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 = ex9.40.dat;
ANALYSIS: TYPE = cross;
estimator = bayes;
proc = 2;
biter = (2000);
model population:
%within%
y1-y3*1.2; [y1-y3@0];
f by y1-y3*1.3 (&1 1-3);
f@1;
f on f&1*.3;
%between level2b%
! across subject variation in measurement intercepts
! and factor
fsubj by y1-y3*1.3 (1-3);
fsubj*1;
y1-y3*.5;
[y1-y3*1]; ! estimating the intercepts on the level with most
! intercept variance
%between level2a%
! across time variation of measurement intercepts and factor
ftime by y1-y3*1.3 (1-3);
ftime*0.5;
y1-y3*.3;
model:
%within%
y1-y3*1.2; [y1-y3@0];
f by y1-y3*1.3 (&1 1-3);
f@1;
f on f&1*.3;
%between level2b%
! across subject variation in measurement intercepts
! and factor
fsubj by y1-y3*1.3 (1-3);
fsubj*1;
y1-y3*.5;
[y1-y3*1]; ! estimating the intercepts on the level with most
! intercept variance
%between level2a%
! across time variation of measurement intercepts and factor
ftime by y1-y3*1.3 (1-3);
ftime*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 4
Observed dependent variables
Continuous
Y1 Y2 Y3
Continuous latent variables
F F&1 FTIME FSUBJ
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 18
Information Criteria
Deviance (DIC)
Mean 197712.860
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 197712.860 197712.860
0.980 0.000 197712.860 197712.860
0.950 0.000 197712.860 197712.860
0.900 0.000 197712.860 197712.860
0.800 0.000 197712.860 197712.860
0.700 0.000 197712.860 197712.860
0.500 0.000 197712.860 197712.860
0.300 0.000 197712.860 197712.860
0.200 0.000 197712.860 197712.860
0.100 0.000 197712.860 197712.860
0.050 0.000 197712.860 197712.860
0.020 0.000 197712.860 197712.860
0.010 0.000 197712.860 197712.860
Estimated Number of Parameters (pD)
Mean 16481.857
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 16481.857 16481.857
0.980 0.000 16481.857 16481.857
0.950 0.000 16481.857 16481.857
0.900 0.000 16481.857 16481.857
0.800 0.000 16481.857 16481.857
0.700 0.000 16481.857 16481.857
0.500 0.000 16481.857 16481.857
0.300 0.000 16481.857 16481.857
0.200 0.000 16481.857 16481.857
0.100 0.000 16481.857 16481.857
0.050 0.000 16481.857 16481.857
0.020 0.000 16481.857 16481.857
0.010 0.000 16481.857 16481.857
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
F BY
Y1 1.300 1.2797 0.0000 0.0111 0.0004 1.000 1.000
Y2 1.300 1.2967 0.0000 0.0109 0.0000 1.000 1.000
Y3 1.300 1.2678 0.0000 0.0111 0.0010 0.000 1.000
F ON
F&1 0.300 0.2988 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 1.1987 0.0000 0.0181 0.0000 1.000 1.000
Y2 1.200 1.1725 0.0000 0.0189 0.0008 1.000 1.000
Y3 1.200 1.2319 0.0000 0.0178 0.0010 1.000 1.000
F 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Between LEVEL2A Level
FTIME BY
Y1 1.300 1.2797 0.0000 0.0111 0.0004 1.000 1.000
Y2 1.300 1.2967 0.0000 0.0109 0.0000 1.000 1.000
Y3 1.300 1.2678 0.0000 0.0111 0.0010 0.000 1.000
Variances
FTIME 0.500 0.6191 0.0000 0.1023 0.0142 1.000 1.000
Residual Variances
Y1 0.300 0.1281 0.0000 0.0480 0.0296 0.000 1.000
Y2 0.300 0.3705 0.0000 0.0752 0.0050 1.000 1.000
Y3 0.300 0.3521 0.0000 0.0713 0.0027 1.000 1.000
Between LEVEL2B Level
FSUBJ BY
Y1 1.300 1.2797 0.0000 0.0111 0.0004 1.000 1.000
Y2 1.300 1.2967 0.0000 0.0109 0.0000 1.000 1.000
Y3 1.300 1.2678 0.0000 0.0111 0.0010 0.000 1.000
Intercepts
Y1 1.000 0.9852 0.0000 0.1520 0.0002 1.000 1.000
Y2 1.000 1.0180 0.0000 0.1372 0.0003 1.000 1.000
Y3 1.000 0.8339 0.0000 0.1452 0.0276 1.000 1.000
Variances
FSUBJ 1.000 0.8908 0.0000 0.1084 0.0119 1.000 1.000
Residual Variances
Y1 0.500 0.5350 0.0000 0.0815 0.0012 1.000 1.000
Y2 0.500 0.5036 0.0000 0.0828 0.0000 1.000 1.000
Y3 0.500 0.5895 0.0000 0.0888 0.0080 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.
B2a_Y1 0.993 0.000 0.154 0.000
B2a_Y2 0.994 0.000 0.143 0.000
B2a_Y3 0.995 0.000 0.220 0.000
B2b_Y1 0.988 0.000 0.240 0.000
B2b_Y2 0.987 0.000 0.230 0.000
B2b_Y3 0.989 0.000 0.299 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3
________ ________ ________
0 0 0
LAMBDA
F F&1
________ ________
Y1 1 0
Y2 2 0
Y3 3 0
THETA
Y1 Y2 Y3
________ ________ ________
Y1 4
Y2 0 5
Y3 0 0 6
ALPHA
F F&1
________ ________
0 0
BETA
F F&1
________ ________
F 0 7
F&1 0 0
PSI
F F&1
________ ________
F 0
F&1 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A
NU
Y1 Y2 Y3
________ ________ ________
0 0 0
LAMBDA
FTIME
________
Y1 1
Y2 2
Y3 3
THETA
Y1 Y2 Y3
________ ________ ________
Y1 8
Y2 0 9
Y3 0 0 10
ALPHA
FTIME
________
0
BETA
FTIME
________
FTIME 0
PSI
FTIME
________
FTIME 11
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B
NU
Y1 Y2 Y3
________ ________ ________
12 13 14
LAMBDA
FSUBJ
________
Y1 1
Y2 2
Y3 3
THETA
Y1 Y2 Y3
________ ________ ________
Y1 15
Y2 0 16
Y3 0 0 17
ALPHA
FSUBJ
________
0
BETA
FSUBJ
________
FSUBJ 0
PSI
FSUBJ
________
FSUBJ 18
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
F F&1
________ ________
Y1 1.300 0.000
Y2 1.300 0.000
Y3 1.300 0.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 1.200
Y2 0.000 1.200
Y3 0.000 0.000 1.200
ALPHA
F F&1
________ ________
0.000 0.000
BETA
F F&1
________ ________
F 0.000 0.300
F&1 0.000 0.000
PSI
F F&1
________ ________
F 1.000
F&1 0.000 1.000
STARTING VALUES FOR BETWEEN LEVEL2A
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
FTIME
________
Y1 1.300
Y2 1.300
Y3 1.300
THETA
Y1 Y2 Y3
________ ________ ________
Y1 0.300
Y2 0.000 0.300
Y3 0.000 0.000 0.300
ALPHA
FTIME
________
0.000
BETA
FTIME
________
FTIME 0.000
PSI
FTIME
________
FTIME 0.500
STARTING VALUES FOR BETWEEN LEVEL2B
NU
Y1 Y2 Y3
________ ________ ________
1.000 1.000 1.000
LAMBDA
FSUBJ
________
Y1 1.300
Y2 1.300
Y3 1.300
THETA
Y1 Y2 Y3
________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
ALPHA
FSUBJ
________
0.000
BETA
FSUBJ
________
FSUBJ 0.000
PSI
FSUBJ
________
FSUBJ 1.000
POPULATION VALUES FOR WITHIN
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
F F&1
________ ________
Y1 1.300 0.000
Y2 1.300 0.000
Y3 1.300 0.000
THETA
Y1 Y2 Y3
________ ________ ________
Y1 1.200
Y2 0.000 1.200
Y3 0.000 0.000 1.200
ALPHA
F F&1
________ ________
0.000 0.000
BETA
F F&1
________ ________
F 0.000 0.300
F&1 0.000 0.000
PSI
F F&1
________ ________
F 1.000
F&1 0.000 1.000
POPULATION VALUES FOR BETWEEN LEVEL2A
NU
Y1 Y2 Y3
________ ________ ________
0.000 0.000 0.000
LAMBDA
FTIME
________
Y1 1.300
Y2 1.300
Y3 1.300
THETA
Y1 Y2 Y3
________ ________ ________
Y1 0.300
Y2 0.000 0.300
Y3 0.000 0.000 0.300
ALPHA
FTIME
________
0.000
BETA
FTIME
________
FTIME 0.000
PSI
FTIME
________
FTIME 0.500
POPULATION VALUES FOR BETWEEN LEVEL2B
NU
Y1 Y2 Y3
________ ________ ________
1.000 1.000 1.000
LAMBDA
FSUBJ
________
Y1 1.300
Y2 1.300
Y3 1.300
THETA
Y1 Y2 Y3
________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
ALPHA
FSUBJ
________
0.000
BETA
FSUBJ
________
FSUBJ 0.000
PSI
FSUBJ
________
FSUBJ 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~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~N(0.000,infinity) 0.0000 infinity infinity
Parameter 8~IG(-1.000,0.000) infinity infinity infinity
Parameter 9~IG(-1.000,0.000) infinity infinity infinity
Parameter 10~IG(-1.000,0.000) infinity infinity infinity
Parameter 11~IG(-1.000,0.000) infinity 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~IG(-1.000,0.000) infinity 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
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 1.178 16
200 1.178 8
300 1.276 13
400 1.441 13
500 1.450 14
600 1.533 14
700 1.786 14
800 1.669 14
900 1.843 14
1000 2.033 14
1100 2.331 12
1200 2.297 12
1300 2.065 12
1400 1.692 12
1500 1.400 12
1600 1.215 12
1700 1.069 13
1800 1.024 12
1900 1.008 12
2000 1.013 14
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
LEVEL2A
LEVEL2B
Save file
ex9.40.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:38:31
Ending Time: 22:38:46
Elapsed Time: 00:00:15
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