Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
INPUT INSTRUCTIONS
title: this is an example of a SEM with
continuous factor indicators
montecarlo:
names = y1-y12;
nobs = 500;
nreps = 1;
save = ex5.11.dat;
model montecarlo:
f1 by y1@1 y2-y3*1;
f2 by y4@1 y5-y6*.8;
f3 by y7@1 y8-y9*.9;
f4 by y10@1 y11-y12*.7;
y1-y12*1;
f1-f2*1;
f3-f4*.5;
f3 on f1*.5 f2*.7;
f4 on f3*.6;
model:
f1 by y1@1 y2-y3*1;
f2 by y4@1 y5-y6*.8;
f3 by y7@1 y8-y9*.9;
f4 by y10@1 y11-y12*.7;
y1-y12*1;
f1-f2*1;
f3-f4*.5;
f3 on f1*.5 f2*.7;
f4 on f3*.6;
output:
tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a SEM 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
________ ________ ________ ________ ________
0.011 0.047 0.005 0.104 0.078
Means
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.074 0.051 0.063 0.078 -0.008
Means
Y11 Y12
________ ________
0.039 0.031
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.917
Y2 1.033 2.031
Y3 0.794 1.017 1.914
Y4 -0.038 0.015 0.033 2.039
Y5 0.002 -0.056 -0.190 0.797 1.622
Y6 -0.031 -0.005 -0.024 0.745 0.707
Y7 0.574 0.502 0.330 0.742 0.550
Y8 0.477 0.368 0.323 0.678 0.476
Y9 0.511 0.559 0.387 0.601 0.453
Y10 0.214 0.296 0.184 0.331 0.275
Y11 0.236 0.267 0.138 0.204 0.138
Y12 0.221 0.313 0.198 0.139 0.122
Covariances
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.761
Y7 0.599 2.312
Y8 0.579 1.206 1.977
Y9 0.624 1.178 1.034 1.954
Y10 0.201 0.693 0.555 0.574 2.061
Y11 0.213 0.502 0.430 0.403 0.737
Y12 0.193 0.497 0.385 0.487 0.534
Covariances
Y11 Y12
________ ________
Y11 1.501
Y12 0.494 1.470
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.524 1.000
Y3 0.414 0.516 1.000
Y4 -0.019 0.008 0.017 1.000
Y5 0.001 -0.031 -0.108 0.438 1.000
Y6 -0.017 -0.003 -0.013 0.393 0.419
Y7 0.273 0.232 0.157 0.342 0.284
Y8 0.245 0.183 0.166 0.338 0.266
Y9 0.264 0.281 0.200 0.301 0.254
Y10 0.108 0.145 0.093 0.162 0.150
Y11 0.139 0.153 0.082 0.116 0.088
Y12 0.132 0.181 0.118 0.080 0.079
Correlations
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.000
Y7 0.297 1.000
Y8 0.311 0.564 1.000
Y9 0.337 0.554 0.526 1.000
Y10 0.105 0.317 0.275 0.286 1.000
Y11 0.131 0.269 0.250 0.235 0.419
Y12 0.120 0.269 0.226 0.287 0.307
Correlations
Y11 Y12
________ ________
Y11 1.000
Y12 0.333 1.000
MODEL FIT INFORMATION
Number of Free Parameters 40
Loglikelihood
H0 Value
Mean -9646.960
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -9646.960 -9646.960
0.980 0.000 -9646.960 -9646.960
0.950 0.000 -9646.960 -9646.960
0.900 0.000 -9646.960 -9646.960
0.800 0.000 -9646.960 -9646.960
0.700 0.000 -9646.960 -9646.960
0.500 0.000 -9646.960 -9646.960
0.300 0.000 -9646.960 -9646.960
0.200 0.000 -9646.960 -9646.960
0.100 0.000 -9646.960 -9646.960
0.050 0.000 -9646.960 -9646.960
0.020 0.000 -9646.960 -9646.960
0.010 0.000 -9646.960 -9646.960
H1 Value
Mean -9620.108
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -9620.108 -9620.108
0.980 0.000 -9620.108 -9620.108
0.950 0.000 -9620.108 -9620.108
0.900 0.000 -9620.108 -9620.108
0.800 0.000 -9620.108 -9620.108
0.700 0.000 -9620.108 -9620.108
0.500 0.000 -9620.108 -9620.108
0.300 0.000 -9620.108 -9620.108
0.200 0.000 -9620.108 -9620.108
0.100 0.000 -9620.108 -9620.108
0.050 0.000 -9620.108 -9620.108
0.020 0.000 -9620.108 -9620.108
0.010 0.000 -9620.108 -9620.108
Information Criteria
Akaike (AIC)
Mean 19373.920
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 19373.920 19373.920
0.980 0.000 19373.920 19373.920
0.950 0.000 19373.920 19373.920
0.900 0.000 19373.920 19373.920
0.800 0.000 19373.920 19373.920
0.700 0.000 19373.920 19373.920
0.500 0.000 19373.920 19373.920
0.300 0.000 19373.920 19373.920
0.200 0.000 19373.920 19373.920
0.100 0.000 19373.920 19373.920
0.050 0.000 19373.920 19373.920
0.020 0.000 19373.920 19373.920
0.010 0.000 19373.920 19373.920
Bayesian (BIC)
Mean 19542.505
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 19542.505 19542.505
0.980 0.000 19542.505 19542.505
0.950 0.000 19542.505 19542.505
0.900 0.000 19542.505 19542.505
0.800 0.000 19542.505 19542.505
0.700 0.000 19542.505 19542.505
0.500 0.000 19542.505 19542.505
0.300 0.000 19542.505 19542.505
0.200 0.000 19542.505 19542.505
0.100 0.000 19542.505 19542.505
0.050 0.000 19542.505 19542.505
0.020 0.000 19542.505 19542.505
0.010 0.000 19542.505 19542.505
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 19415.542
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 19415.542 19415.542
0.980 0.000 19415.542 19415.542
0.950 0.000 19415.542 19415.542
0.900 0.000 19415.542 19415.542
0.800 0.000 19415.542 19415.542
0.700 0.000 19415.542 19415.542
0.500 0.000 19415.542 19415.542
0.300 0.000 19415.542 19415.542
0.200 0.000 19415.542 19415.542
0.100 0.000 19415.542 19415.542
0.050 0.000 19415.542 19415.542
0.020 0.000 19415.542 19415.542
0.010 0.000 19415.542 19415.542
Chi-Square Test of Model Fit
Degrees of freedom 50
Mean 53.704
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 29.707 53.704
0.980 1.000 31.664 53.704
0.950 1.000 34.764 53.704
0.900 1.000 37.689 53.704
0.800 1.000 41.449 53.704
0.700 1.000 44.313 53.704
0.500 1.000 49.335 53.704
0.300 0.000 54.723 53.704
0.200 0.000 58.164 53.704
0.100 0.000 63.167 53.704
0.050 0.000 67.505 53.704
0.020 0.000 72.613 53.704
0.010 0.000 76.154 53.704
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.012
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 0.000
CFI/TLI
CFI
Mean 0.997
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 0.997
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 0.027
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 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.1825 0.0000 0.1039 0.0333 1.000 1.000
Y3 1.000 0.9376 0.0000 0.0867 0.0039 1.000 1.000
F2 BY
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 0.800 0.8695 0.0000 0.0852 0.0048 1.000 1.000
Y6 0.800 0.8906 0.0000 0.0915 0.0082 1.000 1.000
F3 BY
Y7 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y8 0.900 0.8717 0.0000 0.0593 0.0008 1.000 1.000
Y9 0.900 0.8825 0.0000 0.0604 0.0003 1.000 1.000
F4 BY
Y10 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y11 0.700 0.8259 0.0000 0.0937 0.0159 1.000 1.000
Y12 0.700 0.6820 0.0000 0.0886 0.0003 1.000 1.000
F3 ON
F1 0.500 0.5629 0.0000 0.0701 0.0040 1.000 1.000
F2 0.700 0.7901 0.0000 0.0856 0.0081 1.000 1.000
F4 ON
F3 0.600 0.4730 0.0000 0.0570 0.0161 0.000 1.000
F2 WITH
F1 0.000 -0.0301 0.0000 0.0553 0.0009 1.000 0.000
Intercepts
Y1 0.000 0.0113 0.0000 0.0619 0.0001 1.000 0.000
Y2 0.000 0.0470 0.0000 0.0637 0.0022 1.000 0.000
Y3 0.000 0.0048 0.0000 0.0619 0.0000 1.000 0.000
Y4 0.000 0.1039 0.0000 0.0639 0.0108 1.000 0.000
Y5 0.000 0.0775 0.0000 0.0570 0.0060 1.000 0.000
Y6 0.000 0.0736 0.0000 0.0593 0.0054 1.000 0.000
Y7 0.000 0.0513 0.0000 0.0680 0.0026 1.000 0.000
Y8 0.000 0.0628 0.0000 0.0629 0.0039 1.000 0.000
Y9 0.000 0.0780 0.0000 0.0625 0.0061 1.000 0.000
Y10 0.000 -0.0082 0.0000 0.0642 0.0001 1.000 0.000
Y11 0.000 0.0392 0.0000 0.0548 0.0015 1.000 0.000
Y12 0.000 0.0305 0.0000 0.0542 0.0009 1.000 0.000
Variances
F1 1.000 0.8838 0.0000 0.1222 0.0135 1.000 1.000
F2 1.000 0.8883 0.0000 0.1300 0.0125 1.000 1.000
Residual Variances
Y1 1.000 1.0331 0.0000 0.0936 0.0011 1.000 1.000
Y2 1.000 0.7955 0.0000 0.1012 0.0418 0.000 1.000
Y3 1.000 1.1369 0.0000 0.0918 0.0187 1.000 1.000
Y4 1.000 1.1512 0.0000 0.1043 0.0228 1.000 1.000
Y5 1.000 0.9502 0.0000 0.0829 0.0025 1.000 1.000
Y6 1.000 1.0563 0.0000 0.0905 0.0032 1.000 1.000
Y7 1.000 0.9542 0.0000 0.0887 0.0021 1.000 1.000
Y8 1.000 0.9448 0.0000 0.0789 0.0031 1.000 1.000
Y9 1.000 0.8962 0.0000 0.0774 0.0108 1.000 1.000
Y10 1.000 1.2025 0.0000 0.1179 0.0410 1.000 1.000
Y11 1.000 0.9155 0.0000 0.0850 0.0071 1.000 1.000
Y12 1.000 1.0708 0.0000 0.0834 0.0050 1.000 1.000
F3 0.500 0.5501 0.0000 0.0923 0.0025 1.000 1.000
F4 0.500 0.5546 0.0000 0.1023 0.0030 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.448E-01
(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 0 0 0 0
Y2 13 0 0 0
Y3 14 0 0 0
Y4 0 0 0 0
Y5 0 15 0 0
Y6 0 16 0 0
Y7 0 0 0 0
Y8 0 0 17 0
Y9 0 0 18 0
Y10 0 0 0 0
Y11 0 0 0 19
Y12 0 0 0 20
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 21
Y2 0 22
Y3 0 0 23
Y4 0 0 0 24
Y5 0 0 0 0 25
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 26
Y7 0 27
Y8 0 0 28
Y9 0 0 0 29
Y10 0 0 0 0 30
Y11 0 0 0 0 0
Y12 0 0 0 0 0
THETA
Y11 Y12
________ ________
Y11 31
Y12 0 32
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 33 34 0 0
F4 0 0 35 0
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 36
F2 37 38
F3 0 0 39
F4 0 0 0 40
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 1.000 0.000 0.000 0.000
Y2 1.281 0.000 0.000 0.000
Y3 0.984 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000
Y5 0.000 0.800 0.000 0.000
Y6 0.000 0.800 0.000 0.000
Y7 0.000 0.000 1.000 0.000
Y8 0.000 0.000 0.900 0.000
Y9 0.000 0.000 0.900 0.000
Y10 0.000 0.000 0.000 1.000
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 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
Y5 0.000 0.000 0.000 0.000 1.000
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 1.000
Y7 0.000 1.000
Y8 0.000 0.000 1.000
Y9 0.000 0.000 0.000 1.000
Y10 0.000 0.000 0.000 0.000 1.000
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 1.000
Y12 0.000 1.000
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 0.500 0.700 0.000 0.000
F4 0.000 0.000 0.600 0.000
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 0.500
F4 0.000 0.000 0.000 0.500
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 1.000 0.000 0.000 0.000
Y2 1.000 0.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000
Y5 0.000 0.800 0.000 0.000
Y6 0.000 0.800 0.000 0.000
Y7 0.000 0.000 1.000 0.000
Y8 0.000 0.000 0.900 0.000
Y9 0.000 0.000 0.900 0.000
Y10 0.000 0.000 0.000 1.000
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 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
Y5 0.000 0.000 0.000 0.000 1.000
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 1.000
Y7 0.000 1.000
Y8 0.000 0.000 1.000
Y9 0.000 0.000 0.000 1.000
Y10 0.000 0.000 0.000 0.000 1.000
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 1.000
Y12 0.000 1.000
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 0.500 0.700 0.000 0.000
F4 0.000 0.000 0.600 0.000
PSI
F1 F2 F3 F4
________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 0.500
F4 0.000 0.000 0.000 0.500
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
ex5.11.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:22:57
Ending Time: 22:22:57
Elapsed Time: 00:00:00
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