Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:27 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level confirmatory factor
analysis (CFA) with continuous factor indicators,
covariates, and a factor with a random residual variance
MONTECARLO:
NAMES ARE y1-y4 x1 x2 w;
NOBSERVATIONS = 1000;
NCSIZES = 3;
CSIZES = 40 (5) 50 (10) 20 (15);
SEED = 58459;
NREPS = 1;
WITHIN = x1 x2;
BETWEEN = w;
SAVE = ex9.29.dat;
MODEL POPULATION:
%WITHIN%
x1-x2@1;
fw BY y1@1
y2*1
y3*1
y4*1;
fw ON x1*1 x2*.5;
y1-y4*1;
logv | fw;
%BETWEEN%
[w@0]; w@.7;
fb BY y1@1
y2*1
y3*1
y4*1;
fb ON w*.5;
fb*.4;
y1-y4*.1;
logv ON w*.3;
[logv*0]; logv*.1;
ANALYSIS:
TYPE = TWOLEVEL RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (10000);
MODEL:
%WITHIN%
fw BY y1@1
y2*1
y3*1
y4*1;
fw ON x1*1 x2*.5;
y1-y4*1;
logv | fw;
%BETWEEN%
fb BY y1@1
y2*1
y3*1
y4*1;
fb ON w*.5;
fb*.4;
y1-y4*.1;
logv ON w*.3;
[logv*0]; logv*.1;
OUTPUT:
TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level confirmatory factor
analysis (CFA) with continuous factor indicators,
covariates, and a factor with a random residual variance
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of replications
Requested 1
Completed 1
Value of seed 58459
Number of dependent variables 4
Number of independent variables 3
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Observed independent variables
X1 X2 W
Continuous latent variables
FW FB LOGV
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 25
Information Criteria
Deviance (DIC)
Mean 13116.455
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 13116.455 13116.455
0.980 0.000 13116.455 13116.455
0.950 0.000 13116.455 13116.455
0.900 0.000 13116.455 13116.455
0.800 0.000 13116.455 13116.455
0.700 0.000 13116.455 13116.455
0.500 0.000 13116.455 13116.455
0.300 0.000 13116.455 13116.455
0.200 0.000 13116.455 13116.455
0.100 0.000 13116.455 13116.455
0.050 0.000 13116.455 13116.455
0.020 0.000 13116.455 13116.455
0.010 0.000 13116.455 13116.455
Estimated Number of Parameters (pD)
Mean 269.545
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 269.545 269.545
0.980 0.000 269.545 269.545
0.950 0.000 269.545 269.545
0.900 0.000 269.545 269.545
0.800 0.000 269.545 269.545
0.700 0.000 269.545 269.545
0.500 0.000 269.545 269.545
0.300 0.000 269.545 269.545
0.200 0.000 269.545 269.545
0.100 0.000 269.545 269.545
0.050 0.000 269.545 269.545
0.020 0.000 269.545 269.545
0.010 0.000 269.545 269.545
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
FW BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0754 0.0000 0.0355 0.0057 0.000 1.000
Y3 1.000 1.0587 0.0000 0.0348 0.0034 1.000 1.000
Y4 1.000 1.0371 0.0000 0.0350 0.0014 1.000 1.000
FW ON
X1 1.000 0.9707 0.0000 0.0399 0.0009 1.000 1.000
X2 0.500 0.4343 0.0000 0.0350 0.0043 1.000 1.000
Residual Variances
Y1 1.000 0.9973 0.0000 0.0593 0.0000 1.000 1.000
Y2 1.000 0.9816 0.0000 0.0611 0.0003 1.000 1.000
Y3 1.000 0.9316 0.0000 0.0584 0.0047 1.000 1.000
Y4 1.000 1.0228 0.0000 0.0617 0.0005 1.000 1.000
Between Level
FB BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.2973 0.0000 0.1601 0.0884 0.000 1.000
Y3 1.000 1.2002 0.0000 0.1458 0.0401 1.000 1.000
Y4 1.000 1.2146 0.0000 0.1626 0.0460 1.000 1.000
FB ON
W 0.500 0.4822 0.0000 0.0832 0.0003 1.000 1.000
LOGV ON
W 0.300 0.3947 0.0000 0.0811 0.0090 1.000 1.000
Intercepts
Y1 0.000 -0.0730 0.0000 0.0710 0.0053 1.000 0.000
Y2 0.000 0.0162 0.0000 0.0820 0.0003 1.000 0.000
Y3 0.000 -0.0759 0.0000 0.0750 0.0058 1.000 0.000
Y4 0.000 0.0201 0.0000 0.0834 0.0004 1.000 0.000
LOGV 0.000 -0.1193 0.0000 0.0772 0.0142 1.000 0.000
Residual Variances
Y1 0.100 0.1036 0.0000 0.0403 0.0000 1.000 1.000
Y2 0.100 0.1384 0.0000 0.0483 0.0015 1.000 1.000
Y3 0.100 0.0566 0.0000 0.0339 0.0019 1.000 1.000
Y4 0.100 0.1895 0.0000 0.0545 0.0080 0.000 1.000
FB 0.400 0.1956 0.0000 0.0566 0.0418 0.000 1.000
LOGV 0.100 0.0667 0.0000 0.0568 0.0011 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 0.866 0.000 0.382 0.000
LOGV 0.653 0.000 0.319 0.000
Y1 0.868 0.000 0.408 0.000
Y2 0.878 0.000 0.402 0.000
Y3 0.861 0.000 0.412 0.000
Y4 0.841 0.000 0.461 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
0 0 0 0 0
NU
X2
________
0
LAMBDA
FW X1 X2
________ ________ ________
Y1 0 0 0
Y2 1 0 0
Y3 2 0 0
Y4 3 0 0
X1 0 0 0
X2 0 0 0
THETA
Y1 Y2 Y3 Y4 X1
________ ________ ________ ________ ________
Y1 4
Y2 0 5
Y3 0 0 6
Y4 0 0 0 7
X1 0 0 0 0 0
X2 0 0 0 0 0
THETA
X2
________
X2 0
ALPHA
FW X1 X2
________ ________ ________
0 0 0
BETA
FW X1 X2
________ ________ ________
FW 0 8 9
X1 0 0 0
X2 0 0 0
PSI
FW X1 X2
________ ________ ________
FW 0
X1 0 0
X2 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
10 11 12 13 0
LAMBDA
FB LOGV W
________ ________ ________
Y1 0 0 0
Y2 14 0 0
Y3 15 0 0
Y4 16 0 0
W 0 0 0
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 17
Y2 0 18
Y3 0 0 19
Y4 0 0 0 20
W 0 0 0 0 0
ALPHA
FB LOGV W
________ ________ ________
0 21 0
BETA
FB LOGV W
________ ________ ________
FB 0 0 22
LOGV 0 0 23
W 0 0 0
PSI
FB LOGV W
________ ________ ________
FB 24
LOGV 0 25
W 0 0 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
FW X1 X2
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 1.000 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
FW X1 X2
________ ________ ________
0.000 0.000 0.000
BETA
FW X1 X2
________ ________ ________
FW 0.000 1.000 0.500
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
PSI
FW X1 X2
________ ________ ________
FW 0.000
X1 0.000 0.500
X2 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
FB LOGV W
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 1.000 0.000 0.000
W 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0.100
Y2 0.000 0.100
Y3 0.000 0.000 0.100
Y4 0.000 0.000 0.000 0.100
W 0.000 0.000 0.000 0.000 0.000
ALPHA
FB LOGV W
________ ________ ________
0.000 0.000 0.000
BETA
FB LOGV W
________ ________ ________
FB 0.000 0.000 0.500
LOGV 0.000 0.000 0.300
W 0.000 0.000 0.000
PSI
FB LOGV W
________ ________ ________
FB 0.400
LOGV 0.000 0.100
W 0.000 0.000 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
FW X1 X2
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 1.000 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
FW X1 X2
________ ________ ________
0.000 0.000 0.000
BETA
FW X1 X2
________ ________ ________
FW 0.000 1.000 0.500
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
PSI
FW X1 X2
________ ________ ________
FW 0.000
X1 0.000 1.000
X2 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
FB LOGV W
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 1.000 0.000 0.000
W 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0.100
Y2 0.000 0.100
Y3 0.000 0.000 0.100
Y4 0.000 0.000 0.000 0.100
W 0.000 0.000 0.000 0.000 0.000
ALPHA
FB LOGV W
________ ________ ________
0.000 0.000 0.000
BETA
FB LOGV W
________ ________ ________
FB 0.000 0.000 0.500
LOGV 0.000 0.000 0.300
W 0.000 0.000 0.000
PSI
FB LOGV W
________ ________ ________
FB 0.400
LOGV 0.000 0.100
W 0.000 0.000 0.700
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~N(0.000,infinity) 0.0000 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~IG(-1.000,0.000) infinity infinity infinity
Parameter 21~N(0.000,infinity) 0.0000 infinity infinity
Parameter 22~N(0.000,infinity) 0.0000 infinity infinity
Parameter 23~N(0.000,infinity) 0.0000 infinity infinity
Parameter 24~IG(-1.000,0.000) infinity infinity infinity
Parameter 25~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 2.761 23
200 1.505 25
300 1.878 21
400 2.598 25
500 3.001 25
600 2.635 25
700 2.204 25
800 1.928 21
900 1.876 21
1000 1.824 21
1100 1.732 21
1200 1.638 25
1300 1.721 21
1400 1.607 21
1500 1.589 23
1600 1.492 21
1700 1.396 21
1800 1.359 21
1900 1.241 21
2000 1.186 21
2100 1.138 21
2200 1.141 21
2300 1.137 21
2400 1.105 21
2500 1.079 21
2600 1.102 25
2700 1.116 25
2800 1.157 25
2900 1.218 25
3000 1.271 25
3100 1.262 25
3200 1.203 25
3300 1.110 25
3400 1.065 25
3500 1.057 12
3600 1.057 10
3700 1.042 10
3800 1.027 10
3900 1.018 10
4000 1.018 10
4100 1.014 16
4200 1.016 16
4300 1.019 25
4400 1.022 25
4500 1.029 25
4600 1.037 25
4700 1.046 25
4800 1.053 25
4900 1.053 25
5000 1.073 23
5100 1.083 23
5200 1.095 23
5300 1.116 25
5400 1.133 25
5500 1.159 25
5600 1.182 25
5700 1.234 25
5800 1.292 25
5900 1.361 25
6000 1.393 25
6100 1.395 25
6200 1.328 25
6300 1.285 25
6400 1.261 25
6500 1.243 25
6600 1.231 25
6700 1.208 25
6800 1.208 25
6900 1.203 25
7000 1.197 25
7100 1.194 25
7200 1.198 25
7300 1.214 25
7400 1.229 25
7500 1.238 25
7600 1.254 25
7700 1.263 25
7800 1.241 25
7900 1.230 25
8000 1.217 25
8100 1.198 25
8200 1.180 25
8300 1.173 25
8400 1.167 25
8500 1.156 25
8600 1.146 25
8700 1.137 25
8800 1.131 25
8900 1.116 25
9000 1.106 25
9100 1.096 25
9200 1.080 25
9300 1.080 25
9400 1.079 25
9500 1.072 25
9600 1.072 25
9700 1.076 25
9800 1.085 25
9900 1.088 25
10000 1.091 25
10100 1.088 25
10200 1.080 25
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
X1
X2
W
CLUSTER
Save file
ex9.29.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:27:41
Ending Time: 22:27:58
Elapsed Time: 00:00:17
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