Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:09 PM
INPUT INSTRUCTIONS
TITLE: this is an example of an exploratory
factor analysis with categorical factor
indicators
DATA: FILE IS ex4.2.dat;
VARIABLE: NAMES ARE u1-u12;
CATEGORICAL ARE u1-u12;
ANALYSIS: TYPE = EFA 1 4;
INPUT READING TERMINATED NORMALLY
this is an example of an exploratory
factor analysis with categorical factor
indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of dependent variables 12
Number of independent variables 0
Number of continuous latent variables 0
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5 U6
U7 U8 U9 U10 U11 U12
Estimator WLSMV
Rotation GEOMIN
Row standardization CORRELATION
Type of rotation OBLIQUE
Epsilon value Varies
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
Link PROBIT
Input data file(s)
ex4.2.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.494 247.000
Category 2 0.506 253.000
U2
Category 1 0.484 242.000
Category 2 0.516 258.000
U3
Category 1 0.528 264.000
Category 2 0.472 236.000
U4
Category 1 0.504 252.000
Category 2 0.496 248.000
U5
Category 1 0.486 243.000
Category 2 0.514 257.000
U6
Category 1 0.504 252.000
Category 2 0.496 248.000
U7
Category 1 0.496 248.000
Category 2 0.504 252.000
U8
Category 1 0.492 246.000
Category 2 0.508 254.000
U9
Category 1 0.514 257.000
Category 2 0.486 243.000
U10
Category 1 0.496 248.000
Category 2 0.504 252.000
U11
Category 1 0.490 245.000
Category 2 0.510 255.000
U12
Category 1 0.502 251.000
Category 2 0.498 249.000
SUMMARY OF MODEL FIT INFORMATION
Number of Degrees of
Model Parameters Chi-Square Freedom P-Value
1-factor 12 730.699 54 0.0000
2-factor 23 485.520 43 0.0000
3-factor 33 268.580 33 0.0000
4-factor 42 22.796 24 0.5319
Degrees of
Models Compared Chi-Square Freedom P-Value
1-factor against 2-factor 228.003 11 0.0000
2-factor against 3-factor 183.837 10 0.0000
3-factor against 4-factor 158.815 9 0.0000
RESULTS FOR EXPLORATORY FACTOR ANALYSIS
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
1 2 3 4 5
________ ________ ________ ________ ________
2.326 2.230 2.009 1.710 0.659
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
6 7 8 9 10
________ ________ ________ ________ ________
0.655 0.524 0.496 0.471 0.350
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
11 12
________ ________
0.320 0.248
EXPLORATORY FACTOR ANALYSIS WITH 1 FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 12
Chi-Square Test of Model Fit
Value 730.699*
Degrees of Freedom 54
P-Value 0.0000
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.158
90 Percent C.I. 0.148 0.169
Probability RMSEA <= .05 0.000
CFI/TLI
CFI 0.230
TLI 0.059
Chi-Square Test of Model Fit for the Baseline Model
Value 944.923
Degrees of Freedom 66
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.205
MINIMUM ROTATION FUNCTION VALUE 1.89948
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
U1 0.608*
U2 0.689*
U3 0.596*
U4 0.038
U5 -0.019
U6 0.099
U7 0.460*
U8 0.398*
U9 0.390*
U10 -0.249*
U11 -0.286*
U12 -0.143*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.630 0.526 0.645 0.999 1.000
ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.990 0.788 0.841 0.848 0.938
ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
0.918 0.980
S.E. GEOMIN ROTATED LOADINGS
1
________
U1 0.057
U2 0.056
U3 0.055
U4 0.069
U5 0.069
U6 0.068
U7 0.060
U8 0.062
U9 0.061
U10 0.066
U11 0.065
U12 0.067
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.069 0.078 0.065 0.005 0.003
S.E. ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.013 0.055 0.050 0.048 0.033
S.E. ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
0.037 0.019
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
U1 10.660
U2 12.218
U3 10.939
U4 0.549
U5 -0.274
U6 1.448
U7 7.711
U8 6.403
U9 6.358
U10 -3.784
U11 -4.375
U12 -2.125
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
9.078 6.766 9.917 192.068 386.794
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
73.492 14.351 16.993 17.691 28.597
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
24.568 50.944
EXPLORATORY FACTOR ANALYSIS WITH 2 FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 23
Chi-Square Test of Model Fit
Value 485.520*
Degrees of Freedom 43
P-Value 0.0000
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.143
90 Percent C.I. 0.132 0.155
Probability RMSEA <= .05 0.000
CFI/TLI
CFI 0.497
TLI 0.227
Chi-Square Test of Model Fit for the Baseline Model
Value 944.923
Degrees of Freedom 66
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.160
MINIMUM ROTATION FUNCTION VALUE 0.76540
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2
________ ________
U1 0.630* 0.109
U2 0.793* -0.004
U3 0.670* -0.008
U4 -0.171* 0.361*
U5 -0.290* 0.452*
U6 -0.126 0.438*
U7 0.326* 0.431*
U8 0.256* 0.422*
U9 0.267* 0.382*
U10 -0.012 -0.475*
U11 -0.001 -0.599*
U12 0.132 -0.499*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2
________ ________
1 1.000
2 -0.054 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.599 0.371 0.551 0.834 0.697
ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.786 0.723 0.767 0.793 0.775
ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
0.642 0.727
S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 0.057 0.071
U2 0.055 0.020
U3 0.055 0.048
U4 0.079 0.066
U5 0.080 0.067
U6 0.079 0.064
U7 0.078 0.067
U8 0.080 0.066
U9 0.075 0.066
U10 0.063 0.062
U11 0.012 0.057
U12 0.070 0.062
S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 0.108 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.071 0.088 0.074 0.052 0.067
S.E. ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.057 0.062 0.059 0.055 0.059
S.E. ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
0.069 0.064
Est./S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 11.113 1.522
U2 14.296 -0.213
U3 12.127 -0.175
U4 -2.173 5.458
U5 -3.637 6.731
U6 -1.593 6.828
U7 4.151 6.417
U8 3.219 6.354
U9 3.588 5.771
U10 -0.195 -7.657
U11 -0.083 -10.457
U12 1.891 -8.108
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 -0.493 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
8.481 4.216 7.465 16.093 10.416
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
13.705 11.617 13.112 14.527 13.168
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
9.363 11.426
FACTOR STRUCTURE
1 2
________ ________
U1 0.624 0.075
U2 0.793 -0.047
U3 0.670 -0.044
U4 -0.190 0.370
U5 -0.314 0.468
U6 -0.149 0.445
U7 0.303 0.413
U8 0.234 0.409
U9 0.247 0.368
U10 0.013 -0.474
U11 0.031 -0.599
U12 0.159 -0.506
EXPLORATORY FACTOR ANALYSIS WITH 3 FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 33
Chi-Square Test of Model Fit
Value 268.580*
Degrees of Freedom 33
P-Value 0.0000
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.119
90 Percent C.I. 0.106 0.133
Probability RMSEA <= .05 0.000
CFI/TLI
CFI 0.732
TLI 0.464
Chi-Square Test of Model Fit for the Baseline Model
Value 944.923
Degrees of Freedom 66
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.103
MINIMUM ROTATION FUNCTION VALUE 0.20241
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2 3
________ ________ ________
U1 0.646* 0.105 -0.047
U2 0.875* -0.007 0.025
U3 0.713* -0.013 0.021
U4 -0.014 -0.115 -0.502*
U5 -0.181* -0.007 -0.536*
U6 -0.046 0.068 -0.468*
U7 0.018 0.807* 0.023
U8 -0.039 0.722* -0.016
U9 -0.002 0.667* 0.002
U10 -0.181* 0.029 0.566*
U11 -0.145 -0.073 0.639*
U12 -0.004 -0.001 0.573*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2 3
________ ________ ________
1 1.000
2 0.025 1.000
3 0.064 -0.057 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.570 0.230 0.490 0.740 0.668
ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.768 0.349 0.478 0.555 0.661
ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
0.571 0.672
S.E. GEOMIN ROTATED LOADINGS
1 2 3
________ ________ ________
U1 0.057 0.073 0.068
U2 0.057 0.035 0.043
U3 0.056 0.050 0.042
U4 0.043 0.073 0.065
U5 0.071 0.036 0.062
U6 0.073 0.074 0.063
U7 0.043 0.061 0.056
U8 0.070 0.059 0.049
U9 0.039 0.059 0.045
U10 0.085 0.070 0.063
U11 0.084 0.085 0.062
U12 0.059 0.069 0.062
S.E. GEOMIN FACTOR CORRELATIONS
1 2 3
________ ________ ________
1 0.000
2 0.080 0.000
3 0.096 0.092 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.074 0.100 0.080 0.066 0.070
S.E. ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.060 0.097 0.085 0.078 0.072
S.E. ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
0.078 0.070
Est./S.E. GEOMIN ROTATED LOADINGS
1 2 3
________ ________ ________
U1 11.336 1.437 -0.683
U2 15.239 -0.210 0.592
U3 12.670 -0.267 0.501
U4 -0.323 -1.570 -7.759
U5 -2.538 -0.186 -8.592
U6 -0.625 0.917 -7.412
U7 0.412 13.267 0.406
U8 -0.563 12.195 -0.323
U9 -0.046 11.365 0.052
U10 -2.131 0.417 9.054
U11 -1.721 -0.862 10.329
U12 -0.068 -0.020 9.300
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2 3
________ ________ ________
1 0.000
2 0.318 0.000
3 0.661 -0.617 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
7.692 2.310 6.154 11.275 9.514
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
12.887 3.582 5.624 7.104 9.151
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
7.351 9.596
FACTOR STRUCTURE
1 2 3
________ ________ ________
U1 0.645 0.124 -0.011
U2 0.877 0.013 0.081
U3 0.714 0.004 0.067
U4 -0.049 -0.087 -0.496
U5 -0.215 0.019 -0.547
U6 -0.074 0.093 -0.475
U7 0.040 0.806 -0.022
U8 -0.022 0.721 -0.059
U9 0.015 0.667 -0.036
U10 -0.144 -0.008 0.553
U11 -0.106 -0.113 0.634
U12 0.032 -0.034 0.572
EXPLORATORY FACTOR ANALYSIS WITH 4 FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 42
Chi-Square Test of Model Fit
Value 22.796*
Degrees of Freedom 24
P-Value 0.5319
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.000
90 Percent C.I. 0.000 0.034
Probability RMSEA <= .05 0.998
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 944.923
Degrees of Freedom 66
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.026
MINIMUM ROTATION FUNCTION VALUE 0.38499
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2 3 4
________ ________ ________ ________
U1 0.628* -0.003 0.098 -0.060
U2 0.937* 0.041 -0.011 0.071
U3 0.690* -0.072 -0.020 -0.037
U4 0.072 0.705* -0.121 -0.005
U5 -0.130 0.805* 0.018 0.016
U6 0.015 0.602* 0.089 -0.045
U7 0.026 -0.014 0.805* 0.009
U8 -0.036 -0.003 0.720* -0.029
U9 0.017 0.034 0.669* 0.025
U10 -0.066 -0.017 0.057 0.654*
U11 -0.005 0.040 -0.056 0.872*
U12 0.110 -0.069 0.022 0.624*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2 3 4
________ ________ ________ ________
1 1.000
2 -0.026 1.000
3 0.025 0.033 1.000
4 -0.030 -0.150* -0.059 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.586 0.122 0.515 0.491 0.331
ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.615 0.352 0.479 0.550 0.563
ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
0.239 0.586
S.E. GEOMIN ROTATED LOADINGS
1 2 3 4
________ ________ ________ ________
U1 0.057 0.049 0.066 0.062
U2 0.060 0.040 0.029 0.049
U3 0.057 0.064 0.047 0.043
U4 0.058 0.067 0.074 0.048
U5 0.078 0.072 0.017 0.043
U6 0.033 0.064 0.070 0.065
U7 0.041 0.044 0.060 0.042
U8 0.051 0.047 0.059 0.053
U9 0.048 0.056 0.059 0.052
U10 0.060 0.049 0.058 0.064
U11 0.019 0.043 0.049 0.070
U12 0.066 0.065 0.044 0.064
S.E. GEOMIN FACTOR CORRELATIONS
1 2 3 4
________ ________ ________ ________
1 0.000
2 0.083 0.000
3 0.067 0.077 0.000
4 0.070 0.070 0.071 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.072 0.112 0.078 0.093 0.114
S.E. ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
0.075 0.096 0.084 0.078 0.083
S.E. ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
0.120 0.078
Est./S.E. GEOMIN ROTATED LOADINGS
1 2 3 4
________ ________ ________ ________
U1 11.004 -0.066 1.500 -0.976
U2 15.616 1.038 -0.394 1.432
U3 12.047 -1.129 -0.424 -0.857
U4 1.237 10.455 -1.641 -0.103
U5 -1.680 11.109 1.091 0.376
U6 0.465 9.382 1.283 -0.698
U7 0.648 -0.309 13.376 0.214
U8 -0.707 -0.057 12.202 -0.546
U9 0.363 0.598 11.403 0.493
U10 -1.112 -0.353 0.985 10.153
U11 -0.270 0.926 -1.146 12.389
U12 1.664 -1.061 0.497 9.795
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2 3 4
________ ________ ________ ________
1 0.000
2 -0.310 0.000
3 0.368 0.422 0.000
4 -0.427 -2.152 -0.831 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
8.086 1.085 6.582 5.280 2.913
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6 U7 U8 U9 U10
________ ________ ________ ________ ________
8.158 3.652 5.670 7.047 6.797
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U11 U12
________ ________
1.987 7.474
FACTOR STRUCTURE
1 2 3 4
________ ________ ________ ________
U1 0.633 -0.007 0.117 -0.084
U2 0.934 0.006 0.009 0.037
U3 0.692 -0.085 -0.003 -0.045
U4 0.051 0.700 -0.096 -0.106
U5 -0.151 0.807 0.040 -0.102
U6 0.003 0.612 0.112 -0.141
U7 0.046 0.011 0.804 -0.037
U8 -0.017 0.026 0.721 -0.070
U9 0.032 0.051 0.669 -0.020
U10 -0.084 -0.112 0.016 0.655
U11 -0.033 -0.093 -0.107 0.870
U12 0.094 -0.164 -0.014 0.630
Beginning Time: 23:09:26
Ending Time: 23:09:27
Elapsed Time: 00:00:01
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