Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:11 PM
INPUT INSTRUCTIONS
TITLE: this is an example of an EFA with residual variances constrained to be greater than
DATA: FILE = ex5.28.dat;
VARIABLE: NAMES = y1-y10;
ANALYSIS: ROTATION = GEOMIN;
MODEL: f1-f2 BY y1-y10 (*1);
y1-y10 (v1-v10);
MODEL CONSTRAINT:
DO(1,10) v#>0;
OUTPUT: STDY;
INPUT READING TERMINATED NORMALLY
this is an example of an EFA with residual variances constrained to be greater than
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 50
Number of dependent variables 10
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10
Continuous latent variables
EFA factors
*1: F1 F2
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)
ex5.28.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 -0.191 -0.023 -2.304 2.00% -1.200 -0.402 -0.209
50.000 0.950 -0.514 1.747 2.00% 0.047 0.540
Y2 0.041 0.068 -1.867 2.00% -0.890 -0.244 0.135
50.000 0.872 -0.319 2.266 2.00% 0.413 0.693
Y3 -0.072 -0.253 -2.091 2.00% -1.144 -0.374 -0.026
50.000 1.080 -0.770 1.756 2.00% 0.362 0.855
Y4 -0.041 -0.436 -3.003 2.00% -0.877 -0.485 0.091
50.000 0.979 0.102 1.750 2.00% 0.235 0.827
Y5 0.052 -0.147 -2.637 2.00% -0.922 -0.328 -0.086
50.000 1.381 -0.742 2.392 2.00% 0.507 1.164
Y6 0.095 -0.207 -1.856 2.00% -0.861 -0.343 0.289
50.000 0.853 -0.818 1.946 2.00% 0.404 0.913
Y7 0.058 0.159 -2.233 2.00% -0.869 -0.357 -0.041
50.000 1.135 -0.446 2.330 2.00% 0.321 0.911
Y8 0.046 -0.200 -2.834 2.00% -0.924 -0.228 -0.075
50.000 1.190 0.402 2.907 2.00% 0.237 0.916
Y9 -0.142 0.215 -2.477 2.00% -0.783 -0.470 -0.362
50.000 0.979 -0.032 2.070 2.00% -0.109 0.786
Y10 -0.196 0.205 -2.484 2.00% -1.021 -0.468 -0.213
50.000 1.020 0.180 2.383 2.00% 0.065 0.522
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 39
Loglikelihood
H0 Value -540.347
H1 Value -528.971
Information Criteria
Akaike (AIC) 1158.693
Bayesian (BIC) 1233.262
Sample-Size Adjusted BIC 1110.847
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 22.751
Degrees of Freedom 26
P-Value 0.6470
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.000
90 Percent C.I. 0.000 0.094
Probability RMSEA <= .05 0.783
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 377.580
Degrees of Freedom 45
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.029
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 0.813 0.114 7.137 0.000
Y2 0.728 0.114 6.406 0.000
Y3 0.882 0.121 7.314 0.000
Y4 0.798 0.118 6.763 0.000
Y5 0.888 0.139 6.411 0.000
Y6 0.794 0.107 7.407 0.000
Y7 0.775 0.132 5.867 0.000
Y8 0.797 0.136 5.856 0.000
Y9 0.009 0.007 1.272 0.203
Y10 -0.024 0.063 -0.372 0.710
F2 BY
Y1 -0.001 0.058 -0.010 0.992
Y2 0.019 0.091 0.206 0.837
Y3 0.006 0.074 0.084 0.933
Y4 -0.022 0.093 -0.235 0.814
Y5 -0.196 0.116 -1.692 0.091
Y6 0.152 0.084 1.813 0.070
Y7 -0.065 0.112 -0.575 0.565
Y8 0.000 0.085 0.006 0.996
Y9 0.991 0.099 9.985 0.000
Y10 0.891 0.112 7.994 0.000
F2 WITH
F1 -0.129 0.148 -0.870 0.384
Intercepts
Y1 -0.191 0.138 -1.383 0.167
Y2 0.041 0.132 0.311 0.756
Y3 -0.072 0.147 -0.489 0.625
Y4 -0.041 0.140 -0.294 0.769
Y5 0.052 0.166 0.315 0.753
Y6 0.095 0.131 0.729 0.466
Y7 0.058 0.151 0.385 0.700
Y8 0.046 0.154 0.295 0.768
Y9 -0.142 0.140 -1.015 0.310
Y10 -0.196 0.143 -1.370 0.171
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.289 0.069 4.206 0.000
Y2 0.345 0.077 4.464 0.000
Y3 0.303 0.074 4.088 0.000
Y4 0.338 0.078 4.311 0.000
Y5 0.508 0.114 4.446 0.000
Y6 0.230 0.058 4.001 0.000
Y7 0.517 0.113 4.572 0.000
Y8 0.555 0.121 4.588 0.000
Y9 0.000 0.000 597.014 0.000
Y10 0.219 0.044 4.998 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.882E-07
(ratio of smallest to largest eigenvalue)
STANDARDIZED MODEL RESULTS
STDY Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 0.834 0.050 16.786 0.000
Y2 0.780 0.063 12.436 0.000
Y3 0.849 0.047 18.040 0.000
Y4 0.806 0.057 14.194 0.000
Y5 0.756 0.065 11.551 0.000
Y6 0.860 0.050 17.247 0.000
Y7 0.728 0.073 9.994 0.000
Y8 0.730 0.072 10.087 0.000
Y9 0.009 0.007 1.288 0.198
Y10 -0.023 0.063 -0.372 0.710
F2 BY
Y1 -0.001 0.059 -0.010 0.992
Y2 0.020 0.098 0.206 0.837
Y3 0.006 0.071 0.084 0.933
Y4 -0.022 0.094 -0.235 0.814
Y5 -0.167 0.098 -1.707 0.088
Y6 0.164 0.090 1.817 0.069
Y7 -0.061 0.105 -0.576 0.565
Y8 0.000 0.078 0.006 0.996
Y9 1.001 0.001 697.561 0.000
Y10 0.883 0.032 27.441 0.000
F2 WITH
F1 -0.129 0.148 -0.870 0.384
Intercepts
Y1 -0.196 0.143 -1.370 0.171
Y2 0.044 0.141 0.311 0.756
Y3 -0.069 0.142 -0.489 0.625
Y4 -0.042 0.141 -0.294 0.769
Y5 0.045 0.141 0.315 0.753
Y6 0.103 0.142 0.727 0.467
Y7 0.054 0.142 0.385 0.700
Y8 0.042 0.141 0.295 0.768
Y9 -0.144 0.142 -1.010 0.312
Y10 -0.194 0.143 -1.358 0.175
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.304 0.082 3.721 0.000
Y2 0.395 0.096 4.133 0.000
Y3 0.281 0.078 3.595 0.000
Y4 0.345 0.089 3.887 0.000
Y5 0.368 0.091 4.044 0.000
Y6 0.270 0.077 3.516 0.000
Y7 0.455 0.103 4.410 0.000
Y8 0.467 0.105 4.464 0.000
Y9 0.000 0.000 5.000 0.000
Y10 0.215 0.054 3.990 0.000
R-SQUARE
Observed Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
Y1 0.696 0.082 8.519 0.000
Y2 0.605 0.096 6.319 0.000
Y3 0.719 0.078 9.206 0.000
Y4 0.655 0.089 7.381 0.000
Y5 0.632 0.091 6.948 0.000
Y6 0.730 0.077 9.510 0.000
Y7 0.545 0.103 5.280 0.000
Y8 0.533 0.105 5.104 0.000
Y9 1.000 0.000 ******** 0.000
Y10 0.785 0.054 14.554 0.000
Beginning Time: 23:11:22
Ending Time: 23:11:23
Elapsed Time: 00:00:01
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