Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:26 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
DATA: FILE = ex9.29.dat;
VARIABLE: NAMES ARE y1-y4 x1 x2 w clus;
WITHIN = x1 x2;
BETWEEN = w;
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (10000);
MODEL: %WITHIN%
fw BY y1-y4;
fw ON x1 x2;
logv | fw;
%BETWEEN%
fb BY y1-y4;
fb ON w;
logv ON w;
OUTPUT: TECH1 TECH8;
PLOT: TYPE = PLOT3;
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 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
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)
ex9.29.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 -0.191 0.259 -5.793 0.10% -1.750 -0.712 -0.244
1000.000 3.539 0.296 6.579 0.10% 0.205 1.311
Y2 -0.140 0.159 -7.127 0.10% -1.888 -0.744 -0.192
1000.000 4.098 0.243 7.313 0.10% 0.369 1.555
Y3 -0.219 -0.006 -6.025 0.10% -1.930 -0.750 -0.175
1000.000 3.804 0.001 6.523 0.10% 0.329 1.429
Y4 -0.142 0.166 -5.993 0.10% -1.863 -0.723 -0.170
1000.000 3.911 -0.045 7.001 0.10% 0.341 1.537
X1 -0.054 0.034 -3.052 0.10% -0.870 -0.330 -0.053
1000.000 0.961 -0.036 2.855 0.10% 0.180 0.750
X2 0.035 0.060 -3.093 0.10% -0.821 -0.239 0.038
1000.000 0.996 -0.226 2.959 0.10% 0.286 0.913
W -0.165 0.246 -2.091 0.91% -0.796 -0.285 -0.187
110.000 0.676 1.163 2.584 0.91% -0.013 0.439
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 25
Information Criteria
Deviance (DIC) 13113.698
Estimated Number of Parameters (pD) 269.080
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
Within Level
FW BY
Y1 1.000 0.000 0.000 1.000 1.000
Y2 1.076 0.036 0.000 1.008 1.149 *
Y3 1.060 0.035 0.000 0.993 1.131 *
Y4 1.038 0.035 0.000 0.971 1.108 *
FW ON
X1 0.970 0.040 0.000 0.892 1.049 *
X2 0.433 0.035 0.000 0.364 0.502 *
Residual Variances
Y1 0.998 0.059 0.000 0.887 1.121 *
Y2 0.982 0.061 0.000 0.869 1.110 *
Y3 0.932 0.058 0.000 0.823 1.052 *
Y4 1.022 0.062 0.000 0.907 1.150 *
Between Level
FB BY
Y1 1.000 0.000 0.000 1.000 1.000
Y2 1.298 0.159 0.000 1.029 1.656 *
Y3 1.200 0.145 0.000 0.963 1.516 *
Y4 1.213 0.162 0.000 0.942 1.578 *
FB ON
W 0.483 0.083 0.000 0.324 0.652 *
LOGV ON
W 0.399 0.087 0.000 0.224 0.569 *
Intercepts
Y1 -0.073 0.071 0.159 -0.205 0.075
Y2 0.017 0.081 0.412 -0.140 0.181
Y3 -0.075 0.075 0.164 -0.218 0.079
Y4 0.021 0.083 0.403 -0.139 0.188
LOGV -0.127 0.079 0.043 -0.294 0.016
Residual Variances
Y1 0.104 0.040 0.000 0.034 0.193 *
Y2 0.138 0.048 0.000 0.059 0.247 *
Y3 0.056 0.034 0.000 0.007 0.136 *
Y4 0.190 0.054 0.000 0.102 0.319 *
FB 0.196 0.057 0.000 0.108 0.328 *
LOGV 0.077 0.061 0.000 0.010 0.248 *
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 1.770
Y2 0.000 2.049
Y3 0.000 0.000 1.902
Y4 0.000 0.000 0.000 1.956
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 0.000 0.000
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
PSI
FW X1 X2
________ ________ ________
FW 0.000
X1 0.000 0.481
X2 0.000 0.000 0.498
STARTING VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
-0.191 -0.140 -0.219 -0.142 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 1.770
Y2 0.000 2.049
Y3 0.000 0.000 1.902
Y4 0.000 0.000 0.000 1.956
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 0.000
LOGV 0.000 0.000 0.000
W 0.000 0.000 0.000
PSI
FB LOGV W
________ ________ ________
FB 1.000
LOGV 0.000 1.000
W 0.000 0.000 0.329
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
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 5.464 23
200 2.608 21
300 3.835 25
400 3.377 23
500 2.521 25
600 1.687 21
700 1.568 21
800 1.440 21
900 1.496 21
1000 1.537 21
1100 1.740 23
1200 2.014 23
1300 2.013 23
1400 1.939 23
1500 2.012 23
1600 1.876 23
1700 1.625 21
1800 1.629 21
1900 1.518 21
2000 1.402 21
2100 1.311 21
2200 1.282 21
2300 1.281 21
2400 1.284 21
2500 1.270 21
2600 1.191 21
2700 1.149 21
2800 1.179 25
2900 1.245 25
3000 1.290 25
3100 1.321 25
3200 1.297 25
3300 1.266 25
3400 1.243 25
3500 1.173 25
3600 1.121 25
3700 1.078 25
3800 1.045 25
3900 1.036 25
4000 1.026 25
4100 1.015 16
4200 1.018 16
4300 1.016 16
4400 1.010 16
4500 1.011 16
4600 1.016 16
4700 1.020 21
4800 1.018 19
4900 1.011 19
5000 1.009 19
5100 1.010 19
5200 1.021 25
5300 1.042 25
5400 1.056 25
5500 1.080 25
5600 1.097 25
5700 1.115 25
5800 1.139 25
5900 1.189 25
6000 1.229 25
6100 1.266 25
6200 1.270 25
6300 1.250 25
6400 1.223 25
6500 1.214 25
6600 1.199 25
6700 1.175 25
6800 1.174 25
6900 1.166 25
7000 1.147 25
7100 1.120 25
7200 1.103 25
7300 1.092 25
7400 1.079 25
7500 1.063 25
7600 1.050 25
7700 1.038 25
7800 1.025 25
7900 1.023 25
8000 1.019 25
8100 1.016 25
8200 1.013 25
8300 1.011 25
8400 1.008 25
8500 1.006 25
8600 1.003 24
8700 1.003 24
8800 1.006 21
8900 1.013 25
9000 1.023 25
9100 1.033 25
9200 1.041 25
9300 1.039 25
9400 1.036 25
9500 1.035 25
9600 1.031 25
9700 1.024 25
9800 1.018 25
9900 1.018 25
10000 1.018 25
PLOT INFORMATION
The following plots are available:
Histograms (sample values)
Scatterplots (sample values)
Between-level histograms (sample values, sample means/variances)
Between-level scatterplots (sample values, sample means/variances)
Bayesian posterior parameter distributions
Bayesian posterior parameter trace plots
Bayesian autocorrelation plots
Beginning Time: 23:26:08
Ending Time: 23:26:29
Elapsed Time: 00:00:21
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