Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:38 PM
INPUT INSTRUCTIONS
title: this is an example of a cross-classified time
series analysis with a first-order
autoregressive AR(1) confirmatory factor
analysis (CFA) model for continuous factor
indicators with random intercepts, random
factor loadings, and a factor varying across
both subjects and time
montecarlo:
names are y1-y3;
nobservations = 20000;
nreps = 1;
CSIZES = 200[100(1)]; ! 200 subjects (2b), 100 time points (2a)
ncsize = 1[1];
save = ex9.40part2.dat;
ANALYSIS: TYPE = cross random;
estimator = bayes;
proc = 2;
biter = (2000);
model population:
%within%
y1-y3*1.2; [y1-y3@0];
s1-s3 | f by y1-y3 (&1);
f@1;
f on f&1*.3;
%between level2b%
! across subject variation in measurement intercepts,
! loadings, and factor
f*1;
y1-y3*.5;
[y1-y3*1]; ! estimating the intercepts on the level with most
! intercept variance
s1-s3*0.1;
[s1-s3*1.3];
%between level2a%
! across time variation of measurement intercepts and factor
f*0.5;
y1-y3*.3;
model:
%within%
y1-y3*1.2; [y1-y3@0];
s1-s3 | f by y1-y3 (&1);
f@1;
f on f&1*.3;
%between level2b%
! across subject variation in measurement intercepts,
! loadings, and factor
f*1;
y1-y3*.5;
[y1-y3*1]; ! estimating the intercepts on the level with most
! intercept variance
s1-s3*0.1;
[s1-s3*1.3];
%between level2a%
! across time variation of measurement intercepts and factor
f*0.5;
y1-y3*.3;
output:
tech8;
INPUT READING TERMINATED NORMALLY
this is an example of a cross-classified time
series analysis with a first-order
autoregressive AR(1) confirmatory factor
analysis (CFA) model for continuous factor
indicators with random intercepts, random
factor loadings, and a factor varying across
both subjects and time
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 3
Number of independent variables 0
Number of continuous latent variables 5
Observed dependent variables
Continuous
Y1 Y2 Y3
Continuous latent variables
F F&1 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 200
MODEL FIT INFORMATION
Number of Free Parameters 21
Information Criteria
Deviance (DIC)
Mean 198711.622
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 198711.622 198711.622
0.980 0.000 198711.622 198711.622
0.950 0.000 198711.622 198711.622
0.900 0.000 198711.622 198711.622
0.800 0.000 198711.622 198711.622
0.700 0.000 198711.622 198711.622
0.500 0.000 198711.622 198711.622
0.300 0.000 198711.622 198711.622
0.200 0.000 198711.622 198711.622
0.100 0.000 198711.622 198711.622
0.050 0.000 198711.622 198711.622
0.020 0.000 198711.622 198711.622
0.010 0.000 198711.622 198711.622
Estimated Number of Parameters (pD)
Mean 17156.030
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 17156.030 17156.030
0.980 0.000 17156.030 17156.030
0.950 0.000 17156.030 17156.030
0.900 0.000 17156.030 17156.030
0.800 0.000 17156.030 17156.030
0.700 0.000 17156.030 17156.030
0.500 0.000 17156.030 17156.030
0.300 0.000 17156.030 17156.030
0.200 0.000 17156.030 17156.030
0.100 0.000 17156.030 17156.030
0.050 0.000 17156.030 17156.030
0.020 0.000 17156.030 17156.030
0.010 0.000 17156.030 17156.030
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
F ON
F&1 0.300 0.3059 0.0000 0.0085 0.0000 1.000 1.000
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
Residual Variances
Y1 1.200 1.2201 0.0000 0.0181 0.0004 1.000 1.000
Y2 1.200 1.1819 0.0000 0.0180 0.0003 1.000 1.000
Y3 1.200 1.2191 0.0000 0.0183 0.0004 1.000 1.000
F 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Between LEVEL2A Level
Variances
Y1 0.300 0.3113 0.0000 0.0524 0.0001 1.000 1.000
Y2 0.300 0.2700 0.0000 0.0468 0.0009 1.000 1.000
Y3 0.300 0.3453 0.0000 0.0573 0.0021 1.000 1.000
F 0.500 0.4924 0.0000 0.0786 0.0001 1.000 1.000
Between LEVEL2B Level
Means
Y1 1.000 1.0436 0.0000 0.1485 0.0019 1.000 1.000
Y2 1.000 1.0252 0.0000 0.1556 0.0006 1.000 1.000
Y3 1.000 0.9718 0.0000 0.1479 0.0008 1.000 1.000
S1 1.300 1.3157 0.0000 0.0263 0.0002 1.000 1.000
S2 1.300 1.3162 0.0000 0.0258 0.0003 1.000 1.000
S3 1.300 1.3163 0.0000 0.0245 0.0003 1.000 1.000
Variances
Y1 0.500 0.5712 0.0000 0.0843 0.0051 1.000 1.000
Y2 0.500 0.5807 0.0000 0.0842 0.0065 1.000 1.000
Y3 0.500 0.3897 0.0000 0.0699 0.0122 1.000 1.000
F 1.000 0.8762 0.0000 0.0975 0.0153 1.000 1.000
S1 0.100 0.1105 0.0000 0.0132 0.0001 1.000 1.000
S2 0.100 0.1036 0.0000 0.0124 0.0000 1.000 1.000
S3 0.100 0.0952 0.0000 0.0116 0.0000 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%2a 0.972 0.000 0.162 0.000
S1%2a 0.000 0.000 0.029 0.000
S2%2a 0.000 0.000 0.031 0.000
S3%2a 0.000 0.000 0.030 0.000
F%2b 0.972 0.000 0.233 0.000
S1%2b 0.927 0.000 0.124 0.000
S2%2b 0.928 0.000 0.115 0.000
S3%2b 0.916 0.000 0.124 0.000
B2a_Y1 0.936 0.000 0.204 0.000
B2a_Y2 0.920 0.000 0.199 0.000
B2a_Y3 0.928 0.000 0.216 0.000
B2b_Y1 0.810 0.000 0.425 0.000
B2b_Y2 0.830 0.000 0.380 0.000
B2b_Y3 0.794 0.000 0.390 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3
________ ________ ________
0 0 0
LAMBDA
F%W F&1
________ ________
Y1 0 0
Y2 0 0
Y3 0 0
THETA
Y1 Y2 Y3
________ ________ ________
Y1 1
Y2 0 2
Y3 0 0 3
ALPHA
F%W F&1
________ ________
0 0
BETA
F%W F&1
________ ________
F%W 0 4
F&1 0 0
PSI
F%W F&1
________ ________
F%W 0
F&1 0 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 5
Y2 0 6
Y3 0 0 7
ALPHA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
0 0 0 0
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 8
S1%2a 0 0
S2%2a 0 0 0
S3%2a 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B
NU
Y1 Y2 Y3
________ ________ ________
9 10 11
LAMBDA
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
Y1 0 0 0 0
Y2 0 0 0 0
Y3 0 0 0 0
THETA
Y1 Y2 Y3
________ ________ ________
Y1 12
Y2 0 13
Y3 0 0 14
ALPHA
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
0 15 16 17
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 18
S1%2b 0 19
S2%2b 0 0 20
S3%2b 0 0 0 21
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
F%W F&1
________ ________
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 1.200
Y2 0.000 1.200
Y3 0.000 0.000 1.200
ALPHA
F%W F&1
________ ________
0.000 0.000
BETA
F%W F&1
________ ________
F%W 0.000 0.300
F&1 0.000 0.000
PSI
F%W F&1
________ ________
F%W 1.000
F&1 0.000 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 0.300
Y2 0.000 0.300
Y3 0.000 0.000 0.300
ALPHA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
0.000 0.000 0.000 0.000
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 0.500
S1%2a 0.000 0.000
S2%2a 0.000 0.000 0.000
S3%2a 0.000 0.000 0.000 0.000
STARTING VALUES FOR BETWEEN LEVEL2B
NU
Y1 Y2 Y3
________ ________ ________
1.000 1.000 1.000
LAMBDA
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
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%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
0.000 1.300 1.300 1.300
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 0.100
S2%2b 0.000 0.000 0.100
S3%2b 0.000 0.000 0.000 0.100
POPULATION VALUES FOR WITHIN
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
F%W F&1
________ ________
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 1.200
Y2 0.000 1.200
Y3 0.000 0.000 1.200
ALPHA
F%W F&1
________ ________
0.000 0.000
BETA
F%W F&1
________ ________
F%W 0.000 0.300
F&1 0.000 0.000
PSI
F%W F&1
________ ________
F%W 1.000
F&1 0.000 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 0.300
Y2 0.000 0.300
Y3 0.000 0.000 0.300
ALPHA
F%2a S1%2a S2%2a S3%2a
________ ________ ________ ________
0.000 0.000 0.000 0.000
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 0.500
S1%2a 0.000 0.000
S2%2a 0.000 0.000 0.000
S3%2a 0.000 0.000 0.000 0.000
POPULATION VALUES FOR BETWEEN LEVEL2B
NU
Y1 Y2 Y3
________ ________ ________
1.000 1.000 1.000
LAMBDA
F%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
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%2b S1%2b S2%2b S3%2b
________ ________ ________ ________
0.000 1.300 1.300 1.300
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 0.100
S2%2b 0.000 0.000 0.100
S3%2b 0.000 0.000 0.000 0.100
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~N(0.000,infinity) 0.0000 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~IG(-1.000,0.000) infinity 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~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~IG(-1.000,0.000) infinity infinity infinity
Parameter 19~IG(-1.000,0.000) infinity infinity infinity
Parameter 20~IG(-1.000,0.000) infinity infinity infinity
Parameter 21~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 1.744 11
200 1.637 14
300 1.711 14
400 1.517 12
500 1.462 12
600 1.412 11
700 1.355 11
800 1.441 11
900 1.220 11
1000 1.210 11
1100 1.195 11
1200 1.187 14
1300 1.169 12
1400 1.159 12
1500 1.123 12
1600 1.061 12
1700 1.077 10
1800 1.121 11
1900 1.171 11
2000 1.206 11
2100 1.253 11
2200 1.290 11
2300 1.303 11
2400 1.371 11
2500 1.436 11
2600 1.509 11
2700 1.664 11
2800 1.728 11
2900 1.569 11
3000 1.497 11
3100 1.493 11
3200 1.482 11
3300 1.410 11
3400 1.366 11
3500 1.339 11
3600 1.310 11
3700 1.252 11
3800 1.185 11
3900 1.169 11
4000 1.177 11
4100 1.177 11
4200 1.169 11
4300 1.194 11
4400 1.238 11
4500 1.275 11
4600 1.320 11
4700 1.353 11
4800 1.387 11
4900 1.414 11
5000 1.442 11
5100 1.484 11
5200 1.510 11
5300 1.521 11
5400 1.532 11
5500 1.573 11
5600 1.600 9
5700 1.630 9
5800 1.639 9
5900 1.598 9
6000 1.523 9
6100 1.446 9
6200 1.390 9
6300 1.344 9
6400 1.301 10
6500 1.265 10
6600 1.233 10
6700 1.216 10
6800 1.187 9
6900 1.176 9
7000 1.163 9
7100 1.151 9
7200 1.140 9
7300 1.126 9
7400 1.120 9
7500 1.119 9
7600 1.109 9
7700 1.105 9
7800 1.103 9
7900 1.103 9
8000 1.099 9
8100 1.094 9
8200 1.092 9
8300 1.094 10
8400 1.095 10
8500 1.089 10
8600 1.087 10
8700 1.087 10
8800 1.085 10
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
LEVEL2A
LEVEL2B
Save file
ex9.40part2.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:38:47
Ending Time: 22:46:41
Elapsed Time: 00:07:54
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