Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:23 PM
INPUT INSTRUCTIONS
TITLE:
this is an example of EFA using ESEM
with residual variances restricted to
be greater than zero
MONTECARLO:
NAMES = y1-y10;
NOBSERVATIONS = 50;
NREPS = 1;
SAVE = ex5.28.dat;
MODEL POPULATION:
f1 BY y1-y8*0.8;
f2 BY y9-y10*0.9;
f1-f2@1;
f1 WITH f2*0;
y1-y8*0.36 y9-y10*0.1;
ANALYSIS:
ROTATION = GEOMIN;
MODEL:
f1 BY y1-y8*0.8 y9-y10*0 (*1);
f2 BY y1-y8*0 y9-y10*0.9 (*1);
y1-y8*0.36 y9-y10*0.1;
*** WARNING in MODEL command
Values given in the MODEL command for EFA factors are used only as
population values in computing coverage. EFA factors cannot be given
starting values.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of EFA using ESEM
with residual variances restricted to
be greater than zero
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 50
Number of replications
Requested 1
Completed 1
Value of seed 0
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
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
-0.191 0.041 -0.072 -0.041 0.052
Means
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.095 0.058 0.046 -0.142 -0.196
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.950
Y2 0.629 0.872
Y3 0.705 0.632 1.080
Y4 0.646 0.586 0.716 0.979
Y5 0.690 0.641 0.805 0.688 1.381
Y6 0.651 0.538 0.739 0.568 0.719
Y7 0.637 0.603 0.640 0.729 0.726
Y8 0.637 0.565 0.641 0.687 0.839
Y9 -0.097 -0.068 -0.099 -0.116 -0.300
Y10 -0.093 -0.061 -0.078 -0.146 -0.315
Covariances
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.853
Y7 0.545 1.135
Y8 0.586 0.638 1.190
Y9 0.056 -0.156 -0.094 0.979
Y10 0.014 -0.161 -0.192 0.885 1.020
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.691 1.000
Y3 0.696 0.651 1.000
Y4 0.670 0.634 0.696 1.000
Y5 0.603 0.584 0.659 0.592 1.000
Y6 0.724 0.623 0.770 0.622 0.663
Y7 0.614 0.606 0.578 0.691 0.580
Y8 0.600 0.555 0.566 0.636 0.655
Y9 -0.101 -0.073 -0.096 -0.119 -0.258
Y10 -0.094 -0.064 -0.074 -0.146 -0.265
Correlations
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.000
Y7 0.554 1.000
Y8 0.581 0.549 1.000
Y9 0.061 -0.148 -0.087 1.000
Y10 0.014 -0.149 -0.174 0.885 1.000
MODEL FIT INFORMATION
Number of Free Parameters 39
Loglikelihood
H0 Value
Mean -540.346
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -540.346 -540.346
0.980 0.000 -540.346 -540.346
0.950 0.000 -540.346 -540.346
0.900 0.000 -540.346 -540.346
0.800 0.000 -540.346 -540.346
0.700 0.000 -540.346 -540.346
0.500 0.000 -540.346 -540.346
0.300 0.000 -540.346 -540.346
0.200 0.000 -540.346 -540.346
0.100 0.000 -540.346 -540.346
0.050 0.000 -540.346 -540.346
0.020 0.000 -540.346 -540.346
0.010 0.000 -540.346 -540.346
H1 Value
Mean -528.971
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -528.971 -528.971
0.980 0.000 -528.971 -528.971
0.950 0.000 -528.971 -528.971
0.900 0.000 -528.971 -528.971
0.800 0.000 -528.971 -528.971
0.700 0.000 -528.971 -528.971
0.500 0.000 -528.971 -528.971
0.300 0.000 -528.971 -528.971
0.200 0.000 -528.971 -528.971
0.100 0.000 -528.971 -528.971
0.050 0.000 -528.971 -528.971
0.020 0.000 -528.971 -528.971
0.010 0.000 -528.971 -528.971
Information Criteria
Akaike (AIC)
Mean 1158.691
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1158.691 1158.691
0.980 0.000 1158.691 1158.691
0.950 0.000 1158.691 1158.691
0.900 0.000 1158.691 1158.691
0.800 0.000 1158.691 1158.691
0.700 0.000 1158.691 1158.691
0.500 0.000 1158.691 1158.691
0.300 0.000 1158.691 1158.691
0.200 0.000 1158.691 1158.691
0.100 0.000 1158.691 1158.691
0.050 0.000 1158.691 1158.691
0.020 0.000 1158.691 1158.691
0.010 0.000 1158.691 1158.691
Bayesian (BIC)
Mean 1233.260
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1233.260 1233.260
0.980 0.000 1233.260 1233.260
0.950 0.000 1233.260 1233.260
0.900 0.000 1233.260 1233.260
0.800 0.000 1233.260 1233.260
0.700 0.000 1233.260 1233.260
0.500 0.000 1233.260 1233.260
0.300 0.000 1233.260 1233.260
0.200 0.000 1233.260 1233.260
0.100 0.000 1233.260 1233.260
0.050 0.000 1233.260 1233.260
0.020 0.000 1233.260 1233.260
0.010 0.000 1233.260 1233.260
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 1110.846
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1110.846 1110.846
0.980 0.000 1110.846 1110.846
0.950 0.000 1110.846 1110.846
0.900 0.000 1110.846 1110.846
0.800 0.000 1110.846 1110.846
0.700 0.000 1110.846 1110.846
0.500 0.000 1110.846 1110.846
0.300 0.000 1110.846 1110.846
0.200 0.000 1110.846 1110.846
0.100 0.000 1110.846 1110.846
0.050 0.000 1110.846 1110.846
0.020 0.000 1110.846 1110.846
0.010 0.000 1110.846 1110.846
Chi-Square Test of Model Fit
Degrees of freedom 26
Mean 22.749
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 12.198 22.749
0.980 1.000 13.409 22.749
0.950 1.000 15.379 22.749
0.900 1.000 17.292 22.749
0.800 1.000 19.820 22.749
0.700 1.000 21.792 22.749
0.500 0.000 25.336 22.749
0.300 0.000 29.246 22.749
0.200 0.000 31.795 22.749
0.100 0.000 35.563 22.749
0.050 0.000 38.885 22.749
0.020 0.000 42.856 22.749
0.010 0.000 45.642 22.749
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 1.000
0.200 1.000
0.100 1.000
0.050 1.000
0.020 1.000
0.010 1.000
CFI/TLI
CFI
Mean 1.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 0.000
0.980 0.000
0.950 0.000
0.900 0.000
0.800 0.000
0.700 0.000
0.500 0.000
0.300 0.000
0.200 0.000
0.100 0.000
0.050 0.000
0.020 0.000
0.010 0.000
TLI
Mean 1.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 0.000
0.980 0.000
0.950 0.000
0.900 0.000
0.800 0.000
0.700 0.000
0.500 0.000
0.300 0.000
0.200 0.000
0.100 0.000
0.050 0.000
0.020 0.000
0.010 0.000
SRMR (Standardized Root Mean Square Residual)
Mean 0.029
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 1.000
0.200 1.000
0.100 1.000
0.050 1.000
0.020 0.000
0.010 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
F1 BY
Y1 0.800 0.8127 0.0000 0.1139 0.0002 1.000 1.000
Y2 0.800 0.7282 0.0000 0.1136 0.0052 1.000 1.000
Y3 0.800 0.8817 0.0000 0.1208 0.0067 1.000 1.000
Y4 0.800 0.7984 0.0000 0.1191 0.0000 1.000 1.000
Y5 0.800 0.8892 0.0000 0.1405 0.0080 1.000 1.000
Y6 0.800 0.7937 0.0000 0.1074 0.0000 1.000 1.000
Y7 0.800 0.7759 0.0000 0.1330 0.0006 1.000 1.000
Y8 0.800 0.7982 0.0000 0.1408 0.0000 1.000 1.000
Y9 0.000 0.0085 0.0000 0.0142 0.0001 1.000 0.000
Y10 0.000 -0.0264 0.0000 0.0987 0.0007 1.000 0.000
F2 BY
Y1 0.000 -0.0026 0.0000 0.0619 0.0000 1.000 0.000
Y2 0.000 0.0175 0.0000 0.0893 0.0003 1.000 0.000
Y3 0.000 0.0025 0.0000 0.0879 0.0000 1.000 0.000
Y4 0.000 -0.0190 0.0000 0.1367 0.0004 1.000 0.000
Y5 0.000 -0.1922 0.0000 0.1781 0.0369 1.000 0.000
Y6 0.000 0.1517 0.0000 0.0838 0.0230 1.000 0.000
Y7 0.000 -0.0626 0.0000 0.1361 0.0039 1.000 0.000
Y8 0.000 0.0100 0.0000 0.2872 0.0001 1.000 0.000
Y9 0.900 1.0016 0.0000 0.2980 0.0103 1.000 1.000
Y10 0.900 0.8814 0.0000 0.2840 0.0003 1.000 1.000
F2 WITH
F1 0.000 -0.1278 0.0000 0.1456 0.0163 1.000 0.000
Intercepts
Y1 0.000 -0.1906 0.0000 0.1378 0.0363 1.000 0.000
Y2 0.000 0.0411 0.0000 0.1321 0.0017 1.000 0.000
Y3 0.000 -0.0719 0.0000 0.1470 0.0052 1.000 0.000
Y4 0.000 -0.0411 0.0000 0.1400 0.0017 1.000 0.000
Y5 0.000 0.0523 0.0000 0.1662 0.0027 1.000 0.000
Y6 0.000 0.0952 0.0000 0.1306 0.0091 1.000 0.000
Y7 0.000 0.0580 0.0000 0.1507 0.0034 1.000 0.000
Y8 0.000 0.0456 0.0000 0.1543 0.0021 1.000 0.000
Y9 0.000 -0.1421 0.0000 0.1400 0.0202 1.000 0.000
Y10 0.000 -0.1957 0.0000 0.1428 0.0383 1.000 0.000
Variances
F1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y1 0.360 0.2887 0.0000 0.0687 0.0051 1.000 1.000
Y2 0.360 0.3449 0.0000 0.0773 0.0002 1.000 1.000
Y3 0.360 0.3036 0.0000 0.0743 0.0032 1.000 1.000
Y4 0.360 0.3378 0.0000 0.0784 0.0005 1.000 1.000
Y5 0.360 0.5094 0.0000 0.1215 0.0223 1.000 1.000
Y6 0.360 0.2305 0.0000 0.0587 0.0168 0.000 1.000
Y7 0.360 0.5166 0.0000 0.1130 0.0245 1.000 1.000
Y8 0.360 0.5552 0.0000 0.1213 0.0381 1.000 1.000
Y9 0.100 -0.0217 0.0000 0.5662 0.0148 1.000 0.000
Y10 0.100 0.2368 0.0000 0.4435 0.0187 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.343E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
TECHNICAL 1 OUTPUT FOR THE UNROTATED SOLUTION
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
6 7 8 9 10
LAMBDA
F1 F2
________ ________
Y1 11 0
Y2 12 13
Y3 14 15
Y4 16 17
Y5 18 19
Y6 20 21
Y7 22 23
Y8 24 25
Y9 26 27
Y10 28 29
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 30
Y2 0 31
Y3 0 0 32
Y4 0 0 0 33
Y5 0 0 0 0 34
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
Y9 0 0 0 0 0
Y10 0 0 0 0 0
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 35
Y7 0 36
Y8 0 0 37
Y9 0 0 0 38
Y10 0 0 0 0 39
ALPHA
F1 F2
________ ________
0 0
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 0
F2 0 0
STARTING VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F1 F2
________ ________
Y1 0.813 0.000
Y2 0.726 0.020
Y3 0.881 0.005
Y4 0.801 -0.016
Y5 0.914 -0.188
Y6 0.774 0.153
Y7 0.784 -0.060
Y8 0.797 0.012
Y9 -0.123 0.993
Y10 -0.142 0.874
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.289
Y2 0.000 0.345
Y3 0.000 0.000 0.304
Y4 0.000 0.000 0.000 0.338
Y5 0.000 0.000 0.000 0.000 0.509
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
Y9 0.000 0.000 0.000 0.000 0.000
Y10 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.231
Y7 0.000 0.517
Y8 0.000 0.000 0.555
Y9 0.000 0.000 0.000 1.000
Y10 0.000 0.000 0.000 0.000 0.237
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
TECHNICAL 1 OUTPUT FOR THE ROTATED SOLUTION
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
6 7 8 9 10
LAMBDA
F1 F2
________ ________
Y1 11 12
Y2 13 14
Y3 15 16
Y4 17 18
Y5 19 20
Y6 21 22
Y7 23 24
Y8 25 26
Y9 27 28
Y10 29 30
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 31
Y2 0 32
Y3 0 0 33
Y4 0 0 0 34
Y5 0 0 0 0 35
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
Y9 0 0 0 0 0
Y10 0 0 0 0 0
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 36
Y7 0 37
Y8 0 0 38
Y9 0 0 0 39
Y10 0 0 0 0 40
ALPHA
F1 F2
________ ________
0 0
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 0
F2 41 0
STARTING VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F1 F2
________ ________
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
Y5 0.000 0.000
Y6 0.000 0.000
Y7 0.000 0.000
Y8 0.000 0.000
Y9 0.000 0.000
Y10 0.000 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.360
Y2 0.000 0.360
Y3 0.000 0.000 0.360
Y4 0.000 0.000 0.000 0.360
Y5 0.000 0.000 0.000 0.000 0.360
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
Y9 0.000 0.000 0.000 0.000 0.000
Y10 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.360
Y7 0.000 0.360
Y8 0.000 0.000 0.360
Y9 0.000 0.000 0.000 0.100
Y10 0.000 0.000 0.000 0.000 0.100
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
POPULATION VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F1 F2
________ ________
Y1 0.800 0.000
Y2 0.800 0.000
Y3 0.800 0.000
Y4 0.800 0.000
Y5 0.800 0.000
Y6 0.800 0.000
Y7 0.800 0.000
Y8 0.800 0.000
Y9 0.000 0.900
Y10 0.000 0.900
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.360
Y2 0.000 0.360
Y3 0.000 0.000 0.360
Y4 0.000 0.000 0.000 0.360
Y5 0.000 0.000 0.000 0.000 0.360
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
Y9 0.000 0.000 0.000 0.000 0.000
Y10 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.360
Y7 0.000 0.360
Y8 0.000 0.000 0.360
Y9 0.000 0.000 0.000 0.100
Y10 0.000 0.000 0.000 0.000 0.100
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y9
Y10
Save file
ex5.28.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:23:09
Ending Time: 22:23:10
Elapsed Time: 00:00:01
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