Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
INPUT INSTRUCTIONS
title: this is an example of an exploratory
factor analysis with continuous
factor indicators
montecarlo:
names = y1-y12;
nobs = 500;
nreps = 1;
save = ex4.1a.dat;
model population:
f1 by y1-y3*.7;
f2 by y4-y6*.7;
f3 by y7-y9*.7;
f4 by y10-y12*.7;
y1-y12*.51;
!this gives unit y variances so that
!EFA estimates are in the same metric
f1-f4@1;
model:
f1 by y1-y3*.7;
f2 by y4-y6*.7;
f3 by y7-y9*.7;
f4 by y10-y12*.7;
y1-y12*.51;
f1-f4@1;
output:
tech9;
INPUT READING TERMINATED NORMALLY
this is an example of an exploratory
factor analysis with continuous
factor indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 0
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
F1 F2 F3 F4
Estimator ML
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.008 0.033 0.003 0.073 0.063
Means
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.062 -0.004 0.009 0.021 -0.037
Means
Y11 Y12
________ ________
0.002 -0.002
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.958
Y2 0.507 1.015
Y3 0.386 0.500 0.959
Y4 -0.019 0.008 0.017 1.020
Y5 0.000 -0.030 -0.102 0.489 0.990
Y6 -0.017 -0.005 -0.021 0.462 0.525
Y7 0.064 -0.002 -0.058 0.023 0.009
Y8 0.044 -0.046 -0.044 0.028 -0.001
Y9 0.062 0.051 -0.013 -0.011 -0.018
Y10 -0.056 -0.004 -0.029 -0.055 -0.030
Y11 -0.004 0.030 -0.022 -0.067 -0.062
Y12 -0.008 0.060 0.010 -0.107 -0.080
Covariances
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.071
Y7 0.016 1.031
Y8 0.038 0.539 0.993
Y9 0.062 0.513 0.498 0.952
Y10 -0.104 -0.003 -0.035 -0.024 1.142
Y11 -0.058 -0.003 -0.017 -0.029 0.612
Y12 -0.072 -0.001 -0.038 0.018 0.494
Covariances
Y11 Y12
________ ________
Y11 1.097
Y12 0.558 1.037
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.514 1.000
Y3 0.403 0.506 1.000
Y4 -0.019 0.008 0.017 1.000
Y5 0.000 -0.030 -0.104 0.487 1.000
Y6 -0.017 -0.005 -0.021 0.442 0.510
Y7 0.065 -0.001 -0.059 0.022 0.009
Y8 0.045 -0.046 -0.046 0.028 -0.002
Y9 0.065 0.052 -0.013 -0.011 -0.018
Y10 -0.053 -0.004 -0.027 -0.051 -0.028
Y11 -0.003 0.028 -0.021 -0.063 -0.060
Y12 -0.008 0.058 0.010 -0.105 -0.079
Correlations
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.000
Y7 0.016 1.000
Y8 0.037 0.533 1.000
Y9 0.061 0.517 0.512 1.000
Y10 -0.094 -0.003 -0.033 -0.023 1.000
Y11 -0.053 -0.003 -0.016 -0.029 0.547
Y12 -0.069 -0.001 -0.037 0.018 0.454
Correlations
Y11 Y12
________ ________
Y11 1.000
Y12 0.523 1.000
MODEL FIT INFORMATION
Number of Free Parameters 42
Loglikelihood
H0 Value
Mean -7878.959
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -7878.959 -7878.959
0.980 0.000 -7878.959 -7878.959
0.950 0.000 -7878.959 -7878.959
0.900 0.000 -7878.959 -7878.959
0.800 0.000 -7878.959 -7878.959
0.700 0.000 -7878.959 -7878.959
0.500 0.000 -7878.959 -7878.959
0.300 0.000 -7878.959 -7878.959
0.200 0.000 -7878.959 -7878.959
0.100 0.000 -7878.959 -7878.959
0.050 0.000 -7878.959 -7878.959
0.020 0.000 -7878.959 -7878.959
0.010 0.000 -7878.959 -7878.959
H1 Value
Mean -7856.478
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -7856.478 -7856.478
0.980 0.000 -7856.478 -7856.478
0.950 0.000 -7856.478 -7856.478
0.900 0.000 -7856.478 -7856.478
0.800 0.000 -7856.478 -7856.478
0.700 0.000 -7856.478 -7856.478
0.500 0.000 -7856.478 -7856.478
0.300 0.000 -7856.478 -7856.478
0.200 0.000 -7856.478 -7856.478
0.100 0.000 -7856.478 -7856.478
0.050 0.000 -7856.478 -7856.478
0.020 0.000 -7856.478 -7856.478
0.010 0.000 -7856.478 -7856.478
Information Criteria
Akaike (AIC)
Mean 15841.919
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 15841.919 15841.919
0.980 0.000 15841.919 15841.919
0.950 0.000 15841.919 15841.919
0.900 0.000 15841.919 15841.919
0.800 0.000 15841.919 15841.919
0.700 0.000 15841.919 15841.919
0.500 0.000 15841.919 15841.919
0.300 0.000 15841.919 15841.919
0.200 0.000 15841.919 15841.919
0.100 0.000 15841.919 15841.919
0.050 0.000 15841.919 15841.919
0.020 0.000 15841.919 15841.919
0.010 0.000 15841.919 15841.919
Bayesian (BIC)
Mean 16018.932
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 16018.932 16018.932
0.980 0.000 16018.932 16018.932
0.950 0.000 16018.932 16018.932
0.900 0.000 16018.932 16018.932
0.800 0.000 16018.932 16018.932
0.700 0.000 16018.932 16018.932
0.500 0.000 16018.932 16018.932
0.300 0.000 16018.932 16018.932
0.200 0.000 16018.932 16018.932
0.100 0.000 16018.932 16018.932
0.050 0.000 16018.932 16018.932
0.020 0.000 16018.932 16018.932
0.010 0.000 16018.932 16018.932
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 15885.622
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 15885.622 15885.622
0.980 0.000 15885.622 15885.622
0.950 0.000 15885.622 15885.622
0.900 0.000 15885.622 15885.622
0.800 0.000 15885.622 15885.622
0.700 0.000 15885.622 15885.622
0.500 0.000 15885.622 15885.622
0.300 0.000 15885.622 15885.622
0.200 0.000 15885.622 15885.622
0.100 0.000 15885.622 15885.622
0.050 0.000 15885.622 15885.622
0.020 0.000 15885.622 15885.622
0.010 0.000 15885.622 15885.622
Chi-Square Test of Model Fit
Degrees of freedom 48
Mean 44.963
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 28.177 44.963
0.980 1.000 30.080 44.963
0.950 1.000 33.098 44.963
0.900 1.000 35.949 44.963
0.800 1.000 39.621 44.963
0.700 1.000 42.420 44.963
0.500 0.000 47.335 44.963
0.300 0.000 52.616 44.963
0.200 0.000 55.993 44.963
0.100 0.000 60.907 44.963
0.050 0.000 65.171 44.963
0.020 0.000 70.197 44.963
0.010 0.000 73.683 44.963
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 0.024
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 0.700 0.6268 0.0000 0.0477 0.0054 1.000 1.000
Y2 0.700 0.8089 0.0000 0.0513 0.0119 0.000 1.000
Y3 0.700 0.6175 0.0000 0.0476 0.0068 1.000 1.000
F2 BY
Y4 0.700 0.6568 0.0000 0.0487 0.0019 1.000 1.000
Y5 0.700 0.7438 0.0000 0.0490 0.0019 1.000 1.000
Y6 0.700 0.7054 0.0000 0.0502 0.0000 1.000 1.000
F3 BY
Y7 0.700 0.7448 0.0000 0.0470 0.0020 1.000 1.000
Y8 0.700 0.7241 0.0000 0.0462 0.0006 1.000 1.000
Y9 0.700 0.6882 0.0000 0.0451 0.0001 1.000 1.000
F4 BY
Y10 0.700 0.7367 0.0000 0.0500 0.0013 1.000 1.000
Y11 0.700 0.8292 0.0000 0.0496 0.0167 0.000 1.000
Y12 0.700 0.6738 0.0000 0.0476 0.0007 1.000 1.000
F2 WITH
F1 0.000 -0.0382 0.0000 0.0597 0.0015 1.000 0.000
F3 WITH
F1 0.000 0.0091 0.0000 0.0589 0.0001 1.000 0.000
F2 0.000 0.0277 0.0000 0.0594 0.0008 1.000 0.000
F4 WITH
F1 0.000 0.0105 0.0000 0.0587 0.0001 1.000 0.000
F2 0.000 -0.1247 0.0000 0.0587 0.0155 0.000 1.000
F3 0.000 -0.0274 0.0000 0.0582 0.0008 1.000 0.000
Intercepts
Y1 0.000 0.0080 0.0000 0.0438 0.0001 1.000 0.000
Y2 0.000 0.0334 0.0000 0.0451 0.0011 1.000 0.000
Y3 0.000 0.0032 0.0000 0.0438 0.0000 1.000 0.000
Y4 0.000 0.0735 0.0000 0.0452 0.0054 1.000 0.000
Y5 0.000 0.0633 0.0000 0.0445 0.0040 1.000 0.000
Y6 0.000 0.0622 0.0000 0.0463 0.0039 1.000 0.000
Y7 0.000 -0.0035 0.0000 0.0454 0.0000 1.000 0.000
Y8 0.000 0.0090 0.0000 0.0446 0.0001 1.000 0.000
Y9 0.000 0.0208 0.0000 0.0436 0.0004 1.000 0.000
Y10 0.000 -0.0369 0.0000 0.0478 0.0014 1.000 0.000
Y11 0.000 0.0016 0.0000 0.0468 0.0000 1.000 0.000
Y12 0.000 -0.0024 0.0000 0.0455 0.0000 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
F3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y1 0.510 0.5656 0.0000 0.0496 0.0031 1.000 1.000
Y2 0.510 0.3611 0.0000 0.0618 0.0222 0.000 1.000
Y3 0.510 0.5773 0.0000 0.0495 0.0045 1.000 1.000
Y4 0.510 0.5884 0.0000 0.0519 0.0061 1.000 1.000
Y5 0.510 0.4362 0.0000 0.0539 0.0054 1.000 1.000
Y6 0.510 0.5736 0.0000 0.0553 0.0040 1.000 1.000
Y7 0.510 0.4762 0.0000 0.0497 0.0011 1.000 1.000
Y8 0.510 0.4691 0.0000 0.0478 0.0017 1.000 1.000
Y9 0.510 0.4783 0.0000 0.0454 0.0010 1.000 1.000
Y10 0.510 0.5997 0.0000 0.0555 0.0080 1.000 1.000
Y11 0.510 0.4096 0.0000 0.0574 0.0101 1.000 1.000
Y12 0.510 0.5832 0.0000 0.0503 0.0054 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.117E+00
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
6 7 8 9 10
NU
Y11 Y12
________ ________
11 12
LAMBDA
F1 F2 F3 F4
________ ________ ________ ________
Y1 13 0 0 0
Y2 14 0 0 0
Y3 15 0 0 0
Y4 0 16 0 0
Y5 0 17 0 0
Y6 0 18 0 0
Y7 0 0 19 0
Y8 0 0 20 0
Y9 0 0 21 0
Y10 0 0 0 22
Y11 0 0 0 23
Y12 0 0 0 24
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 25
Y2 0 26
Y3 0 0 27
Y4 0 0 0 28
Y5 0 0 0 0 29
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
Y11 0 0 0 0 0
Y12 0 0 0 0 0
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 30
Y7 0 31
Y8 0 0 32
Y9 0 0 0 33
Y10 0 0 0 0 34
Y11 0 0 0 0 0
Y12 0 0 0 0 0
THETA
Y11 Y12
________ ________
Y11 35
Y12 0 36
ALPHA
F1 F2 F3 F4
________ ________ ________ ________
0 0 0 0
BETA
F1 F2 F3 F4
________ ________ ________ ________
F1 0 0 0 0
F2 0 0 0 0
F3 0 0 0 0
F4 0 0 0 0
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 0
F2 37 0
F3 38 39 0
F4 40 41 42 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
NU
Y11 Y12
________ ________
0.000 0.000
LAMBDA
F1 F2 F3 F4
________ ________ ________ ________
Y1 0.700 0.000 0.000 0.000
Y2 0.700 0.000 0.000 0.000
Y3 0.700 0.000 0.000 0.000
Y4 0.000 0.700 0.000 0.000
Y5 0.000 0.700 0.000 0.000
Y6 0.000 0.700 0.000 0.000
Y7 0.000 0.000 0.700 0.000
Y8 0.000 0.000 0.700 0.000
Y9 0.000 0.000 0.700 0.000
Y10 0.000 0.000 0.000 0.700
Y11 0.000 0.000 0.000 0.700
Y12 0.000 0.000 0.000 0.700
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.510
Y2 0.000 0.510
Y3 0.000 0.000 0.510
Y4 0.000 0.000 0.000 0.510
Y5 0.000 0.000 0.000 0.000 0.510
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
Y11 0.000 0.000 0.000 0.000 0.000
Y12 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.510
Y7 0.000 0.510
Y8 0.000 0.000 0.510
Y9 0.000 0.000 0.000 0.510
Y10 0.000 0.000 0.000 0.000 0.510
Y11 0.000 0.000 0.000 0.000 0.000
Y12 0.000 0.000 0.000 0.000 0.000
THETA
Y11 Y12
________ ________
Y11 0.510
Y12 0.000 0.510
ALPHA
F1 F2 F3 F4
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
F1 F2 F3 F4
________ ________ ________ ________
F1 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000
F3 0.000 0.000 0.000 0.000
F4 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 1.000
F4 0.000 0.000 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
NU
Y11 Y12
________ ________
0.000 0.000
LAMBDA
F1 F2 F3 F4
________ ________ ________ ________
Y1 0.700 0.000 0.000 0.000
Y2 0.700 0.000 0.000 0.000
Y3 0.700 0.000 0.000 0.000
Y4 0.000 0.700 0.000 0.000
Y5 0.000 0.700 0.000 0.000
Y6 0.000 0.700 0.000 0.000
Y7 0.000 0.000 0.700 0.000
Y8 0.000 0.000 0.700 0.000
Y9 0.000 0.000 0.700 0.000
Y10 0.000 0.000 0.000 0.700
Y11 0.000 0.000 0.000 0.700
Y12 0.000 0.000 0.000 0.700
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.510
Y2 0.000 0.510
Y3 0.000 0.000 0.510
Y4 0.000 0.000 0.000 0.510
Y5 0.000 0.000 0.000 0.000 0.510
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
Y11 0.000 0.000 0.000 0.000 0.000
Y12 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.510
Y7 0.000 0.510
Y8 0.000 0.000 0.510
Y9 0.000 0.000 0.000 0.510
Y10 0.000 0.000 0.000 0.000 0.510
Y11 0.000 0.000 0.000 0.000 0.000
Y12 0.000 0.000 0.000 0.000 0.000
THETA
Y11 Y12
________ ________
Y11 0.510
Y12 0.000 0.510
ALPHA
F1 F2 F3 F4
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
F1 F2 F3 F4
________ ________ ________ ________
F1 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000
F3 0.000 0.000 0.000 0.000
F4 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 1.000
F4 0.000 0.000 0.000 1.000
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y9
Y10
Y11
Y12
Save file
ex4.1a.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:22:38
Ending Time: 22:22:38
Elapsed Time: 00:00:00
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