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) confirmatory factor
analysis (CFA) with continuous factor indicators,
random indicator intercepts, random residual factor variance,
and a between-level factor
montecarlo:
names are y1-y4;
NOBS = 20000;
NREP = 1;
NCSIZES = 1;
CSIZES = 200(100);
save = ex9.34.dat;
ANALYSIS:
TYPE = TWOLEVEL RANDOM;
estimator=bayes;
biter=(2000);
proc=2;
model population:
%within%
f by y1@1 y2-y4*1(&1);
y1-y4*.5;
logv | f;
s | f on f&1;
%between%
fb BY y1-y4*.7;
fb@1;
y1-y4*.3;
[logv*0]; logv*.01;
[s*0.3]; s*.02;
model:
%within%
f by y1@1 y2-y4*1(&1);
y1-y4*.5;
logv | f;
s | f on f&1;
%between%
fb BY y1-y4*.7;
fb@1;
y1-y4*.3;
[logv*0]; logv*.01;
[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) confirmatory factor
analysis (CFA) with continuous factor indicators,
random indicator intercepts, 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
Continuous
Y1 Y2 Y3 Y4
Continuous latent variables
F F&1 FB LOGV 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
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 23
Information Criteria
Deviance (DIC)
Mean 189916.524
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 189916.524 189916.524
0.980 0.000 189916.524 189916.524
0.950 0.000 189916.524 189916.524
0.900 0.000 189916.524 189916.524
0.800 0.000 189916.524 189916.524
0.700 0.000 189916.524 189916.524
0.500 0.000 189916.524 189916.524
0.300 0.000 189916.524 189916.524
0.200 0.000 189916.524 189916.524
0.100 0.000 189916.524 189916.524
0.050 0.000 189916.524 189916.524
0.020 0.000 189916.524 189916.524
0.010 0.000 189916.524 189916.524
Estimated Number of Parameters (pD)
Mean 18189.418
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 18189.418 18189.418
0.980 0.000 18189.418 18189.418
0.950 0.000 18189.418 18189.418
0.900 0.000 18189.418 18189.418
0.800 0.000 18189.418 18189.418
0.700 0.000 18189.418 18189.418
0.500 0.000 18189.418 18189.418
0.300 0.000 18189.418 18189.418
0.200 0.000 18189.418 18189.418
0.100 0.000 18189.418 18189.418
0.050 0.000 18189.418 18189.418
0.020 0.000 18189.418 18189.418
0.010 0.000 18189.418 18189.418
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
F BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0004 0.0000 0.0074 0.0000 1.000 1.000
Y3 1.000 0.9980 0.0000 0.0074 0.0000 1.000 1.000
Y4 1.000 0.9934 0.0000 0.0075 0.0000 1.000 1.000
Residual Variances
Y1 0.500 0.4946 0.0000 0.0068 0.0000 1.000 1.000
Y2 0.500 0.5005 0.0000 0.0068 0.0000 1.000 1.000
Y3 0.500 0.4989 0.0000 0.0067 0.0000 1.000 1.000
Y4 0.500 0.5108 0.0000 0.0069 0.0001 1.000 1.000
Between Level
FB BY
Y1 0.700 0.6040 0.0000 0.0563 0.0092 1.000 1.000
Y2 0.700 0.6618 0.0000 0.0589 0.0015 1.000 1.000
Y3 0.700 0.6563 0.0000 0.0594 0.0019 1.000 1.000
Y4 0.700 0.6070 0.0000 0.0591 0.0087 1.000 1.000
Means
LOGV 0.000 0.0060 0.0000 0.0174 0.0000 1.000 0.000
S 0.300 0.2976 0.0000 0.0125 0.0000 1.000 1.000
Intercepts
Y1 0.000 0.0780 0.0000 0.0593 0.0061 1.000 0.000
Y2 0.000 0.0350 0.0000 0.0627 0.0012 1.000 0.000
Y3 0.000 0.0184 0.0000 0.0630 0.0003 1.000 0.000
Y4 0.000 -0.0418 0.0000 0.0613 0.0017 1.000 0.000
Variances
FB 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
LOGV 0.010 0.0110 0.0000 0.0036 0.0000 1.000 1.000
S 0.020 0.0180 0.0000 0.0030 0.0000 1.000 1.000
Residual Variances
Y1 0.300 0.2995 0.0000 0.0399 0.0000 1.000 1.000
Y2 0.300 0.2917 0.0000 0.0438 0.0001 1.000 1.000
Y3 0.300 0.3069 0.0000 0.0449 0.0000 1.000 1.000
Y4 0.300 0.3175 0.0000 0.0421 0.0003 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 0.891 0.000 0.419 0.000
LOGV 0.521 0.000 0.088 0.000
S 0.795 0.000 0.085 0.000
Y1 0.981 0.000 0.159 0.000
Y2 0.983 0.000 0.156 0.000
Y3 0.983 0.000 0.154 0.000
Y4 0.983 0.000 0.153 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0 0 0 0
LAMBDA
F F&1
________ ________
Y1 0 0
Y2 1 0
Y3 2 0
Y4 3 0
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 4
Y2 0 5
Y3 0 0 6
Y4 0 0 0 7
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
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
8 9 10 11
LAMBDA
FB LOGV S
________ ________ ________
Y1 12 0 0
Y2 13 0 0
Y3 14 0 0
Y4 15 0 0
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 16
Y2 0 17
Y3 0 0 18
Y4 0 0 0 19
ALPHA
FB LOGV S
________ ________ ________
0 20 21
BETA
FB LOGV S
________ ________ ________
FB 0 0 0
LOGV 0 0 0
S 0 0 0
PSI
FB LOGV S
________ ________ ________
FB 0
LOGV 0 22
S 0 0 23
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
F F&1
________ ________
Y1 1.000 0.000
Y2 1.000 0.000
Y3 1.000 0.000
Y4 1.000 0.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
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
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
FB LOGV S
________ ________ ________
Y1 0.700 0.000 0.000
Y2 0.700 0.000 0.000
Y3 0.700 0.000 0.000
Y4 0.700 0.000 0.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.300
Y2 0.000 0.300
Y3 0.000 0.000 0.300
Y4 0.000 0.000 0.000 0.300
ALPHA
FB LOGV S
________ ________ ________
0.000 0.000 0.300
BETA
FB LOGV S
________ ________ ________
FB 0.000 0.000 0.000
LOGV 0.000 0.000 0.000
S 0.000 0.000 0.000
PSI
FB LOGV S
________ ________ ________
FB 1.000
LOGV 0.000 0.010
S 0.000 0.000 0.020
POPULATION VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
F F&1
________ ________
Y1 1.000 0.000
Y2 1.000 0.000
Y3 1.000 0.000
Y4 1.000 0.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
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
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
FB LOGV S
________ ________ ________
Y1 0.700 0.000 0.000
Y2 0.700 0.000 0.000
Y3 0.700 0.000 0.000
Y4 0.700 0.000 0.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.300
Y2 0.000 0.300
Y3 0.000 0.000 0.300
Y4 0.000 0.000 0.000 0.300
ALPHA
FB LOGV S
________ ________ ________
0.000 0.000 0.300
BETA
FB LOGV S
________ ________ ________
FB 0.000 0.000 0.000
LOGV 0.000 0.000 0.000
S 0.000 0.000 0.000
PSI
FB LOGV S
________ ________ ________
FB 1.000
LOGV 0.000 0.010
S 0.000 0.000 0.020
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~N(0.000,infinity) 0.0000 infinity infinity
Parameter 2~N(0.000,infinity) 0.0000 infinity infinity
Parameter 3~N(0.000,infinity) 0.0000 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~IG(-1.000,0.000) 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~N(0.000,infinity) 0.0000 infinity infinity
Parameter 13~N(0.000,infinity) 0.0000 infinity infinity
Parameter 14~N(0.000,infinity) 0.0000 infinity infinity
Parameter 15~N(0.000,infinity) 0.0000 infinity infinity
Parameter 16~IG(-1.000,0.000) infinity infinity infinity
Parameter 17~IG(-1.000,0.000) infinity infinity infinity
Parameter 18~IG(-1.000,0.000) infinity infinity infinity
Parameter 19~IG(-1.000,0.000) infinity infinity infinity
Parameter 20~N(0.000,infinity) 0.0000 infinity infinity
Parameter 21~N(0.000,infinity) 0.0000 infinity infinity
Parameter 22~IG(-1.000,0.000) infinity infinity infinity
Parameter 23~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 1.251 20
200 1.112 22
300 1.064 15
400 1.047 13
500 1.056 12
600 1.028 15
700 1.023 20
800 1.017 19
900 1.043 20
1000 1.068 20
1100 1.155 20
1200 1.056 20
1300 1.049 20
1400 1.048 20
1500 1.013 20
1600 1.011 20
1700 1.011 18
1800 1.014 20
1900 1.050 20
2000 1.038 20
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
CLUSTER
Save file
ex9.34.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:31:28
Ending Time: 22:31:58
Elapsed Time: 00:00:30
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