Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:11 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a Bayesian bi-factor CFA with two items
loading on only the general factor and cross-loadings with
zero-mean and small-variance priors
DATA: FILE = ex5.31.dat;
VARIABLE: NAMES = y1-y10;
ANALYSIS: ESTIMATOR = BAYES;
PROCESSORS = 2;
MODEL: fg BY y1-y10*;
fg@1;
f1 BY y1-y4
y5-y10 (f1xlam5-f1xlam10);
f2 BY y5-y8
y1-y4 y9-y10(f2xlam1-f2xlam6);
fg WITH f1-f2@0;
MODEL PRIORS:
f1xlam5-f2xlam6~N(0,0.01);
PLOT: TYPE = PLOT2;
INPUT READING TERMINATED NORMALLY
this is an example of a Bayesian bi-factor CFA with two items
loading on only the general factor and cross-loadings with
zero-mean and small-variance priors
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of dependent variables 10
Number of independent variables 0
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10
Continuous latent variables
FG F1 F2
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)
ex5.31.dat
Input data format FREE
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 -0.073 0.041 -2.518 0.20% -0.928 -0.356 -0.050
500.000 0.990 -0.354 2.797 0.20% 0.175 0.743
Y2 0.049 0.117 -2.908 0.20% -0.805 -0.269 0.003
500.000 1.033 -0.089 3.240 0.20% 0.295 0.885
Y3 0.012 -0.075 -2.473 0.20% -0.922 -0.230 0.034
500.000 0.967 -0.424 2.645 0.20% 0.312 0.844
Y4 -0.042 -0.033 -3.179 0.20% -0.901 -0.303 -0.041
500.000 1.059 -0.092 2.923 0.20% 0.218 0.845
Y5 0.021 -0.037 -2.795 0.20% -0.863 -0.249 0.043
500.000 1.047 -0.191 2.902 0.20% 0.298 0.919
Y6 -0.025 0.105 -2.537 0.20% -0.856 -0.270 -0.061
500.000 0.976 -0.072 2.874 0.20% 0.189 0.752
Y7 0.022 0.029 -3.404 0.20% -0.809 -0.257 -0.029
500.000 1.028 -0.049 2.933 0.20% 0.214 0.888
Y8 0.059 0.017 -3.018 0.20% -0.850 -0.193 0.066
500.000 1.142 -0.044 3.332 0.20% 0.313 0.935
Y9 -0.018 0.064 -3.308 0.20% -0.828 -0.287 -0.053
500.000 0.989 0.026 3.174 0.20% 0.169 0.820
Y10 -0.003 0.048 -2.327 0.20% -0.860 -0.310 -0.003
500.000 0.959 -0.321 3.071 0.20% 0.279 0.846
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 51
Bayesian Posterior Predictive Checking using Chi-Square
95% Confidence Interval for the Difference Between
the Observed and the Replicated Chi-Square Values
-31.351 35.584
Posterior Predictive P-Value 0.387
Prior Posterior Predictive P-Value 0.361
Information Criteria
Deviance (DIC) 11569.991
Estimated Number of Parameters (pD) 40.498
Bayesian (BIC) 11804.965
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.020
90 Percent C.I. 0.000 0.045
Probability RMSEA <= .05 0.993
CFI/TLI
CFI 0.998
90 Percent C.I. 0.991 1.000
TLI 0.997
90 Percent C.I. 0.983 1.000
MODEL RESULTS
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance
FG BY
Y1 0.683 0.045 0.000 0.597 0.774 *
Y2 0.728 0.048 0.000 0.636 0.817 *
Y3 0.744 0.045 0.000 0.661 0.834 *
Y4 0.742 0.048 0.000 0.652 0.841 *
Y5 0.753 0.045 0.000 0.664 0.840 *
Y6 0.705 0.045 0.000 0.619 0.795 *
Y7 0.671 0.049 0.000 0.571 0.769 *
Y8 0.719 0.050 0.000 0.620 0.816 *
Y9 0.708 0.044 0.000 0.627 0.794 *
Y10 0.628 0.047 0.000 0.541 0.725 *
F1 BY
Y1 1.000 0.000 0.000 1.000 1.000
Y2 0.965 0.157 0.000 0.689 1.325 *
Y3 0.765 0.132 0.000 0.513 1.015 *
Y4 0.847 0.155 0.000 0.525 1.161 *
Y5 -0.012 0.080 0.434 -0.169 0.152
Y6 -0.071 0.078 0.166 -0.226 0.082
Y7 0.088 0.083 0.141 -0.076 0.254
Y8 -0.014 0.081 0.427 -0.174 0.146
Y9 -0.003 0.091 0.487 -0.190 0.175
Y10 0.034 0.090 0.346 -0.159 0.206
F2 BY
Y5 1.000 0.000 0.000 1.000 1.000
Y6 0.957 0.299 0.000 0.558 1.714 *
Y7 1.106 0.574 0.000 0.597 2.858 *
Y8 1.162 0.372 0.000 0.715 2.134 *
Y1 0.017 0.088 0.426 -0.153 0.187
Y2 0.017 0.089 0.430 -0.154 0.197
Y3 -0.070 0.088 0.208 -0.251 0.089
Y4 0.024 0.083 0.389 -0.154 0.179
Y9 0.028 0.095 0.393 -0.162 0.218
Y10 -0.023 0.089 0.385 -0.197 0.150
FG WITH
F1 0.000 0.000 1.000 0.000 0.000
F2 0.000 0.000 1.000 0.000 0.000
F2 WITH
F1 0.024 0.037 0.180 -0.044 0.108
Intercepts
Y1 -0.075 0.049 0.054 -0.175 0.016
Y2 0.045 0.049 0.179 -0.050 0.139
Y3 0.010 0.048 0.409 -0.084 0.100
Y4 -0.044 0.050 0.173 -0.140 0.055
Y5 0.022 0.049 0.341 -0.077 0.110
Y6 -0.025 0.048 0.298 -0.121 0.063
Y7 0.022 0.049 0.326 -0.076 0.113
Y8 0.060 0.051 0.116 -0.047 0.165
Y9 -0.019 0.047 0.359 -0.113 0.070
Y10 -0.001 0.047 0.487 -0.097 0.089
Variances
FG 1.000 0.000 0.000 1.000 1.000
F1 0.211 0.054 0.000 0.114 0.322 *
F2 0.109 0.055 0.000 0.028 0.227 *
Residual Variances
Y1 0.328 0.032 0.000 0.260 0.389 *
Y2 0.320 0.030 0.000 0.260 0.378 *
Y3 0.303 0.026 0.000 0.258 0.358 *
Y4 0.370 0.029 0.000 0.317 0.430 *
Y5 0.387 0.033 0.000 0.324 0.455 *
Y6 0.397 0.034 0.000 0.336 0.465 *
Y7 0.440 0.048 0.000 0.334 0.525 *
Y8 0.494 0.042 0.000 0.418 0.583 *
Y9 0.506 0.044 0.000 0.416 0.591 *
Y10 0.576 0.045 0.000 0.492 0.670 *
PLOT INFORMATION
The following plots are available:
Bayesian posterior parameter distributions
Bayesian posterior parameter trace plots
Bayesian autocorrelation plots
Bayesian prior parameter distributions
Bayesian posterior predictive checking scatterplots
Bayesian posterior predictive checking distribution plots
Beginning Time: 23:11:24
Ending Time: 23:11:25
Elapsed Time: 00:00:01
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