```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:28 AM

INPUT INSTRUCTIONS

title:	this is an example of a SEM with continuous factor indicators

montecarlo:
names = y1-y12;
nobs = 500;
nreps = 1;
save = ex5.12.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;

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

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000            0.012          0.012
0.980       0.000            0.012          0.012
0.950       0.000            0.012          0.012
0.900       0.000            0.012          0.012
0.800       0.000            0.012          0.012
0.700       0.000            0.012          0.012
0.500       0.000            0.012          0.012
0.300       0.000            0.012          0.012
0.200       0.000            0.012          0.012
0.100       0.000            0.012          0.012
0.050       0.000            0.012          0.012
0.020       0.000            0.012          0.012
0.010       0.000            0.012          0.012

SRMR (Standardized Root Mean Square Residual)

Mean                                 0.027
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000            0.027          0.027
0.980       0.000            0.027          0.027
0.950       0.000            0.027          0.027
0.900       0.000            0.027          0.027
0.800       0.000            0.027          0.027
0.700       0.000            0.027          0.027
0.500       0.000            0.027          0.027
0.300       0.000            0.027          0.027
0.200       0.000            0.027          0.027
0.100       0.000            0.027          0.027
0.050       0.000            0.027          0.027
0.020       0.000            0.027          0.027
0.010       0.000            0.027          0.027

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
ex5.12.dat

Save file format           Free
Save file record length    10000

Beginning Time:  03:28:07
Ending Time:  03:28:07
Elapsed Time:  00:00:00

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