Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:20 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level MIMIC model with
continuous factor indicators, random factor loadings,
two covariates on within, and one covariate on between.
Analyzed with random within- and fixed between-level
factor loadings
DATA: FILE = ex9.19.dat;
VARIABLE: NAMES = y1-y4 x1 x2 w clus;
CLUSTER = clus;
WITHIN = x1 x2;
BETWEEN = w;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITER = (1000);
MODEL: %WITHIN%
s1-s4 | f BY y1-y4;
f@1;
f ON x1 x2;
%BETWEEN%
fb BY y1-y4;
fb ON w;
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT2;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level MIMIC model with
continuous factor indicators, random factor loadings,
two covariates on within, and one covariate on between.
Analyzed with random within- and fixed between-level
factor loadings
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of dependent variables 4
Number of independent variables 3
Number of continuous latent variables 6
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Observed independent variables
X1 X2 W
Continuous latent variables
F FB S1 S2 S3 S4
Variables with special functions
Cluster variable CLUS
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
Input data file(s)
ex9.19.dat
Input data format FREE
SUMMARY OF DATA
Number of clusters 110
Size (s) Cluster ID with Size s
5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
40
10 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76
77 78 79 80 81 82 83 84 85 86 87 88 89 90
15 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106
107 108 109 110
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
Y1 0.622 0.138 -8.699 0.10% -1.236 0.051 0.577
1000.000 5.389 0.822 10.854 0.10% 1.110 2.353
Y2 0.461 -0.054 -7.418 0.10% -1.231 -0.008 0.440
1000.000 5.129 0.737 7.979 0.10% 0.969 2.248
Y3 0.554 0.238 -6.332 0.10% -1.119 0.022 0.552
1000.000 4.956 0.770 9.120 0.10% 1.001 2.127
Y4 0.431 -0.106 -9.085 0.10% -1.223 -0.026 0.497
1000.000 5.333 1.012 7.892 0.10% 0.917 2.096
X1 -0.036 0.002 -3.279 0.10% -0.872 -0.294 -0.041
1000.000 1.010 0.148 3.500 0.10% 0.235 0.799
X2 0.029 0.101 -2.824 0.10% -0.815 -0.258 0.000
1000.000 1.003 -0.110 3.610 0.10% 0.236 0.899
W 0.215 -0.244 -3.147 0.91% -0.630 0.035 0.257
110.000 1.102 0.683 3.025 0.91% 0.473 1.017
THE MODEL ESTIMATION TERMINATED NORMALLY
USE THE FBITERATIONS OPTION TO INCREASE THE NUMBER OF ITERATIONS BY A FACTOR
OF AT LEAST TWO TO CHECK CONVERGENCE AND THAT THE PSR VALUE DOES NOT INCREASE.
MODEL FIT INFORMATION
Number of Free Parameters 27
Information Criteria
Deviance (DIC) 13838.368
Estimated Number of Parameters (pD) 652.166
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
F ON
X1 0.826 0.043 0.000 0.748 0.913 *
X2 0.378 0.040 0.000 0.302 0.454 *
Residual Variances
Y1 0.997 0.070 0.000 0.864 1.137 *
Y2 1.154 0.071 0.000 1.018 1.302 *
Y3 0.902 0.059 0.000 0.802 1.028 *
Y4 0.959 0.062 0.000 0.846 1.096 *
F 1.000 0.000 0.000 1.000 1.000
Between Level
FB BY
Y1 1.000 0.000 0.000 1.000 1.000
Y2 1.521 0.354 0.000 1.028 2.388 *
Y3 1.170 0.300 0.000 0.740 1.839 *
Y4 1.092 0.290 0.000 0.657 1.798 *
FB ON
W 0.460 0.098 0.000 0.280 0.655 *
Means
S1 1.104 0.067 0.000 0.962 1.227 *
S2 0.982 0.067 0.000 0.847 1.108 *
S3 1.080 0.073 0.000 0.931 1.219 *
S4 1.089 0.080 0.000 0.937 1.248 *
Intercepts
Y1 0.510 0.109 0.000 0.297 0.725 *
Y2 0.325 0.116 0.001 0.118 0.558 *
Y3 0.413 0.118 0.000 0.179 0.644 *
Y4 0.351 0.119 0.000 0.126 0.592 *
Variances
S1 0.271 0.061 0.000 0.175 0.409 *
S2 0.241 0.056 0.000 0.148 0.362 *
S3 0.335 0.070 0.000 0.228 0.503 *
S4 0.498 0.095 0.000 0.355 0.725 *
Residual Variances
Y1 0.856 0.165 0.000 0.599 1.221 *
Y2 0.739 0.186 0.000 0.415 1.160 *
Y3 0.764 0.158 0.000 0.498 1.114 *
Y4 0.757 0.195 0.000 0.471 1.246 *
FB 0.130 0.087 0.000 0.034 0.382 *
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 FB S1 S2 S3
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 11 0 0 0
Y3 0 12 0 0 0
Y4 0 13 0 0 0
W 0 0 0 0 0
LAMBDA
S4 W
________ ________
Y1 0 0
Y2 0 0
Y3 0 0
Y4 0 0
W 0 0
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 14
Y2 0 15
Y3 0 0 16
Y4 0 0 0 17
W 0 0 0 0 0
ALPHA
F%B FB S1 S2 S3
________ ________ ________ ________ ________
0 0 18 19 20
ALPHA
S4 W
________ ________
21 0
BETA
F%B FB S1 S2 S3
________ ________ ________ ________ ________
F%B 0 0 0 0 0
FB 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
S4 W
________ ________
F%B 0 0
FB 0 22
S1 0 0
S2 0 0
S3 0 0
S4 0 0
W 0 0
PSI
F%B FB S1 S2 S3
________ ________ ________ ________ ________
F%B 0
FB 0 23
S1 0 0 24
S2 0 0 0 25
S3 0 0 0 0 26
S4 0 0 0 0 0
W 0 0 0 0 0
PSI
S4 W
________ ________
S4 27
W 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
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 2.695
Y2 0.000 2.565
Y3 0.000 0.000 2.478
Y4 0.000 0.000 0.000 2.667
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 0.000 0.000
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 0.505
X2 0.000 0.000 0.501
STARTING VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0.622 0.461 0.554 0.431 0.000
LAMBDA
F%B FB S1 S2 S3
________ ________ ________ ________ ________
Y1 0.000 1.000 0.000 0.000 0.000
Y2 0.000 1.000 0.000 0.000 0.000
Y3 0.000 1.000 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
LAMBDA
S4 W
________ ________
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
W 0.000 1.000
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 2.695
Y2 0.000 2.565
Y3 0.000 0.000 2.478
Y4 0.000 0.000 0.000 2.667
W 0.000 0.000 0.000 0.000 0.000
ALPHA
F%B FB S1 S2 S3
________ ________ ________ ________ ________
0.000 0.000 1.000 1.000 1.000
ALPHA
S4 W
________ ________
1.000 0.000
BETA
F%B FB S1 S2 S3
________ ________ ________ ________ ________
F%B 0.000 0.000 0.000 0.000 0.000
FB 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
S4 W
________ ________
F%B 0.000 0.000
FB 0.000 0.000
S1 0.000 0.000
S2 0.000 0.000
S3 0.000 0.000
S4 0.000 0.000
W 0.000 0.000
PSI
F%B FB S1 S2 S3
________ ________ ________ ________ ________
F%B 0.000
FB 0.000 1.000
S1 0.000 0.000 1.000
S2 0.000 0.000 0.000 1.000
S3 0.000 0.000 0.000 0.000 1.000
S4 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
PSI
S4 W
________ ________
S4 1.000
W 0.000 0.561
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~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~IG(-1.000,0.000) infinity 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~N(0.000,infinity) 0.0000 infinity infinity
Parameter 19~N(0.000,infinity) 0.0000 infinity infinity
Parameter 20~N(0.000,infinity) 0.0000 infinity infinity
Parameter 21~N(0.000,infinity) 0.0000 infinity infinity
Parameter 22~N(0.000,infinity) 0.0000 infinity infinity
Parameter 23~IG(-1.000,0.000) infinity infinity infinity
Parameter 24~IG(-1.000,0.000) infinity infinity infinity
Parameter 25~IG(-1.000,0.000) infinity infinity infinity
Parameter 26~IG(-1.000,0.000) infinity infinity infinity
Parameter 27~IG(-1.000,0.000) infinity infinity infinity
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
CHAIN BSEED
1 0
2 285380
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.921 23
200 1.082 15
300 1.046 7
400 1.104 6
500 1.166 22
600 1.058 5
700 1.054 23
800 1.224 23
900 1.187 23
1000 1.045 23
PLOT INFORMATION
The following plots are available:
Bayesian posterior parameter distributions
Bayesian posterior parameter trace plots
Bayesian autocorrelation plots
Beginning Time: 23:20:39
Ending Time: 23:20:41
Elapsed Time: 00:00:02
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