x2@1;
y on x1*1;
s | y on x2;
y*2;
%between level2a%
w@1;
y on w*.6;
y*1;
s on w*.3;
s*.4;
y with s*0;
%between level2b%
z@1;
y on z*.4;
y*.5;
[y*2];
s on z*.3;
s*.2;
[s*1];
y with s*0;
model:
%within%
! x1-x2@1;
y on x1*1;
s | y on x2;
y*2;
%between level2a%
! w@1;
y on w*.6;
y*1;
s on w*.3;
s*.4;
y with s*0;
%between level2b%
! z@1;
y on z*.4;
y*.5;
[y*2];
s on z*.3;
s*.2;
[s*1];
y with s*0;
output: tech8;
INPUT READING TERMINATED NORMALLY
this is an example of regression with cross-
classified data
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 3000
Number of replications
Requested 1
Completed 1
Value of seed 0
Number of dependent variables 1
Number of independent variables 4
Number of continuous latent variables 1
Observed dependent variables
Continuous
Y
Observed independent variables
X1 X2 W Z
Continuous latent variables
S
Variables with special functions
Within variables
X1 X2
Level 2a between variables
W
Level 2b between variables
Z
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
SUMMARY OF DATA FOR THE FIRST REPLICATION
Cluster information
Number of level 2a clusters 30
Number of level 2b clusters 50
MODEL FIT INFORMATION
Number of Free Parameters 14
Information Criteria
Deviance (DIC)
Mean 10690.173
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 10690.173 10690.173
0.980 0.000 10690.173 10690.173
0.950 0.000 10690.173 10690.173
0.900 0.000 10690.173 10690.173
0.800 0.000 10690.173 10690.173
0.700 0.000 10690.173 10690.173
0.500 0.000 10690.173 10690.173
0.300 0.000 10690.173 10690.173
0.200 0.000 10690.173 10690.173
0.100 0.000 10690.173 10690.173
0.050 0.000 10690.173 10690.173
0.020 0.000 10690.173 10690.173
0.010 0.000 10690.173 10690.173
Estimated Number of Parameters (pD)
Mean 148.893
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 148.893 148.893
0.980 0.000 148.893 148.893
0.950 0.000 148.893 148.893
0.900 0.000 148.893 148.893
0.800 0.000 148.893 148.893
0.700 0.000 148.893 148.893
0.500 0.000 148.893 148.893
0.300 0.000 148.893 148.893
0.200 0.000 148.893 148.893
0.100 0.000 148.893 148.893
0.050 0.000 148.893 148.893
0.020 0.000 148.893 148.893
0.010 0.000 148.893 148.893
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
Y ON
X1 1.000 0.9984 0.0000 0.0258 0.0000 1.000 1.000
Residual Variances
Y 2.000 1.9684 0.0000 0.0533 0.0010 1.000 1.000
Between LEVEL2A Level
S ON
W 0.300 0.5122 0.0000 0.1386 0.0450 1.000 1.000
Y ON
W 0.600 0.6296 0.0000 0.2138 0.0009 1.000 1.000
Y WITH
S 0.000 0.0143 0.0000 0.2251 0.0002 1.000 0.000
Residual Variances
Y 1.000 1.5108 0.0000 0.5241 0.2609 1.000 1.000
S 0.400 0.5994 0.0000 0.2153 0.0398 1.000 1.000
Between LEVEL2B Level
S ON
Z 0.300 0.3352 0.0000 0.0636 0.0012 1.000 1.000
Y ON
Z 0.400 0.6743 0.0000 0.1213 0.0753 0.000 1.000
Y WITH
S 0.000 0.0081 0.0000 0.0608 0.0001 1.000 0.000
Intercepts
Y 2.000 1.5688 0.0000 0.2917 0.1859 1.000 1.000
S 1.000 0.9085 0.0000 0.1611 0.0084 1.000 1.000
Residual Variances
Y 0.500 0.6858 0.0000 0.1628 0.0345 1.000 1.000
S 0.200 0.1622 0.0000 0.0462 0.0014 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.
S%2a 0.991 0.000 0.161 0.000
S%2b 0.942 0.000 0.203 0.000
B2a_Y 0.994 0.000 0.299 0.000
B2b_Y 0.980 0.000 0.277 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y X1 X2
________ ________ ________
0 0 0
LAMBDA
Y X1 X2
________ ________ ________
Y 0 0 0
X1 0 0 0
X2 0 0 0
THETA
Y X1 X2
________ ________ ________
Y 0
X1 0 0
X2 0 0 0
ALPHA
Y X1 X2
________ ________ ________
0 0 0
BETA
Y X1 X2
________ ________ ________
Y 0 1 0
X1 0 0 0
X2 0 0 0
PSI
Y X1 X2
________ ________ ________
Y 2
X1 0 0
X2 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A
NU
Y W
________ ________
0 0
LAMBDA
S%2a Y W
________ ________ ________
Y 0 0 0
W 0 0 0
THETA
Y W
________ ________
Y 0
W 0 0
ALPHA
S%2a Y W
________ ________ ________
0 0 0
BETA
S%2a Y W
________ ________ ________
S%2a 0 0 3
Y 0 0 4
W 0 0 0
PSI
S%2a Y W
________ ________ ________
S%2a 5
Y 6 7
W 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B
NU
Y Z
________ ________
0 0
LAMBDA
S%2b Y Z
________ ________ ________
Y 0 0 0
Z 0 0 0
THETA
Y Z
________ ________
Y 0
Z 0 0
ALPHA
S%2b Y Z
________ ________ ________
8 9 0
BETA
S%2b Y Z
________ ________ ________
S%2b 0 0 10
Y 0 0 11
Z 0 0 0
PSI
S%2b Y Z
________ ________ ________
S%2b 12
Y 13 14
Z 0 0 0
STARTING VALUES FOR WITHIN
NU
Y X1 X2
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y X1 X2
________ ________ ________
Y 1.000 0.000 0.000
X1 0.000 1.000 0.000
X2 0.000 0.000 1.000
THETA
Y X1 X2
________ ________ ________
Y 0.000
X1 0.000 0.000
X2 0.000 0.000 0.000
ALPHA
Y X1 X2
________ ________ ________
0.000 0.000 0.000
BETA
Y X1 X2
________ ________ ________
Y 0.000 1.000 0.000
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
PSI
Y X1 X2
________ ________ ________
Y 2.000
X1 0.000 0.500
X2 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN LEVEL2A
NU
Y W
________ ________
0.000 0.000
LAMBDA
S%2a Y W
________ ________ ________
Y 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
Y W
________ ________
Y 0.000
W 0.000 0.000
ALPHA
S%2a Y W
________ ________ ________
0.000 0.000 0.000
BETA
S%2a Y W
________ ________ ________
S%2a 0.000 0.000 0.300
Y 0.000 0.000 0.600
W 0.000 0.000 0.000
PSI
S%2a Y W
________ ________ ________
S%2a 0.400
Y 0.000 1.000
W 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN LEVEL2B
NU
Y Z
________ ________
0.000 0.000
LAMBDA
S%2b Y Z
________ ________ ________
Y 0.000 1.000 0.000
Z 0.000 0.000 1.000
THETA
Y Z
________ ________
Y 0.000
Z 0.000 0.000
ALPHA
S%2b Y Z
________ ________ ________
1.000 2.000 0.000
BETA
S%2b Y Z
________ ________ ________
S%2b 0.000 0.000 0.300
Y 0.000 0.000 0.400
Z 0.000 0.000 0.000
PSI
S%2b Y Z
________ ________ ________
S%2b 0.200
Y 0.000 0.500
Z 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
NU
Y X1 X2
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y X1 X2
________ ________ ________
Y 1.000 0.000 0.000
X1 0.000 1.000 0.000
X2 0.000 0.000 1.000
THETA
Y X1 X2
________ ________ ________
Y 0.000
X1 0.000 0.000
X2 0.000 0.000 0.000
ALPHA
Y X1 X2
________ ________ ________
0.000 0.000 0.000
BETA
Y X1 X2
________ ________ ________
Y 0.000 1.000 0.000
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
PSI
Y X1 X2
________ ________ ________
Y 2.000
X1 0.000 1.000
X2 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN LEVEL2A
NU
Y W
________ ________
0.000 0.000
LAMBDA
S%2a Y W
________ ________ ________
Y 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
Y W
________ ________
Y 0.000
W 0.000 0.000
ALPHA
S%2a Y W
________ ________ ________
0.000 0.000 0.000
BETA
S%2a Y W
________ ________ ________
S%2a 0.000 0.000 0.300
Y 0.000 0.000 0.600
W 0.000 0.000 0.000
PSI
S%2a Y W
________ ________ ________
S%2a 0.400
Y 0.000 1.000
W 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN LEVEL2B
NU
Y Z
________ ________
0.000 0.000
LAMBDA
S%2b Y Z
________ ________ ________
Y 0.000 1.000 0.000
Z 0.000 0.000 1.000
THETA
Y Z
________ ________
Y 0.000
Z 0.000 0.000
ALPHA
S%2b Y Z
________ ________ ________
1.000 2.000 0.000
BETA
S%2b Y Z
________ ________ ________
S%2b 0.000 0.000 0.300
Y 0.000 0.000 0.400
Z 0.000 0.000 0.000
PSI
S%2b Y Z
________ ________ ________
S%2b 0.200
Y 0.000 0.500
Z 0.000 0.000 1.000
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~N(0.000,infinity) 0.0000 infinity infinity
Parameter 2~IG(-1.000,0.000) infinity infinity infinity
Parameter 3~N(0.000,infinity) 0.0000 infinity infinity
Parameter 4~N(0.000,infinity) 0.0000 infinity infinity
Parameter 5~IW(0.000,-3) infinity infinity infinity
Parameter 6~IW(0.000,-3) infinity infinity infinity
Parameter 7~IW(0.000,-3) infinity infinity infinity
Parameter 8~N(0.000,infinity) 0.0000 infinity infinity
Parameter 9~N(0.000,infinity) 0.0000 infinity infinity
Parameter 10~N(0.000,infinity) 0.0000 infinity infinity
Parameter 11~N(0.000,infinity) 0.0000 infinity infinity
Parameter 12~IW(0.000,-3) infinity infinity infinity
Parameter 13~IW(0.000,-3) infinity infinity infinity
Parameter 14~IW(0.000,-3) infinity infinity infinity
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 1.119 8
200 1.256 9
300 2.018 9
400 2.132 9
500 1.433 8
600 1.372 8
700 1.276 9
800 1.367 9
900 1.549 9
1000 1.384 9
1100 1.282 9
1200 1.076 9
1300 1.018 9
1400 1.053 9
1500 1.090 9
1600 1.064 9
1700 1.016 9
1800 1.007 7
1900 1.008 7
2000 1.007 7
SAVEDATA INFORMATION
Order of variables
Y
X1
X2
W
Z
LEVEL2A
LEVEL2B
Save file
ex9.24.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:27:11
Ending Time: 22:27:14
Elapsed Time: 00:00:03
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