Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:26 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level MIMIC with
continuous factor indicators, random factor loadings,
two covariates on within, and one covariate on between
montecarlo:
names are y1-y4 x1 x2 w;
nobservations = 1000;
nreps = 1;
ncsizes = 3;
CSIZES = 40(5) 50(10) 20(15);
save = ex9.19.dat;
WITHIN = x1 x2;
BETWEEN = w;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
estimator = bayes;
proc = 2;
MODEL POPULATION:
%WITHIN%
x1-x2@1;
s1-s4 | f by y1-y4;
[f@0]; f@1;
f ON x1*.8 x2*.4;
y1-y4*1;
%BETWEEN%
w@1;
f*.4;
[f@0];
y1-y4*.5;
[y1-y4*.5];
s1-s4*.3;
[s1-s4*1];
f ON w*.6;
MODEL:
%WITHIN%
! x1-x2@1;
s1-s4 | f by y1-y4;
[f@0]; f@1;
f ON x1*.8 x2*.4;
y1-y4*1;
%BETWEEN%
! w@1;
f*.4;
[f@0];
y1-y4*.5;
[y1-y4*.5];
s1-s4*.3;
[s1-s4*1];
f ON w*.6;
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level MIMIC with
continuous factor indicators, random factor loadings,
two covariates on within, and one covariate on between
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of replications
Requested 1
Completed 1
Value of seed 0
Number of dependent variables 4
Number of independent variables 3
Number of continuous latent variables 5
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Observed independent variables
X1 X2 W
Continuous latent variables
F S1 S2 S3 S4
Variables with special functions
Within variables
X1 X2
Between variables
W
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
Size (s) Number of clusters of Size s
5 40
10 50
15 20
MODEL FIT INFORMATION
Number of Free Parameters 24
Information Criteria
Deviance (DIC)
Mean 13810.046
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 13810.046 13810.046
0.980 0.000 13810.046 13810.046
0.950 0.000 13810.046 13810.046
0.900 0.000 13810.046 13810.046
0.800 0.000 13810.046 13810.046
0.700 0.000 13810.046 13810.046
0.500 0.000 13810.046 13810.046
0.300 0.000 13810.046 13810.046
0.200 0.000 13810.046 13810.046
0.100 0.000 13810.046 13810.046
0.050 0.000 13810.046 13810.046
0.020 0.000 13810.046 13810.046
0.010 0.000 13810.046 13810.046
Estimated Number of Parameters (pD)
Mean 633.740
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 633.740 633.740
0.980 0.000 633.740 633.740
0.950 0.000 633.740 633.740
0.900 0.000 633.740 633.740
0.800 0.000 633.740 633.740
0.700 0.000 633.740 633.740
0.500 0.000 633.740 633.740
0.300 0.000 633.740 633.740
0.200 0.000 633.740 633.740
0.100 0.000 633.740 633.740
0.050 0.000 633.740 633.740
0.020 0.000 633.740 633.740
0.010 0.000 633.740 633.740
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
F ON
X1 0.800 0.8303 0.0000 0.0413 0.0009 1.000 1.000
X2 0.400 0.3820 0.0000 0.0388 0.0003 1.000 1.000
Intercepts
F 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y1 1.000 0.9892 0.0000 0.0675 0.0001 1.000 1.000
Y2 1.000 1.1517 0.0000 0.0725 0.0230 0.000 1.000
Y3 1.000 0.9224 0.0000 0.0638 0.0060 1.000 1.000
Y4 1.000 0.9606 0.0000 0.0609 0.0016 1.000 1.000
F 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Between Level
F ON
W 0.600 0.5833 0.0000 0.0762 0.0003 1.000 1.000
Means
Y1 0.500 0.4690 0.0000 0.0943 0.0010 1.000 1.000
Y2 0.500 0.4082 0.0000 0.1058 0.0084 1.000 1.000
Y3 0.500 0.3860 0.0000 0.0997 0.0130 1.000 1.000
Y4 0.500 0.3964 0.0000 0.0952 0.0107 1.000 1.000
S1 1.000 1.0796 0.0000 0.0654 0.0063 1.000 1.000
S2 1.000 0.9672 0.0000 0.0636 0.0011 1.000 1.000
S3 1.000 1.0455 0.0000 0.0670 0.0021 1.000 1.000
S4 1.000 1.0539 0.0000 0.0785 0.0029 1.000 1.000
Intercepts
F 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
Y1 0.500 0.5055 0.0000 0.1350 0.0000 1.000 1.000
Y2 0.500 0.7344 0.0000 0.1446 0.0549 0.000 1.000
Y3 0.500 0.5176 0.0000 0.1249 0.0003 1.000 1.000
Y4 0.500 0.4941 0.0000 0.1308 0.0000 1.000 1.000
S1 0.300 0.2780 0.0000 0.0585 0.0005 1.000 1.000
S2 0.300 0.2139 0.0000 0.0543 0.0074 1.000 1.000
S3 0.300 0.3011 0.0000 0.0583 0.0000 1.000 1.000
S4 0.300 0.4806 0.0000 0.0949 0.0326 0.000 1.000
Residual Variances
F 0.400 0.3435 0.0000 0.1017 0.0032 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.
F 0.862 0.000 0.474 0.000
S1 0.815 0.000 0.284 0.000
S2 0.802 0.000 0.323 0.000
S3 0.826 0.000 0.308 0.000
S4 0.873 0.000 0.314 0.000
Y1 0.760 0.000 0.463 0.000
Y2 0.820 0.000 0.444 0.000
Y3 0.759 0.000 0.481 0.000
Y4 0.780 0.000 0.499 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
0 0 0 0 0
NU
X2
________
0
LAMBDA
F%W X1 X2
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
X1 0 0 0
X2 0 0 0
THETA
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
Y1 1
Y2 0 2
Y3 0 0 3
Y4 0 0 0 4
X1 0 0 0 0 0
X2 0 0 0 0 0
THETA
X2
________
X2 0
ALPHA
F%W X1 X2
________ ________ ________
0 0 0
BETA
F%W X1 X2
________ ________ ________
F%W 0 5 6
X1 0 0 0
X2 0 0 0
PSI
F%W X1 X2
________ ________ ________
F%W 0
X1 0 0
X2 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
7 8 9 10 0
LAMBDA
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
W 0 0 0 0 0
LAMBDA
W
________
Y1 0
Y2 0
Y3 0
Y4 0
W 0
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 11
Y2 0 12
Y3 0 0 13
Y4 0 0 0 14
W 0 0 0 0 0
ALPHA
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
0 15 16 17 18
ALPHA
W
________
0
BETA
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
F%B 0 0 0 0 0
S1 0 0 0 0 0
S2 0 0 0 0 0
S3 0 0 0 0 0
S4 0 0 0 0 0
W 0 0 0 0 0
BETA
W
________
F%B 19
S1 0
S2 0
S3 0
S4 0
W 0
PSI
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
F%B 20
S1 0 21
S2 0 0 22
S3 0 0 0 23
S4 0 0 0 0 24
W 0 0 0 0 0
PSI
W
________
W 0
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X2
________
0.000
LAMBDA
F%W X1 X2
________ ________ ________
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000
X1 0.000 1.000 0.000
X2 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
THETA
X2
________
X2 0.000
ALPHA
F%W X1 X2
________ ________ ________
0.000 0.000 0.000
BETA
F%W X1 X2
________ ________ ________
F%W 0.000 0.800 0.400
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
PSI
F%W X1 X2
________ ________ ________
F%W 1.000
X1 0.000 0.500
X2 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0.500 0.500 0.500 0.500 0.000
LAMBDA
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
LAMBDA
W
________
Y1 0.000
Y2 0.000
Y3 0.000
Y4 0.000
W 1.000
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
W 0.000 0.000 0.000 0.000 0.000
ALPHA
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
0.000 1.000 1.000 1.000 1.000
ALPHA
W
________
0.000
BETA
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
F%B 0.000 0.000 0.000 0.000 0.000
S1 0.000 0.000 0.000 0.000 0.000
S2 0.000 0.000 0.000 0.000 0.000
S3 0.000 0.000 0.000 0.000 0.000
S4 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
BETA
W
________
F%B 0.600
S1 0.000
S2 0.000
S3 0.000
S4 0.000
W 0.000
PSI
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
F%B 0.400
S1 0.000 0.300
S2 0.000 0.000 0.300
S3 0.000 0.000 0.000 0.300
S4 0.000 0.000 0.000 0.000 0.300
W 0.000 0.000 0.000 0.000 0.000
PSI
W
________
W 0.500
POPULATION VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X2
________
0.000
LAMBDA
F%W X1 X2
________ ________ ________
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000
X1 0.000 1.000 0.000
X2 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
THETA
X2
________
X2 0.000
ALPHA
F%W X1 X2
________ ________ ________
0.000 0.000 0.000
BETA
F%W X1 X2
________ ________ ________
F%W 0.000 0.800 0.400
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
PSI
F%W X1 X2
________ ________ ________
F%W 1.000
X1 0.000 1.000
X2 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0.500 0.500 0.500 0.500 0.000
LAMBDA
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
LAMBDA
W
________
Y1 0.000
Y2 0.000
Y3 0.000
Y4 0.000
W 1.000
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
W 0.000 0.000 0.000 0.000 0.000
ALPHA
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
0.000 1.000 1.000 1.000 1.000
ALPHA
W
________
0.000
BETA
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
F%B 0.000 0.000 0.000 0.000 0.000
S1 0.000 0.000 0.000 0.000 0.000
S2 0.000 0.000 0.000 0.000 0.000
S3 0.000 0.000 0.000 0.000 0.000
S4 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
BETA
W
________
F%B 0.600
S1 0.000
S2 0.000
S3 0.000
S4 0.000
W 0.000
PSI
F%B S1 S2 S3 S4
________ ________ ________ ________ ________
F%B 0.400
S1 0.000 0.300
S2 0.000 0.000 0.300
S3 0.000 0.000 0.000 0.300
S4 0.000 0.000 0.000 0.000 0.300
W 0.000 0.000 0.000 0.000 0.000
PSI
W
________
W 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~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~N(0.000,infinity) 0.0000 infinity infinity
Parameter 6~N(0.000,infinity) 0.0000 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~N(0.000,infinity) 0.0000 infinity infinity
Parameter 11~IG(-1.000,0.000) infinity infinity infinity
Parameter 12~IG(-1.000,0.000) infinity infinity infinity
Parameter 13~IG(-1.000,0.000) infinity infinity infinity
Parameter 14~IG(-1.000,0.000) infinity infinity infinity
Parameter 15~N(0.000,infinity) 0.0000 infinity infinity
Parameter 16~N(0.000,infinity) 0.0000 infinity infinity
Parameter 17~N(0.000,infinity) 0.0000 infinity infinity
Parameter 18~N(0.000,infinity) 0.0000 infinity infinity
Parameter 19~N(0.000,infinity) 0.0000 infinity infinity
Parameter 20~IG(-1.000,0.000) infinity infinity infinity
Parameter 21~IG(-1.000,0.000) infinity infinity infinity
Parameter 22~IG(-1.000,0.000) infinity infinity infinity
Parameter 23~IG(-1.000,0.000) infinity infinity infinity
Parameter 24~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 1.172 5
200 1.247 20
300 1.136 11
400 1.149 20
500 1.101 20
600 1.044 7
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
X1
X2
W
CLUSTER
Save file
ex9.19.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:26:51
Ending Time: 22:26:53
Elapsed Time: 00:00:02
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