Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:10 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level exploratory
factor analysis with continuous factor indicators
DATA: FILE IS ex4.5.dat;
VARIABLE: NAMES ARE y1-y6 x1 x2 w clus;
USEVARIABLES = y1-y6;
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL EFA 1 2 UW 1 1 UB;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level exploratory
factor analysis with continuous factor indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of dependent variables 6
Number of independent variables 0
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Variables with special functions
Cluster variable CLUS
Estimator ML
Rotation GEOMIN
Row standardization CORRELATION
Type of rotation OBLIQUE
Epsilon value Varies
Information matrix OBSERVED
Maximum number of iterations 100
Convergence criterion 0.100D-05
Maximum number of EM iterations 500
Convergence criteria for the EM algorithm
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-03
Minimum variance 0.100D-03
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
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
Optimization algorithm EMA
Input data file(s)
ex4.5.dat
Input data format FREE
SUMMARY OF DATA
Number of clusters 110
Average cluster size 9.091
Estimated Intraclass Correlations for the Y Variables
Intraclass Intraclass Intraclass
Variable Correlation Variable Correlation Variable Correlation
Y1 0.399 Y2 0.407 Y3 0.369
Y4 0.371 Y5 0.424 Y6 0.445
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 0.007 -0.185 -7.948 0.10% -1.862 -0.499 0.086
1000.000 4.923 0.113 6.878 0.10% 0.629 1.903
Y2 0.034 0.018 -7.942 0.10% -1.868 -0.451 0.113
1000.000 4.605 0.157 8.366 0.10% 0.509 1.815
Y3 0.083 -0.042 -7.565 0.10% -1.748 -0.393 0.129
1000.000 4.282 -0.092 6.520 0.10% 0.702 1.746
Y4 0.059 0.007 -6.365 0.10% -1.664 -0.390 0.146
1000.000 4.069 -0.204 5.934 0.10% 0.639 1.702
Y5 0.000 -0.051 -6.815 0.10% -1.819 -0.478 0.040
1000.000 4.849 0.131 8.749 0.10% 0.575 1.855
Y6 0.165 -0.059 -5.888 0.10% -1.611 -0.373 0.141
1000.000 4.235 -0.286 5.591 0.10% 0.715 1.929
RESULTS FOR EXPLORATORY FACTOR ANALYSIS
EIGENVALUES FOR WITHIN LEVEL SAMPLE CORRELATION MATRIX
1 2 3 4 5
________ ________ ________ ________ ________
2.960 1.522 0.424 0.382 0.364
EIGENVALUES FOR WITHIN LEVEL SAMPLE CORRELATION MATRIX
6
________
0.348
EIGENVALUES FOR BETWEEN LEVEL SAMPLE CORRELATION MATRIX
1 2 3 4 5
________ ________ ________ ________ ________
5.178 0.249 0.188 0.168 0.122
EIGENVALUES FOR BETWEEN LEVEL SAMPLE CORRELATION MATRIX
6
________
0.096
EXPLORATORY FACTOR ANALYSIS WITH 1 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 30
Loglikelihood
H0 Value -11160.512
H1 Value -10754.176
Information Criteria
Akaike (AIC) 22381.023
Bayesian (BIC) 22528.256
Sample-Size Adjusted BIC 22432.974
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 812.672
Degrees of Freedom 18
P-Value 0.0000
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.210
CFI/TLI
CFI 0.711
TLI 0.519
Chi-Square Test of Model Fit for the Baseline Model
Value 2783.122
Degrees of Freedom 30
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.179
Value for Between 0.034
MINIMUM ROTATION FUNCTION VALUE 2.30287
WITHIN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
Y1 0.795*
Y2 0.779*
Y3 0.780*
Y4 0.377*
Y5 0.389*
Y6 0.402*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.368 0.393 0.392 0.858 0.849
ESTIMATED RESIDUAL VARIANCES
Y6
________
0.838
S.E. GEOMIN ROTATED LOADINGS
1
________
Y1 0.017
Y2 0.018
Y3 0.018
Y4 0.034
Y5 0.034
Y6 0.033
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.028 0.028 0.028 0.025 0.026
S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
0.026
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
Y1 45.472
Y2 43.113
Y3 43.345
Y4 11.207
Y5 11.595
Y6 12.225
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
13.259 13.952 13.951 33.827 32.507
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
31.690
EXPLORATORY FACTOR ANALYSIS WITH 1 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):
MINIMUM ROTATION FUNCTION VALUE 5.13290
BETWEEN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
Y1 0.910*
Y2 0.901*
Y3 0.912*
Y4 0.913*
Y5 0.977*
Y6 0.934*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.173 0.188 0.168 0.166 0.046
ESTIMATED RESIDUAL VARIANCES
Y6
________
0.127
S.E. GEOMIN ROTATED LOADINGS
1
________
Y1 0.025
Y2 0.026
Y3 0.026
Y4 0.029
Y5 0.019
Y6 0.023
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.046 0.048 0.047 0.052 0.037
S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
0.043
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
Y1 36.211
Y2 34.131
Y3 35.583
Y4 31.903
Y5 52.100
Y6 40.502
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
3.781 3.955 3.585 3.179 1.246
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
2.953
EXPLORATORY FACTOR ANALYSIS WITH 2 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 35
Loglikelihood
H0 Value -10759.644
H1 Value -10754.176
Information Criteria
Akaike (AIC) 21589.288
Bayesian (BIC) 21761.059
Sample-Size Adjusted BIC 21649.897
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 10.937
Degrees of Freedom 13
P-Value 0.6161
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.000
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 2783.122
Degrees of Freedom 30
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.007
Value for Between 0.015
MINIMUM ROTATION FUNCTION VALUE 0.06784
WITHIN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2
________ ________
Y1 0.801* 0.006
Y2 0.797* -0.009
Y3 0.788* 0.002
Y4 -0.002 0.765*
Y5 -0.008 0.815*
Y6 0.027 0.758*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2
________ ________
1 1.000
2 0.374* 1.000
ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.354 0.371 0.378 0.415 0.340
ESTIMATED RESIDUAL VARIANCES
Y6
________
0.410
S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
Y1 0.021 0.022
Y2 0.022 0.025
Y3 0.020 0.017
Y4 0.014 0.021
Y5 0.023 0.022
Y6 0.032 0.025
S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 0.038 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.029 0.029 0.029 0.030 0.031
S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
0.030
Est./S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
Y1 38.200 0.283
Y2 36.324 -0.366
Y3 38.799 0.109
Y4 -0.138 35.786
Y5 -0.342 36.721
Y6 0.838 30.414
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 9.914 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
12.343 12.730 13.110 13.674 11.021
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
13.628
FACTOR STRUCTURE
1 2
________ ________
Y1 0.803 0.306
Y2 0.793 0.289
Y3 0.789 0.297
Y4 0.285 0.765
Y5 0.297 0.812
Y6 0.310 0.768
EXPLORATORY FACTOR ANALYSIS WITH 2 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):
MINIMUM ROTATION FUNCTION VALUE 5.06570
BETWEEN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
Y1 0.931*
Y2 0.915*
Y3 0.928*
Y4 0.886*
Y5 0.949*
Y6 0.903*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.134 0.163 0.138 0.216 0.100
ESTIMATED RESIDUAL VARIANCES
Y6
________
0.184
S.E. GEOMIN ROTATED LOADINGS
1
________
Y1 0.021
Y2 0.024
Y3 0.023
Y4 0.030
Y5 0.020
Y6 0.026
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.040 0.045 0.042 0.053 0.037
S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
0.047
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
Y1 43.365
Y2 37.478
Y3 40.759
Y4 29.445
Y5 48.228
Y6 35.016
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
3.349 3.651 3.264 4.047 2.689
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
3.949
EXPLORATORY FACTOR ANALYSIS WITH UNRESTRICTED WITHIN COVARIANCE AND 1 BETWEEN FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 18
Loglikelihood
H0 Value -10757.461
H1 Value -10754.176
Information Criteria
Akaike (AIC) 21550.922
Bayesian (BIC) 21639.262
Sample-Size Adjusted BIC 21582.093
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 6.571
Degrees of Freedom 9
P-Value 0.6817
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.000
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 2783.122
Degrees of Freedom 30
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.000
Value for Between 0.015
MINIMUM ROTATION FUNCTION VALUE 5.06118
BETWEEN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
Y1 0.930*
Y2 0.914*
Y3 0.928*
Y4 0.885*
Y5 0.948*
Y6 0.903*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.134 0.164 0.139 0.216 0.102
ESTIMATED RESIDUAL VARIANCES
Y6
________
0.185
S.E. GEOMIN ROTATED LOADINGS
1
________
Y1 0.021
Y2 0.024
Y3 0.023
Y4 0.030
Y5 0.020
Y6 0.026
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.040 0.045 0.042 0.053 0.037
S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
0.047
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
Y1 43.560
Y2 37.450
Y3 40.935
Y4 29.536
Y5 48.440
Y6 35.038
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
3.382 3.675 3.293 4.067 2.748
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
3.964
EXPLORATORY FACTOR ANALYSIS WITH 1 WITHIN FACTOR(S) AND UNRESTRICTED BETWEEN COVARIANCE:
MODEL FIT INFORMATION
Number of Free Parameters 18
Loglikelihood
H0 Value -11156.190
H1 Value -10754.176
Information Criteria
Akaike (AIC) 22348.380
Bayesian (BIC) 22436.719
Sample-Size Adjusted BIC 22379.550
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 804.028
Degrees of Freedom 9
P-Value 0.0000
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.161
CFI/TLI
CFI 0.711
TLI 0.037
Chi-Square Test of Model Fit for the Baseline Model
Value 2783.122
Degrees of Freedom 30
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.177
Value for Between 0.000
MINIMUM ROTATION FUNCTION VALUE 2.30369
WITHIN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
Y1 0.789*
Y2 0.774*
Y3 0.774*
Y4 0.389*
Y5 0.404*
Y6 0.409*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.378 0.401 0.400 0.849 0.837
ESTIMATED RESIDUAL VARIANCES
Y6
________
0.832
S.E. GEOMIN ROTATED LOADINGS
1
________
Y1 0.018
Y2 0.018
Y3 0.018
Y4 0.033
Y5 0.033
Y6 0.033
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.028 0.028 0.028 0.026 0.027
S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
0.027
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
Y1 44.292
Y2 42.126
Y3 42.282
Y4 11.689
Y5 12.302
Y6 12.525
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
13.467 14.081 14.108 32.809 31.525
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
31.084
EXPLORATORY FACTOR ANALYSIS WITH 2 WITHIN FACTOR(S) AND UNRESTRICTED BETWEEN COVARIANCE:
MODEL FIT INFORMATION
Number of Free Parameters 23
Loglikelihood
H0 Value -10756.649
H1 Value -10754.176
Information Criteria
Akaike (AIC) 21559.297
Bayesian (BIC) 21672.175
Sample-Size Adjusted BIC 21599.126
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 4.946
Degrees of Freedom 4
P-Value 0.2929
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.000
CFI/TLI
CFI 1.000
TLI 0.997
Chi-Square Test of Model Fit for the Baseline Model
Value 2783.122
Degrees of Freedom 30
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.006
Value for Between 0.000
MINIMUM ROTATION FUNCTION VALUE 0.06852
WITHIN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2
________ ________
Y1 0.798* 0.009
Y2 0.799* -0.012
Y3 0.788* 0.001
Y4 -0.002 0.763*
Y5 -0.008 0.814*
Y6 0.023 0.760*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2
________ ________
1 1.000
2 0.382* 1.000
ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.358 0.369 0.379 0.418 0.342
ESTIMATED RESIDUAL VARIANCES
Y6
________
0.409
S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
Y1 0.022 0.025
Y2 0.022 0.027
Y3 0.020 0.013
Y4 0.014 0.021
Y5 0.023 0.023
Y6 0.031 0.025
S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 0.038 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.029 0.029 0.029 0.030 0.031
S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
0.030
Est./S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
Y1 36.516 0.378
Y2 35.556 -0.456
Y3 39.844 0.101
Y4 -0.116 35.590
Y5 -0.348 36.177
Y6 0.716 30.410
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 9.977 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
12.488 12.674 13.141 13.760 11.094
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6
________
13.586
FACTOR STRUCTURE
1 2
________ ________
Y1 0.801 0.314
Y2 0.794 0.293
Y3 0.788 0.302
Y4 0.290 0.763
Y5 0.303 0.811
Y6 0.313 0.769
Beginning Time: 23:10:57
Ending Time: 23:10:59
Elapsed Time: 00:00:02
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