Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:27 PM
INPUT INSTRUCTIONS
title: this is an example of longitudinal modeling using a
cross-classified data approach where observations
are nested within the cross-classification of
time and subjects
montecarlo:
names are y1-y3;
nobservations = 7500;
nreps = 1;
csizes = 75[100(1)];! 75 subjects (2b), 100 time points (2a)
ncsize = 1[1];
within = (level2a) y1-y3;
save = ex9.27.dat;
analysis:
type = cross random;
estimator = bayes;
proc = 2;
model population:
%within%
s1-s3 | f by y1-y3;
f@1;
y1-y3*1.2; [y1-y3@0];
%between level2a% ! across time variation
s1-s3*0.1;
[s1-s3*1.3];
y1-y3*.5; [y1-y3@0];
%between level2b% ! across subjects variation
f*1; [f*.5];
s1-s3@0;
[s1-s3@0];
model:
%within%
s1-s3 | f by y1-y3;
f@1;
y1-y3*1.2; [y1-y3@0];
%between level2a% ! across time variation
s1-s3*0.1;
[s1-s3*1.3];
y1-y3*.5; [y1-y3@0];
%between level2b% ! across subjects variation
f*1; [f*.5];
s1-s3@0;
[s1-s3@0];
output:
tech8;
INPUT READING TERMINATED NORMALLY
this is an example of longitudinal modeling using a
cross-classified data approach where observations
are nested within the cross-classification of
time and subjects
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 7500
Number of replications
Requested 1
Completed 1
Value of seed 0
Number of dependent variables 3
Number of independent variables 0
Number of continuous latent variables 4
Observed dependent variables
Continuous
Y1 Y2 Y3
Continuous latent variables
F S1 S2 S3
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 100
Number of level 2b clusters 75
MODEL FIT INFORMATION
Number of Free Parameters 14
Information Criteria
Deviance (DIC)
Mean 81153.044
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 81153.044 81153.044
0.980 0.000 81153.044 81153.044
0.950 0.000 81153.044 81153.044
0.900 0.000 81153.044 81153.044
0.800 0.000 81153.044 81153.044
0.700 0.000 81153.044 81153.044
0.500 0.000 81153.044 81153.044
0.300 0.000 81153.044 81153.044
0.200 0.000 81153.044 81153.044
0.100 0.000 81153.044 81153.044
0.050 0.000 81153.044 81153.044
0.020 0.000 81153.044 81153.044
0.010 0.000 81153.044 81153.044
Estimated Number of Parameters (pD)
Mean 581.304
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 581.304 581.304
0.980 0.000 581.304 581.304
0.950 0.000 581.304 581.304
0.900 0.000 581.304 581.304
0.800 0.000 581.304 581.304
0.700 0.000 581.304 581.304
0.500 0.000 581.304 581.304
0.300 0.000 581.304 581.304
0.200 0.000 581.304 581.304
0.100 0.000 581.304 581.304
0.050 0.000 581.304 581.304
0.020 0.000 581.304 581.304
0.010 0.000 581.304 581.304
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
Intercepts
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
F 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y1 1.200 1.1980 0.0000 0.0297 0.0000 1.000 1.000
Y2 1.200 1.1837 0.0000 0.0282 0.0003 1.000 1.000
Y3 1.200 1.1944 0.0000 0.0256 0.0000 1.000 1.000
Between LEVEL2A Level
Means
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S1 1.300 1.3074 0.0000 0.0302 0.0001 1.000 1.000
S2 1.300 1.3576 0.0000 0.0381 0.0033 1.000 1.000
S3 1.300 1.3122 0.0000 0.0350 0.0001 1.000 1.000
Variances
Y1 0.500 0.4401 0.0000 0.0681 0.0036 1.000 1.000
Y2 0.500 0.4717 0.0000 0.0746 0.0008 1.000 1.000
Y3 0.500 0.4477 0.0000 0.0717 0.0027 1.000 1.000
S1 0.100 0.0867 0.0000 0.0148 0.0002 1.000 1.000
S2 0.100 0.0972 0.0000 0.0184 0.0000 1.000 1.000
S3 0.100 0.1143 0.0000 0.0188 0.0002 1.000 1.000
Between LEVEL2B Level
Means
F 0.500 0.4116 0.0000 0.1128 0.0078 1.000 1.000
S1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
F 1.000 0.9407 0.0000 0.1594 0.0035 1.000 1.000
S1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
CORRELATIONS AND MEAN SQUARE ERROR OF THE TRUE FACTOR VALUES AND THE FACTOR SCORES
CORRELATIONS MEAN SQUARE ERROR
Average Std. Dev. Average Std. Dev.
F%2a 0.000 0.000 0.031 0.000
S1%2a 0.936 0.000 0.105 0.000
S2%2a 0.943 0.000 0.107 0.000
S3%2a 0.924 0.000 0.130 0.000
F%2b 0.992 0.000 0.138 0.000
S1%2b 0.000 0.000 0.035 0.000
S2%2b 0.000 0.000 0.036 0.000
S3%2b 0.000 0.000 0.033 0.000
B2a_Y1 0.966 0.000 0.197 0.000
B2a_Y2 0.963 0.000 0.212 0.000
B2a_Y3 0.966 0.000 0.184 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3
________ ________ ________
0 0 0
LAMBDA
F%W
________
Y1 0
Y2 0
Y3 0
THETA
Y1 Y2 Y3
________ ________ ________
Y1 1
Y2 0 2
Y3 0 0 3
ALPHA
F%W
________
0
BETA
F%W
________
F%W 0
PSI
F%W
________
F%W 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A
NU
Y1 Y2 Y3
________ ________ ________
0 0 0
LAMBDA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
Y1 0 0 0 0
Y2 0 0 0 0
Y3 0 0 0 0
THETA
Y1 Y2 Y3
________ ________ ________
Y1 4
Y2 0 5
Y3 0 0 6
ALPHA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
0 7 8 9
BETA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
F%2a 0 0 0 0
S1%2a 0 0 0 0
S2%2a 0 0 0 0
S3%2a 0 0 0 0
PSI
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
F%2a 0
S1%2a 0 10
S2%2a 0 0 11
S3%2a 0 0 0 12
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B
ALPHA
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
13 0 0 0
BETA
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
F%2b 0 0 0 0
S1%2b 0 0 0 0
S2%2b 0 0 0 0
S3%2b 0 0 0 0
PSI
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
F%2b 14
S1%2b 0 0
S2%2b 0 0 0
S3%2b 0 0 0 0
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
F%W
________
Y1 0.000
Y2 0.000
Y3 0.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 1.200
Y2 0.000 1.200
Y3 0.000 0.000 1.200
ALPHA
F%W
________
0.000
BETA
F%W
________
F%W 0.000
PSI
F%W
________
F%W 1.000
STARTING VALUES FOR BETWEEN LEVEL2A
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
Y1 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
ALPHA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
0.000 1.300 1.300 1.300
BETA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
F%2a 0.000 0.000 0.000 0.000
S1%2a 0.000 0.000 0.000 0.000
S2%2a 0.000 0.000 0.000 0.000
S3%2a 0.000 0.000 0.000 0.000
PSI
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
F%2a 0.000
S1%2a 0.000 0.100
S2%2a 0.000 0.000 0.100
S3%2a 0.000 0.000 0.000 0.100
STARTING VALUES FOR BETWEEN LEVEL2B
ALPHA
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
0.500 0.000 0.000 0.000
BETA
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
F%2b 0.000 0.000 0.000 0.000
S1%2b 0.000 0.000 0.000 0.000
S2%2b 0.000 0.000 0.000 0.000
S3%2b 0.000 0.000 0.000 0.000
PSI
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
F%2b 1.000
S1%2b 0.000 0.000
S2%2b 0.000 0.000 0.000
S3%2b 0.000 0.000 0.000 0.000
POPULATION VALUES FOR WITHIN
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
F%W
________
Y1 0.000
Y2 0.000
Y3 0.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 1.200
Y2 0.000 1.200
Y3 0.000 0.000 1.200
ALPHA
F%W
________
0.000
BETA
F%W
________
F%W 0.000
PSI
F%W
________
F%W 1.000
POPULATION VALUES FOR BETWEEN LEVEL2A
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
Y1 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
ALPHA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
0.000 1.300 1.300 1.300
BETA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
F%2a 0.000 0.000 0.000 0.000
S1%2a 0.000 0.000 0.000 0.000
S2%2a 0.000 0.000 0.000 0.000
S3%2a 0.000 0.000 0.000 0.000
PSI
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
F%2a 0.000
S1%2a 0.000 0.100
S2%2a 0.000 0.000 0.100
S3%2a 0.000 0.000 0.000 0.100
POPULATION VALUES FOR BETWEEN LEVEL2B
ALPHA
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
0.500 0.000 0.000 0.000
BETA
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
F%2b 0.000 0.000 0.000 0.000
S1%2b 0.000 0.000 0.000 0.000
S2%2b 0.000 0.000 0.000 0.000
S3%2b 0.000 0.000 0.000 0.000
PSI
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
F%2b 1.000
S1%2b 0.000 0.000
S2%2b 0.000 0.000 0.000
S3%2b 0.000 0.000 0.000 0.000
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~IG(-1.000,0.000) infinity infinity infinity
Parameter 2~IG(-1.000,0.000) infinity infinity infinity
Parameter 3~IG(-1.000,0.000) infinity infinity infinity
Parameter 4~IG(-1.000,0.000) infinity infinity infinity
Parameter 5~IG(-1.000,0.000) infinity infinity infinity
Parameter 6~IG(-1.000,0.000) infinity infinity infinity
Parameter 7~N(0.000,infinity) 0.0000 infinity infinity
Parameter 8~N(0.000,infinity) 0.0000 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,infinity) 0.0000 infinity infinity
Parameter 14~IG(-1.000,0.000) 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 1.164 3
200 1.045 1
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
LEVEL2A
LEVEL2B
Save file
ex9.27.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:27:17
Ending Time: 22:27:32
Elapsed Time: 00:00:15
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