Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a second-order factor analysis
montecarlo:
names = y1-y12;
nobs = 500;
nreps = 1;
save = ex5.6.dat;
model population:
f1 by y1@1 y2-y3*.7;
f2 by y4@1 y5-y6*.7;
f3 by y7@1 y8-y9*.7;
f4 by y10@1 y11-y12*.7;
y1-y12*.3;
f5 by f1@1 f2-f4*1;
f1-f4*1;
f5*.5;
model:
f1 by y1@1 y2-y3*.7;
f2 by y4@1 y5-y6*.7;
f3 by y7@1 y8-y9*.7;
f4 by y10@1 y11-y12*.7;
y1-y12*.3;
f5 by f1@1 f2-f4*1;
f1-f4*1;
f5*.5;
INPUT READING TERMINATED NORMALLY
this is an example of a second-order factor analysis
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 5
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10 Y11 Y12
Continuous latent variables
F1 F2 F3 F4 F5
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 0.028 0.005 0.100 0.078
Means
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.076 0.024 0.025 0.034 -0.016
Means
Y11 Y12
________ ________
0.010 0.006
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.725
Y2 1.044 1.047
Y3 0.920 0.705 0.936
Y4 0.441 0.345 0.322 1.815
Y5 0.322 0.226 0.167 1.041 1.015
Y6 0.305 0.235 0.208 1.017 0.735
Y7 0.575 0.377 0.291 0.543 0.367
Y8 0.400 0.238 0.202 0.388 0.254
Y9 0.419 0.300 0.224 0.362 0.242
Y10 0.396 0.319 0.253 0.388 0.272
Y11 0.314 0.253 0.187 0.255 0.167
Y12 0.308 0.267 0.203 0.220 0.149
Covariances
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.047
Y7 0.376 1.889
Y8 0.280 1.137 1.080
Y9 0.290 1.117 0.785 1.049
Y10 0.211 0.478 0.306 0.317 1.913
Y11 0.157 0.338 0.222 0.218 1.152
Y12 0.140 0.335 0.207 0.243 1.036
Covariances
Y11 Y12
________ ________
Y11 1.119
Y12 0.770 1.018
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.777 1.000
Y3 0.724 0.712 1.000
Y4 0.249 0.250 0.247 1.000
Y5 0.244 0.219 0.171 0.767 1.000
Y6 0.227 0.224 0.210 0.738 0.713
Y7 0.319 0.268 0.219 0.293 0.265
Y8 0.293 0.224 0.201 0.277 0.242
Y9 0.311 0.286 0.226 0.262 0.235
Y10 0.218 0.226 0.189 0.208 0.195
Y11 0.226 0.234 0.183 0.179 0.157
Y12 0.233 0.259 0.208 0.162 0.147
Correlations
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.000
Y7 0.268 1.000
Y8 0.263 0.796 1.000
Y9 0.276 0.793 0.738 1.000
Y10 0.149 0.251 0.213 0.224 1.000
Y11 0.145 0.233 0.202 0.201 0.787
Y12 0.135 0.241 0.197 0.235 0.743
Correlations
Y11 Y12
________ ________
Y11 1.000
Y12 0.721 1.000
MODEL FIT INFORMATION
Number of Free Parameters 40
Loglikelihood
H0 Value
Mean -7211.373
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -7211.373 -7211.373
0.980 0.000 -7211.373 -7211.373
0.950 0.000 -7211.373 -7211.373
0.900 0.000 -7211.373 -7211.373
0.800 0.000 -7211.373 -7211.373
0.700 0.000 -7211.373 -7211.373
0.500 0.000 -7211.373 -7211.373
0.300 0.000 -7211.373 -7211.373
0.200 0.000 -7211.373 -7211.373
0.100 0.000 -7211.373 -7211.373
0.050 0.000 -7211.373 -7211.373
0.020 0.000 -7211.373 -7211.373
0.010 0.000 -7211.373 -7211.373
H1 Value
Mean -7188.001
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -7188.001 -7188.001
0.980 0.000 -7188.001 -7188.001
0.950 0.000 -7188.001 -7188.001
0.900 0.000 -7188.001 -7188.001
0.800 0.000 -7188.001 -7188.001
0.700 0.000 -7188.001 -7188.001
0.500 0.000 -7188.001 -7188.001
0.300 0.000 -7188.001 -7188.001
0.200 0.000 -7188.001 -7188.001
0.100 0.000 -7188.001 -7188.001
0.050 0.000 -7188.001 -7188.001
0.020 0.000 -7188.001 -7188.001
0.010 0.000 -7188.001 -7188.001
Information Criteria
Akaike (AIC)
Mean 14502.746
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 14502.746 14502.746
0.980 0.000 14502.746 14502.746
0.950 0.000 14502.746 14502.746
0.900 0.000 14502.746 14502.746
0.800 0.000 14502.746 14502.746
0.700 0.000 14502.746 14502.746
0.500 0.000 14502.746 14502.746
0.300 0.000 14502.746 14502.746
0.200 0.000 14502.746 14502.746
0.100 0.000 14502.746 14502.746
0.050 0.000 14502.746 14502.746
0.020 0.000 14502.746 14502.746
0.010 0.000 14502.746 14502.746
Bayesian (BIC)
Mean 14671.330
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 14671.330 14671.330
0.980 0.000 14671.330 14671.330
0.950 0.000 14671.330 14671.330
0.900 0.000 14671.330 14671.330
0.800 0.000 14671.330 14671.330
0.700 0.000 14671.330 14671.330
0.500 0.000 14671.330 14671.330
0.300 0.000 14671.330 14671.330
0.200 0.000 14671.330 14671.330
0.100 0.000 14671.330 14671.330
0.050 0.000 14671.330 14671.330
0.020 0.000 14671.330 14671.330
0.010 0.000 14671.330 14671.330
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 14544.368
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 14544.368 14544.368
0.980 0.000 14544.368 14544.368
0.950 0.000 14544.368 14544.368
0.900 0.000 14544.368 14544.368
0.800 0.000 14544.368 14544.368
0.700 0.000 14544.368 14544.368
0.500 0.000 14544.368 14544.368
0.300 0.000 14544.368 14544.368
0.200 0.000 14544.368 14544.368
0.100 0.000 14544.368 14544.368
0.050 0.000 14544.368 14544.368
0.020 0.000 14544.368 14544.368
0.010 0.000 14544.368 14544.368
Chi-Square Test of Model Fit
Degrees of freedom 50
Mean 46.743
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 29.707 46.743
0.980 1.000 31.664 46.743
0.950 1.000 34.764 46.743
0.900 1.000 37.689 46.743
0.800 1.000 41.449 46.743
0.700 1.000 44.313 46.743
0.500 0.000 49.335 46.743
0.300 0.000 54.723 46.743
0.200 0.000 58.164 46.743
0.100 0.000 63.167 46.743
0.050 0.000 67.505 46.743
0.020 0.000 72.613 46.743
0.010 0.000 76.154 46.743
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 0.019
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
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 0.700 0.7603 0.0000 0.0313 0.0036 1.000 1.000
Y3 0.700 0.6686 0.0000 0.0300 0.0010 1.000 1.000
F2 BY
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 0.700 0.7180 0.0000 0.0299 0.0003 1.000 1.000
Y6 0.700 0.7034 0.0000 0.0308 0.0000 1.000 1.000
F3 BY
Y7 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y8 0.700 0.7022 0.0000 0.0261 0.0000 1.000 1.000
Y9 0.700 0.6913 0.0000 0.0258 0.0001 1.000 1.000
F4 BY
Y10 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y11 0.700 0.7416 0.0000 0.0293 0.0017 1.000 1.000
Y12 0.700 0.6693 0.0000 0.0285 0.0009 1.000 1.000
F5 BY
F1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 1.000 0.9443 0.0000 0.1476 0.0031 1.000 1.000
F3 1.000 1.1678 0.0000 0.1792 0.0282 1.000 1.000
F4 1.000 0.8537 0.0000 0.1390 0.0214 1.000 1.000
Intercepts
Y1 0.000 0.0107 0.0000 0.0587 0.0001 1.000 0.000
Y2 0.000 0.0282 0.0000 0.0458 0.0008 1.000 0.000
Y3 0.000 0.0047 0.0000 0.0433 0.0000 1.000 0.000
Y4 0.000 0.0995 0.0000 0.0603 0.0099 1.000 0.000
Y5 0.000 0.0779 0.0000 0.0451 0.0061 1.000 0.000
Y6 0.000 0.0765 0.0000 0.0458 0.0058 1.000 0.000
Y7 0.000 0.0240 0.0000 0.0615 0.0006 1.000 0.000
Y8 0.000 0.0253 0.0000 0.0465 0.0006 1.000 0.000
Y9 0.000 0.0340 0.0000 0.0458 0.0012 1.000 0.000
Y10 0.000 -0.0162 0.0000 0.0619 0.0003 1.000 0.000
Y11 0.000 0.0095 0.0000 0.0473 0.0001 1.000 0.000
Y12 0.000 0.0060 0.0000 0.0451 0.0000 1.000 0.000
Variances
F5 0.500 0.4642 0.0000 0.0997 0.0013 1.000 1.000
Residual Variances
Y1 0.300 0.3478 0.0000 0.0428 0.0023 1.000 1.000
Y2 0.300 0.2508 0.0000 0.0265 0.0024 1.000 1.000
Y3 0.300 0.3200 0.0000 0.0261 0.0004 1.000 1.000
Y4 0.300 0.3656 0.0000 0.0447 0.0043 1.000 1.000
Y5 0.300 0.2676 0.0000 0.0260 0.0010 1.000 1.000
Y6 0.300 0.3300 0.0000 0.0284 0.0009 1.000 1.000
Y7 0.300 0.2716 0.0000 0.0383 0.0008 1.000 1.000
Y8 0.300 0.2821 0.0000 0.0246 0.0003 1.000 1.000
Y9 0.300 0.2764 0.0000 0.0242 0.0006 1.000 1.000
Y10 0.300 0.3622 0.0000 0.0447 0.0039 1.000 1.000
Y11 0.300 0.2659 0.0000 0.0270 0.0012 1.000 1.000
Y12 0.300 0.3231 0.0000 0.0269 0.0005 1.000 1.000
F1 1.000 0.9133 0.0000 0.1031 0.0075 1.000 1.000
F2 1.000 1.0356 0.0000 0.1071 0.0013 1.000 1.000
F3 1.000 0.9843 0.0000 0.1195 0.0002 1.000 1.000
F4 1.000 1.2126 0.0000 0.1148 0.0452 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.558E-02
(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 F5
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 13 0 0 0 0
Y3 14 0 0 0 0
Y4 0 0 0 0 0
Y5 0 15 0 0 0
Y6 0 16 0 0 0
Y7 0 0 0 0 0
Y8 0 0 17 0 0
Y9 0 0 18 0 0
Y10 0 0 0 0 0
Y11 0 0 0 19 0
Y12 0 0 0 20 0
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 F5
________ ________ ________ ________ ________
0 0 0 0 0
BETA
F1 F2 F3 F4 F5
________ ________ ________ ________ ________
F1 0 0 0 0 0
F2 0 0 0 0 33
F3 0 0 0 0 34
F4 0 0 0 0 35
F5 0 0 0 0 0
PSI
F1 F2 F3 F4 F5
________ ________ ________ ________ ________
F1 36
F2 0 37
F3 0 0 38
F4 0 0 0 39
F5 0 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 F5
________ ________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000 0.000
Y2 0.700 0.000 0.000 0.000 0.000
Y3 0.700 0.000 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000 0.000
Y5 0.000 0.700 0.000 0.000 0.000
Y6 0.000 0.700 0.000 0.000 0.000
Y7 0.000 0.000 1.000 0.000 0.000
Y8 0.000 0.000 0.700 0.000 0.000
Y9 0.000 0.000 0.700 0.000 0.000
Y10 0.000 0.000 0.000 1.000 0.000
Y11 0.000 0.000 0.000 0.700 0.000
Y12 0.000 0.000 0.000 0.700 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.300
Y2 0.000 0.300
Y3 0.000 0.000 0.300
Y4 0.000 0.000 0.000 0.300
Y5 0.000 0.000 0.000 0.000 0.300
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 0.300
Y7 0.000 0.300
Y8 0.000 0.000 0.300
Y9 0.000 0.000 0.000 0.300
Y10 0.000 0.000 0.000 0.000 0.300
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 0.300
Y12 0.000 0.300
ALPHA
F1 F2 F3 F4 F5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
F1 F2 F3 F4 F5
________ ________ ________ ________ ________
F1 0.000 0.000 0.000 0.000 1.000
F2 0.000 0.000 0.000 0.000 1.000
F3 0.000 0.000 0.000 0.000 1.000
F4 0.000 0.000 0.000 0.000 1.000
F5 0.000 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 F4 F5
________ ________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 1.000
F4 0.000 0.000 0.000 1.000
F5 0.000 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 F5
________ ________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000 0.000
Y2 0.700 0.000 0.000 0.000 0.000
Y3 0.700 0.000 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000 0.000
Y5 0.000 0.700 0.000 0.000 0.000
Y6 0.000 0.700 0.000 0.000 0.000
Y7 0.000 0.000 1.000 0.000 0.000
Y8 0.000 0.000 0.700 0.000 0.000
Y9 0.000 0.000 0.700 0.000 0.000
Y10 0.000 0.000 0.000 1.000 0.000
Y11 0.000 0.000 0.000 0.700 0.000
Y12 0.000 0.000 0.000 0.700 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.300
Y2 0.000 0.300
Y3 0.000 0.000 0.300
Y4 0.000 0.000 0.000 0.300
Y5 0.000 0.000 0.000 0.000 0.300
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 0.300
Y7 0.000 0.300
Y8 0.000 0.000 0.300
Y9 0.000 0.000 0.000 0.300
Y10 0.000 0.000 0.000 0.000 0.300
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 0.300
Y12 0.000 0.300
ALPHA
F1 F2 F3 F4 F5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
F1 F2 F3 F4 F5
________ ________ ________ ________ ________
F1 0.000 0.000 0.000 0.000 1.000
F2 0.000 0.000 0.000 0.000 1.000
F3 0.000 0.000 0.000 0.000 1.000
F4 0.000 0.000 0.000 0.000 1.000
F5 0.000 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 F4 F5
________ ________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 1.000
F4 0.000 0.000 0.000 1.000
F5 0.000 0.000 0.000 0.000 0.500
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y9
Y10
Y11
Y12
Save file
ex5.6.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:11
Ending Time: 22:24:11
Elapsed Time: 00:00:00
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