```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;

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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