Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:11 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a bi-factor exploratory factor analysis with
continuous indicators
DATA: FILE = ex4.7.dat;
VARIABLE: NAMES = y1-y10;
ANALYSIS: TYPE = EFA 2 3;
ROTATION = BI-GEOMIN;
INPUT READING TERMINATED NORMALLY
this is an example of a bi-factor exploratory factor analysis with
continuous indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 5000
Number of dependent variables 10
Number of independent variables 0
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10
Estimator ML
Rotation BI-GEOMIN
Row standardization CORRELATION
Type of rotation OBLIQUE
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Optimization Specifications for the Exploratory Factor Analysis
Rotation Algorithm
Number of random starts 30
Maximum number of iterations 10000
Derivative convergence criterion 0.100D-04
Input data file(s)
ex4.7.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 -0.069 -0.021 -8.072 0.02% -1.718 -0.593 -0.064
5000.000 3.951 -0.050 6.765 0.02% 0.462 1.615
Y2 -0.033 -0.006 -6.509 0.02% -1.453 -0.460 -0.037
5000.000 2.984 0.094 5.992 0.02% 0.387 1.390
Y3 -0.055 0.025 -6.330 0.02% -1.584 -0.497 -0.048
5000.000 3.306 -0.003 7.279 0.02% 0.380 1.484
Y4 -0.058 0.027 -9.738 0.02% -2.313 -0.792 -0.069
5000.000 7.133 -0.044 10.394 0.02% 0.631 2.219
Y5 -0.040 -0.037 -7.276 0.02% -1.509 -0.483 -0.022
5000.000 3.001 -0.047 5.370 0.02% 0.382 1.433
Y6 -0.018 -0.040 -6.045 0.02% -1.526 -0.459 -0.024
5000.000 3.279 -0.094 5.984 0.02% 0.438 1.524
Y7 -0.005 0.053 -6.998 0.02% -1.642 -0.510 -0.054
5000.000 3.754 -0.061 8.425 0.02% 0.435 1.667
Y8 0.004 -0.043 -7.447 0.02% -1.703 -0.485 0.013
5000.000 4.190 0.108 7.341 0.02% 0.528 1.702
Y9 0.015 0.006 -7.174 0.02% -1.687 -0.505 0.007
5000.000 4.002 -0.018 6.831 0.02% 0.536 1.702
Y10 0.016 -0.018 -7.589 0.02% -1.796 -0.510 0.035
5000.000 4.599 -0.098 8.354 0.02% 0.581 1.825
SUMMARY OF MODEL FIT INFORMATION
Number of Degrees of
Model Parameters Chi-Square Freedom P-Value
2-factor 39 90.091 26 0.0000
3-factor 47 24.364 18 0.1435
Degrees of
Models Compared Chi-Square Freedom P-Value
2-factor against 3-factor 65.727 8 0.0000
RESULTS FOR EXPLORATORY FACTOR ANALYSIS
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
1 2 3 4 5
________ ________ ________ ________ ________
3.031 1.670 0.847 0.786 0.709
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
6 7 8 9 10
________ ________ ________ ________ ________
0.697 0.639 0.575 0.561 0.485
EXPLORATORY FACTOR ANALYSIS WITH 2 FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 39
Loglikelihood
H0 Value -100466.860
H1 Value -100421.815
Information Criteria
Akaike (AIC) 201011.721
Bayesian (BIC) 201265.891
Sample-Size Adjusted BIC 201141.963
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 90.091
Degrees of Freedom 26
P-Value 0.0000
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.022
90 Percent C.I. 0.017 0.027
Probability RMSEA <= .05 1.000
CFI/TLI
CFI 0.993
TLI 0.988
Chi-Square Test of Model Fit for the Baseline Model
Value 8960.687
Degrees of Freedom 45
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.014
MINIMUM ROTATION FUNCTION VALUE 1.09375
BI-GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2
________ ________
Y1 0.415* 0.485*
Y2 0.338* 0.232*
Y3 0.382* 0.361*
Y4 0.436* 0.624*
Y5 0.392* -0.049*
Y6 0.500* -0.169*
Y7 0.550* -0.211*
Y8 0.610* -0.243*
Y9 0.577* -0.275*
Y10 0.602* -0.272*
BI-GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2
________ ________
1 1.000
2 0.000 1.000
ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.593 0.832 0.724 0.420 0.844
ESTIMATED RESIDUAL VARIANCES
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.722 0.653 0.569 0.592 0.563
S.E. BI-GEOMIN ROTATED LOADINGS
1 2
________ ________
Y1 0.011 0.015
Y2 0.013 0.016
Y3 0.012 0.015
Y4 0.009 0.015
Y5 0.014 0.017
Y6 0.012 0.016
Y7 0.012 0.016
Y8 0.011 0.016
Y9 0.011 0.016
Y10 0.011 0.016
S.E. BI-GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 0.000 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.017 0.012 0.014 0.021 0.011
S.E. ESTIMATED RESIDUAL VARIANCES
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.013 0.014 0.014 0.014 0.014
Est./S.E. BI-GEOMIN ROTATED LOADINGS
1 2
________ ________
Y1 39.445 33.121
Y2 25.126 14.194
Y3 31.999 23.663
Y4 47.407 41.471
Y5 28.426 -2.852
Y6 40.779 -10.357
Y7 47.804 -13.176
Y8 56.987 -15.519
Y9 52.535 -17.650
Y10 56.367 -17.397
Est./S.E. BI-GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 -0.124 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
35.882 71.462 52.080 20.043 77.325
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
54.886 47.309 40.027 41.338 39.208
FACTOR STRUCTURE
1 2
________ ________
Y1 0.415 0.485
Y2 0.338 0.232
Y3 0.382 0.361
Y4 0.436 0.624
Y5 0.392 -0.049
Y6 0.500 -0.169
Y7 0.550 -0.211
Y8 0.610 -0.243
Y9 0.577 -0.275
Y10 0.602 -0.272
EXPLORATORY FACTOR ANALYSIS WITH 3 FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 47
Loglikelihood
H0 Value -100433.997
H1 Value -100421.815
Information Criteria
Akaike (AIC) 200961.994
Bayesian (BIC) 201268.302
Sample-Size Adjusted BIC 201118.952
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 24.364
Degrees of Freedom 18
P-Value 0.1435
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.008
90 Percent C.I. 0.000 0.016
Probability RMSEA <= .05 1.000
CFI/TLI
CFI 0.999
TLI 0.998
Chi-Square Test of Model Fit for the Baseline Model
Value 8960.687
Degrees of Freedom 45
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.007
MINIMUM ROTATION FUNCTION VALUE 0.16024
BI-GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2 3
________ ________ ________
Y1 0.468* 0.365 -0.023
Y2 0.446* 0.124 0.004
Y3 0.460* 0.260 -0.006
Y4 0.388 0.843* 0.004
Y5 0.383* -0.042 0.217*
Y6 0.304* -0.003 0.431*
Y7 0.298* 0.010 0.508*
Y8 0.318* 0.004 0.575*
Y9 0.300* -0.031 0.560*
Y10 0.274* 0.014 0.610*
BI-GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2 3
________ ________ ________
1 1.000
2 0.000* 1.000
3 0.000 -0.029 1.000
ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.646 0.785 0.721 0.138 0.804
ESTIMATED RESIDUAL VARIANCES
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.722 0.654 0.569 0.594 0.553
S.E. BI-GEOMIN ROTATED LOADINGS
1 2 3
________ ________ ________
Y1 0.156 0.216 0.019
Y2 0.054 0.172 0.026
Y3 0.114 0.197 0.013
Y4 0.302 0.113 0.003
Y5 0.054 0.084 0.041
Y6 0.034 0.021 0.025
Y7 0.040 0.014 0.027
Y8 0.036 0.012 0.022
Y9 0.053 0.019 0.028
Y10 0.038 0.018 0.021
S.E. BI-GEOMIN FACTOR CORRELATIONS
1 2 3
________ ________ ________
1 0.000
2 0.000 0.000
3 0.000 0.182 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.022 0.020 0.018 0.181 0.021
S.E. ESTIMATED RESIDUAL VARIANCES
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.013 0.014 0.014 0.014 0.015
Est./S.E. BI-GEOMIN ROTATED LOADINGS
1 2 3
________ ________ ________
Y1 2.997 1.691 -1.214
Y2 8.304 0.724 0.172
Y3 4.046 1.319 -0.420
Y4 1.284 7.466 1.156
Y5 7.152 -0.497 5.237
Y6 8.824 -0.136 17.261
Y7 7.386 0.732 18.781
Y8 8.822 0.374 25.556
Y9 5.699 -1.697 20.009
Y10 7.141 0.784 29.258
Est./S.E. BI-GEOMIN FACTOR CORRELATIONS
1 2 3
________ ________ ________
1 0.000
2 -7.217 0.000
3 -0.155 -0.161 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
29.962 38.370 40.477 0.765 38.907
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
54.911 47.178 39.388 41.556 35.786
FACTOR STRUCTURE
1 2 3
________ ________ ________
Y1 0.468 0.366 -0.033
Y2 0.446 0.124 0.001
Y3 0.460 0.260 -0.013
Y4 0.388 0.843 -0.021
Y5 0.383 -0.048 0.218
Y6 0.304 -0.015 0.432
Y7 0.298 -0.005 0.508
Y8 0.318 -0.012 0.575
Y9 0.300 -0.048 0.561
Y10 0.274 -0.004 0.610
Beginning Time: 23:11:07
Ending Time: 23:11:08
Elapsed Time: 00:00:01
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