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 continuous factor indicators
using exploratory structural equation modeling (ESEM)
DATA: FILE IS ex4.1b.dat;
VARIABLE: NAMES ARE y1-y12;
MODEL: f1-f4 BY y1-y12 (*1);
OUTPUT: MODINDICES standardized;
INPUT READING TERMINATED NORMALLY
this is an example of an exploratory factor
analysis with continuous factor indicators
using exploratory structural equation modeling (ESEM)
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 4
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10 Y11 Y12
Continuous latent variables
EFA factors
*1: F1 F2 F3 F4
Estimator ML
Rotation GEOMIN
Row standardization CORRELATION
Type of rotation OBLIQUE
Epsilon value Varies
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)
ex4.1b.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 0.008 -0.037 -2.887 0.20% -0.831 -0.246 0.013
500.000 0.958 -0.259 2.529 0.20% 0.230 0.874
Y2 0.033 -0.058 -3.691 0.20% -0.797 -0.192 0.069
500.000 1.015 0.124 2.795 0.20% 0.274 0.848
Y3 0.003 0.202 -2.589 0.20% -0.889 -0.333 -0.071
500.000 0.959 -0.413 2.968 0.20% 0.227 0.872
Y4 0.073 -0.027 -3.215 0.20% -0.685 -0.230 -0.007
500.000 1.020 0.052 2.893 0.20% 0.267 0.932
Y5 0.063 -0.075 -2.949 0.20% -0.762 -0.199 0.050
500.000 0.990 -0.036 3.741 0.20% 0.347 0.950
Y6 0.062 0.220 -2.500 0.20% -0.798 -0.264 -0.008
500.000 1.071 -0.211 3.254 0.20% 0.268 0.981
Y7 -0.004 -0.008 -2.799 0.20% -0.873 -0.261 0.002
500.000 1.031 -0.124 3.446 0.20% 0.233 0.866
Y8 0.009 -0.161 -3.582 0.20% -0.785 -0.250 0.030
500.000 0.993 0.197 2.828 0.20% 0.279 0.846
Y9 0.021 0.040 -2.762 0.20% -0.785 -0.246 -0.044
500.000 0.952 -0.064 2.940 0.20% 0.252 0.830
Y10 -0.037 -0.057 -3.629 0.20% -0.965 -0.290 0.012
500.000 1.142 0.051 3.033 0.20% 0.257 0.818
Y11 0.002 0.009 -2.747 0.20% -0.901 -0.243 0.024
500.000 1.097 -0.088 3.273 0.20% 0.266 0.841
Y12 -0.002 0.083 -3.443 0.20% -0.860 -0.296 -0.008
500.000 1.037 0.145 2.972 0.20% 0.216 0.832
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 66
Loglikelihood
H0 Value -7869.377
H1 Value -7856.478
Information Criteria
Akaike (AIC) 15870.755
Bayesian (BIC) 16148.919
Sample-Size Adjusted BIC 15939.431
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 25.799
Degrees of Freedom 24
P-Value 0.3635
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.012
90 Percent C.I. 0.000 0.039
Probability RMSEA <= .05 0.995
CFI/TLI
CFI 0.999
TLI 0.996
Chi-Square Test of Model Fit for the Baseline Model
Value 1436.819
Degrees of Freedom 66
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.012
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 0.623 0.047 13.161 0.000
Y2 0.814 0.051 15.928 0.000
Y3 0.618 0.048 12.964 0.000
Y4 0.027 0.034 0.799 0.424
Y5 -0.029 0.028 -1.034 0.301
Y6 0.011 0.031 0.348 0.728
Y7 -0.006 0.025 -0.244 0.808
Y8 -0.039 0.030 -1.310 0.190
Y9 0.047 0.032 1.475 0.140
Y10 -0.040 0.034 -1.154 0.248
Y11 0.004 0.024 0.160 0.873
Y12 0.035 0.034 1.049 0.294
F2 BY
Y1 0.008 0.031 0.261 0.794
Y2 0.022 0.025 0.869 0.385
Y3 -0.041 0.036 -1.134 0.257
Y4 0.652 0.049 13.210 0.000
Y5 0.756 0.050 15.029 0.000
Y6 0.697 0.051 13.695 0.000
Y7 0.003 0.030 0.101 0.919
Y8 0.002 0.029 0.066 0.948
Y9 -0.007 0.030 -0.227 0.821
Y10 0.007 0.032 0.216 0.829
Y11 0.014 0.027 0.524 0.600
Y12 -0.037 0.036 -1.023 0.306
F3 BY
Y1 0.073 0.038 1.906 0.057
Y2 -0.005 0.015 -0.319 0.750
Y3 -0.057 0.036 -1.599 0.110
Y4 -0.002 0.031 -0.077 0.939
Y5 -0.023 0.027 -0.872 0.383
Y6 0.031 0.034 0.932 0.351
Y7 0.745 0.047 15.878 0.000
Y8 0.724 0.046 15.747 0.000
Y9 0.689 0.045 15.316 0.000
Y10 -0.010 0.032 -0.314 0.753
Y11 0.001 0.027 0.038 0.969
Y12 0.009 0.032 0.264 0.792
F4 BY
Y1 -0.021 0.031 -0.674 0.500
Y2 0.041 0.028 1.459 0.145
Y3 -0.027 0.032 -0.862 0.389
Y4 -0.018 0.034 -0.537 0.591
Y5 0.016 0.027 0.613 0.540
Y6 -0.012 0.032 -0.376 0.707
Y7 0.018 0.030 0.607 0.544
Y8 -0.016 0.029 -0.562 0.574
Y9 -0.001 0.028 -0.043 0.966
Y10 0.740 0.050 14.656 0.000
Y11 0.829 0.050 16.532 0.000
Y12 0.670 0.048 14.020 0.000
F2 WITH
F1 -0.039 0.057 -0.682 0.495
F3 WITH
F1 0.007 0.055 0.130 0.896
F2 0.029 0.057 0.521 0.602
F4 WITH
F1 -0.002 0.056 -0.031 0.976
F2 -0.121 0.056 -2.151 0.031
F3 -0.028 0.056 -0.496 0.620
Intercepts
Y1 0.008 0.044 0.183 0.855
Y2 0.033 0.045 0.741 0.459
Y3 0.003 0.044 0.072 0.942
Y4 0.073 0.045 1.627 0.104
Y5 0.063 0.044 1.423 0.155
Y6 0.062 0.046 1.344 0.179
Y7 -0.004 0.045 -0.077 0.939
Y8 0.009 0.045 0.203 0.839
Y9 0.021 0.044 0.478 0.633
Y10 -0.037 0.048 -0.771 0.441
Y11 0.002 0.047 0.034 0.973
Y12 -0.002 0.046 -0.052 0.958
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
F3 1.000 0.000 999.000 999.000
F4 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.564 0.049 11.500 0.000
Y2 0.352 0.062 5.706 0.000
Y3 0.569 0.049 11.516 0.000
Y4 0.592 0.052 11.336 0.000
Y5 0.419 0.056 7.455 0.000
Y6 0.581 0.056 10.453 0.000
Y7 0.476 0.049 9.632 0.000
Y8 0.467 0.047 9.836 0.000
Y9 0.474 0.045 10.495 0.000
Y10 0.594 0.056 10.644 0.000
Y11 0.413 0.058 7.147 0.000
Y12 0.580 0.050 11.621 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.220E-01
(ratio of smallest to largest eigenvalue)
STANDARDIZED MODEL RESULTS
STDYX Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 0.637 0.038 16.648 0.000
Y2 0.808 0.038 21.069 0.000
Y3 0.631 0.039 16.283 0.000
Y4 0.027 0.033 0.800 0.424
Y5 -0.029 0.028 -1.034 0.301
Y6 0.010 0.030 0.348 0.728
Y7 -0.006 0.024 -0.244 0.808
Y8 -0.040 0.030 -1.310 0.190
Y9 0.049 0.033 1.476 0.140
Y10 -0.037 0.032 -1.155 0.248
Y11 0.004 0.023 0.160 0.873
Y12 0.035 0.033 1.049 0.294
F2 BY
Y1 0.008 0.032 0.261 0.794
Y2 0.022 0.025 0.869 0.385
Y3 -0.042 0.037 -1.135 0.256
Y4 0.646 0.039 16.735 0.000
Y5 0.760 0.039 19.673 0.000
Y6 0.674 0.038 17.545 0.000
Y7 0.003 0.029 0.101 0.919
Y8 0.002 0.029 0.066 0.948
Y9 -0.007 0.030 -0.227 0.821
Y10 0.006 0.030 0.216 0.829
Y11 0.013 0.026 0.524 0.600
Y12 -0.036 0.035 -1.023 0.306
F3 BY
Y1 0.074 0.039 1.909 0.056
Y2 -0.005 0.015 -0.319 0.750
Y3 -0.058 0.036 -1.602 0.109
Y4 -0.002 0.031 -0.077 0.939
Y5 -0.023 0.027 -0.872 0.383
Y6 0.030 0.033 0.932 0.351
Y7 0.734 0.033 22.121 0.000
Y8 0.727 0.033 21.838 0.000
Y9 0.707 0.034 20.985 0.000
Y10 -0.010 0.030 -0.314 0.753
Y11 0.001 0.026 0.038 0.969
Y12 0.008 0.032 0.264 0.792
F4 BY
Y1 -0.021 0.031 -0.674 0.500
Y2 0.041 0.028 1.459 0.144
Y3 -0.028 0.032 -0.862 0.389
Y4 -0.018 0.033 -0.537 0.591
Y5 0.017 0.027 0.613 0.540
Y6 -0.012 0.031 -0.376 0.707
Y7 0.018 0.029 0.607 0.544
Y8 -0.016 0.029 -0.562 0.574
Y9 -0.001 0.029 -0.043 0.966
Y10 0.692 0.035 19.541 0.000
Y11 0.791 0.035 22.901 0.000
Y12 0.658 0.036 18.342 0.000
F2 WITH
F1 -0.039 0.057 -0.682 0.495
F3 WITH
F1 0.007 0.055 0.130 0.896
F2 0.029 0.057 0.521 0.602
F4 WITH
F1 -0.002 0.056 -0.031 0.976
F2 -0.121 0.056 -2.151 0.031
F3 -0.028 0.056 -0.496 0.620
Intercepts
Y1 0.008 0.045 0.183 0.855
Y2 0.033 0.045 0.741 0.459
Y3 0.003 0.045 0.072 0.942
Y4 0.073 0.045 1.625 0.104
Y5 0.064 0.045 1.421 0.155
Y6 0.060 0.045 1.343 0.179
Y7 -0.003 0.045 -0.077 0.939
Y8 0.009 0.045 0.203 0.839
Y9 0.021 0.045 0.478 0.633
Y10 -0.034 0.045 -0.771 0.441
Y11 0.002 0.045 0.034 0.973
Y12 -0.002 0.045 -0.052 0.958
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
F3 1.000 0.000 999.000 999.000
F4 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.588 0.049 12.075 0.000
Y2 0.346 0.062 5.595 0.000
Y3 0.594 0.049 12.138 0.000
Y4 0.581 0.049 11.838 0.000
Y5 0.424 0.058 7.332 0.000
Y6 0.543 0.051 10.653 0.000
Y7 0.462 0.049 9.499 0.000
Y8 0.470 0.048 9.723 0.000
Y9 0.498 0.047 10.486 0.000
Y10 0.520 0.048 10.740 0.000
Y11 0.376 0.054 6.973 0.000
Y12 0.559 0.047 12.008 0.000
STDY Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 0.637 0.038 16.648 0.000
Y2 0.808 0.038 21.069 0.000
Y3 0.631 0.039 16.283 0.000
Y4 0.027 0.033 0.800 0.424
Y5 -0.029 0.028 -1.034 0.301
Y6 0.010 0.030 0.348 0.728
Y7 -0.006 0.024 -0.244 0.808
Y8 -0.040 0.030 -1.310 0.190
Y9 0.049 0.033 1.476 0.140
Y10 -0.037 0.032 -1.155 0.248
Y11 0.004 0.023 0.160 0.873
Y12 0.035 0.033 1.049 0.294
F2 BY
Y1 0.008 0.032 0.261 0.794
Y2 0.022 0.025 0.869 0.385
Y3 -0.042 0.037 -1.135 0.256
Y4 0.646 0.039 16.735 0.000
Y5 0.760 0.039 19.673 0.000
Y6 0.674 0.038 17.545 0.000
Y7 0.003 0.029 0.101 0.919
Y8 0.002 0.029 0.066 0.948
Y9 -0.007 0.030 -0.227 0.821
Y10 0.006 0.030 0.216 0.829
Y11 0.013 0.026 0.524 0.600
Y12 -0.036 0.035 -1.023 0.306
F3 BY
Y1 0.074 0.039 1.909 0.056
Y2 -0.005 0.015 -0.319 0.750
Y3 -0.058 0.036 -1.602 0.109
Y4 -0.002 0.031 -0.077 0.939
Y5 -0.023 0.027 -0.872 0.383
Y6 0.030 0.033 0.932 0.351
Y7 0.734 0.033 22.121 0.000
Y8 0.727 0.033 21.838 0.000
Y9 0.707 0.034 20.985 0.000
Y10 -0.010 0.030 -0.314 0.753
Y11 0.001 0.026 0.038 0.969
Y12 0.008 0.032 0.264 0.792
F4 BY
Y1 -0.021 0.031 -0.674 0.500
Y2 0.041 0.028 1.459 0.144
Y3 -0.028 0.032 -0.862 0.389
Y4 -0.018 0.033 -0.537 0.591
Y5 0.017 0.027 0.613 0.540
Y6 -0.012 0.031 -0.376 0.707
Y7 0.018 0.029 0.607 0.544
Y8 -0.016 0.029 -0.562 0.574
Y9 -0.001 0.029 -0.043 0.966
Y10 0.692 0.035 19.541 0.000
Y11 0.791 0.035 22.901 0.000
Y12 0.658 0.036 18.342 0.000
F2 WITH
F1 -0.039 0.057 -0.682 0.495
F3 WITH
F1 0.007 0.055 0.130 0.896
F2 0.029 0.057 0.521 0.602
F4 WITH
F1 -0.002 0.056 -0.031 0.976
F2 -0.121 0.056 -2.151 0.031
F3 -0.028 0.056 -0.496 0.620
Intercepts
Y1 0.008 0.045 0.183 0.855
Y2 0.033 0.045 0.741 0.459
Y3 0.003 0.045 0.072 0.942
Y4 0.073 0.045 1.625 0.104
Y5 0.064 0.045 1.421 0.155
Y6 0.060 0.045 1.343 0.179
Y7 -0.003 0.045 -0.077 0.939
Y8 0.009 0.045 0.203 0.839
Y9 0.021 0.045 0.478 0.633
Y10 -0.034 0.045 -0.771 0.441
Y11 0.002 0.045 0.034 0.973
Y12 -0.002 0.045 -0.052 0.958
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
F3 1.000 0.000 999.000 999.000
F4 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.588 0.049 12.075 0.000
Y2 0.346 0.062 5.595 0.000
Y3 0.594 0.049 12.138 0.000
Y4 0.581 0.049 11.838 0.000
Y5 0.424 0.058 7.332 0.000
Y6 0.543 0.051 10.653 0.000
Y7 0.462 0.049 9.499 0.000
Y8 0.470 0.048 9.723 0.000
Y9 0.498 0.047 10.486 0.000
Y10 0.520 0.048 10.740 0.000
Y11 0.376 0.054 6.973 0.000
Y12 0.559 0.047 12.008 0.000
STD Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 0.623 0.047 13.161 0.000
Y2 0.814 0.051 15.928 0.000
Y3 0.618 0.048 12.964 0.000
Y4 0.027 0.034 0.799 0.424
Y5 -0.029 0.028 -1.034 0.301
Y6 0.011 0.031 0.348 0.728
Y7 -0.006 0.025 -0.244 0.808
Y8 -0.039 0.030 -1.310 0.190
Y9 0.047 0.032 1.475 0.140
Y10 -0.040 0.034 -1.154 0.248
Y11 0.004 0.024 0.160 0.873
Y12 0.035 0.034 1.049 0.294
F2 BY
Y1 0.008 0.031 0.261 0.794
Y2 0.022 0.025 0.869 0.385
Y3 -0.041 0.036 -1.134 0.257
Y4 0.652 0.049 13.210 0.000
Y5 0.756 0.050 15.029 0.000
Y6 0.697 0.051 13.695 0.000
Y7 0.003 0.030 0.101 0.919
Y8 0.002 0.029 0.066 0.948
Y9 -0.007 0.030 -0.227 0.821
Y10 0.007 0.032 0.216 0.829
Y11 0.014 0.027 0.524 0.600
Y12 -0.037 0.036 -1.023 0.306
F3 BY
Y1 0.073 0.038 1.906 0.057
Y2 -0.005 0.015 -0.319 0.750
Y3 -0.057 0.036 -1.599 0.110
Y4 -0.002 0.031 -0.077 0.939
Y5 -0.023 0.027 -0.872 0.383
Y6 0.031 0.034 0.932 0.351
Y7 0.745 0.047 15.878 0.000
Y8 0.724 0.046 15.747 0.000
Y9 0.689 0.045 15.316 0.000
Y10 -0.010 0.032 -0.314 0.753
Y11 0.001 0.027 0.038 0.969
Y12 0.009 0.032 0.264 0.792
F4 BY
Y1 -0.021 0.031 -0.674 0.500
Y2 0.041 0.028 1.459 0.145
Y3 -0.027 0.032 -0.862 0.389
Y4 -0.018 0.034 -0.537 0.591
Y5 0.016 0.027 0.613 0.540
Y6 -0.012 0.032 -0.376 0.707
Y7 0.018 0.030 0.607 0.544
Y8 -0.016 0.029 -0.562 0.574
Y9 -0.001 0.028 -0.043 0.966
Y10 0.740 0.050 14.656 0.000
Y11 0.829 0.050 16.532 0.000
Y12 0.670 0.048 14.020 0.000
F2 WITH
F1 -0.039 0.057 -0.682 0.495
F3 WITH
F1 0.007 0.055 0.130 0.896
F2 0.029 0.057 0.521 0.602
F4 WITH
F1 -0.002 0.056 -0.031 0.976
F2 -0.121 0.056 -2.151 0.031
F3 -0.028 0.056 -0.496 0.620
Intercepts
Y1 0.008 0.044 0.183 0.855
Y2 0.033 0.045 0.741 0.459
Y3 0.003 0.044 0.072 0.942
Y4 0.073 0.045 1.627 0.104
Y5 0.063 0.044 1.423 0.155
Y6 0.062 0.046 1.344 0.179
Y7 -0.004 0.045 -0.077 0.939
Y8 0.009 0.045 0.203 0.839
Y9 0.021 0.044 0.478 0.633
Y10 -0.037 0.048 -0.771 0.441
Y11 0.002 0.047 0.034 0.973
Y12 -0.002 0.046 -0.052 0.958
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
F3 1.000 0.000 999.000 999.000
F4 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.564 0.049 11.500 0.000
Y2 0.352 0.062 5.706 0.000
Y3 0.569 0.049 11.516 0.000
Y4 0.592 0.052 11.336 0.000
Y5 0.419 0.056 7.455 0.000
Y6 0.581 0.056 10.453 0.000
Y7 0.476 0.049 9.632 0.000
Y8 0.467 0.047 9.836 0.000
Y9 0.474 0.045 10.495 0.000
Y10 0.594 0.056 10.644 0.000
Y11 0.413 0.058 7.147 0.000
Y12 0.580 0.050 11.621 0.000
R-SQUARE
Observed Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
Y1 0.412 0.049 8.463 0.000
Y2 0.654 0.062 10.561 0.000
Y3 0.406 0.049 8.293 0.000
Y4 0.419 0.049 8.547 0.000
Y5 0.576 0.058 9.973 0.000
Y6 0.457 0.051 8.983 0.000
Y7 0.538 0.049 11.069 0.000
Y8 0.530 0.048 10.981 0.000
Y9 0.502 0.047 10.567 0.000
Y10 0.480 0.048 9.924 0.000
Y11 0.624 0.054 11.555 0.000
Y12 0.441 0.047 9.483 0.000
MODEL MODIFICATION INDICES
NOTE: Modification indices for direct effects of observed dependent variables
regressed on covariates may not be included. To include these, request
MODINDICES (ALL).
Minimum M.I. value for printing the modification index 10.000
M.I. E.P.C. Std E.P.C. StdYX E.P.C.
No modification indices above the minimum value.
Beginning Time: 23:09:26
Ending Time: 23:09:26
Elapsed Time: 00:00:00
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2022 Muthen & Muthen