```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:29 AM

INPUT INSTRUCTIONS

TITLE:	this is an example of a CFA with
covariates (MIMIC) with continuous factor indicators

montecarlo:
names = y1-y6 x1-x3;
nobs = 500;
nreps = 1;
save = ex5.8.dat;

model population:

[x1@0 x2@1 x3@2]; x1@3 x2@2 x3@1;

f1 by y1@1 y2-y3*1;
f2 by y4@1 y5-y6*1;
f1 on x1*.5 x2*.6 x3*.7;
f2 on x1*.7 x2*.6 x3*.5;

f1-f2*.7;
f1 with f2*.25;

y1-y6*.5;

model:

f1 by y1@1 y2-y3*1;
f2 by y4@1 y5-y6*1;
f1 on x1*.5 x2*.6 x3*.7;
f2 on x1*.7 x2*.6 x3*.5;

f1-f2*.7;
f1 with f2*.25;

y1-y6*.5;

output:
tech9;

this is an example of a CFA with
covariates (MIMIC) 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                                    6
Number of independent variables                                  3
Number of continuous latent variables                            2

Observed dependent variables

Continuous
Y1          Y2          Y3          Y4          Y5          Y6

Observed independent variables
X1          X2          X3

Continuous latent variables
F1          F2

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
________      ________      ________      ________      ________
2.066         2.088         2.088         1.663         1.623

Means
Y6            X1            X2            X3
________      ________      ________      ________
1.596        -0.061         1.033         2.090

Covariances
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1             3.227
Y2             2.790         3.388
Y3             2.752         2.847         3.295
Y4             2.385         2.441         2.434         3.595
Y5             2.206         2.305         2.296         2.990         3.290
Y6             2.248         2.344         2.374         2.953         2.905
X1             1.426         1.486         1.500         2.044         1.964
X2             1.367         1.411         1.356         1.380         1.364
X3             0.727         0.722         0.737         0.429         0.404

Covariances
Y6            X1            X2            X3
________      ________      ________      ________
Y6             3.434
X1             1.957         2.921
X2             1.465         0.176         2.082
X3             0.418        -0.151         0.125         1.042

Correlations
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1             1.000
Y2             0.844         1.000
Y3             0.844         0.852         1.000
Y4             0.700         0.699         0.707         1.000
Y5             0.677         0.690         0.697         0.869         1.000
Y6             0.675         0.687         0.706         0.841         0.864
X1             0.465         0.472         0.484         0.631         0.634
X2             0.527         0.531         0.518         0.504         0.521
X3             0.396         0.384         0.398         0.222         0.218

Correlations
Y6            X1            X2            X3
________      ________      ________      ________
Y6             1.000
X1             0.618         1.000
X2             0.548         0.071         1.000
X3             0.221        -0.087         0.085         1.000

MODEL FIT INFORMATION

Number of Free Parameters                       25

Loglikelihood

H0 Value

Mean                             -4000.617
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        -4000.617      -4000.617
0.980       0.000        -4000.617      -4000.617
0.950       0.000        -4000.617      -4000.617
0.900       0.000        -4000.617      -4000.617
0.800       0.000        -4000.617      -4000.617
0.700       0.000        -4000.617      -4000.617
0.500       0.000        -4000.617      -4000.617
0.300       0.000        -4000.617      -4000.617
0.200       0.000        -4000.617      -4000.617
0.100       0.000        -4000.617      -4000.617
0.050       0.000        -4000.617      -4000.617
0.020       0.000        -4000.617      -4000.617
0.010       0.000        -4000.617      -4000.617

H1 Value

Mean                             -3990.606
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        -3990.606      -3990.606
0.980       0.000        -3990.606      -3990.606
0.950       0.000        -3990.606      -3990.606
0.900       0.000        -3990.606      -3990.606
0.800       0.000        -3990.606      -3990.606
0.700       0.000        -3990.606      -3990.606
0.500       0.000        -3990.606      -3990.606
0.300       0.000        -3990.606      -3990.606
0.200       0.000        -3990.606      -3990.606
0.100       0.000        -3990.606      -3990.606
0.050       0.000        -3990.606      -3990.606
0.020       0.000        -3990.606      -3990.606
0.010       0.000        -3990.606      -3990.606

Information Criteria

Akaike (AIC)

Mean                              8051.235
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         8051.235       8051.235
0.980       0.000         8051.235       8051.235
0.950       0.000         8051.235       8051.235
0.900       0.000         8051.235       8051.235
0.800       0.000         8051.235       8051.235
0.700       0.000         8051.235       8051.235
0.500       0.000         8051.235       8051.235
0.300       0.000         8051.235       8051.235
0.200       0.000         8051.235       8051.235
0.100       0.000         8051.235       8051.235
0.050       0.000         8051.235       8051.235
0.020       0.000         8051.235       8051.235
0.010       0.000         8051.235       8051.235

Bayesian (BIC)

Mean                              8156.600
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         8156.600       8156.600
0.980       0.000         8156.600       8156.600
0.950       0.000         8156.600       8156.600
0.900       0.000         8156.600       8156.600
0.800       0.000         8156.600       8156.600
0.700       0.000         8156.600       8156.600
0.500       0.000         8156.600       8156.600
0.300       0.000         8156.600       8156.600
0.200       0.000         8156.600       8156.600
0.100       0.000         8156.600       8156.600
0.050       0.000         8156.600       8156.600
0.020       0.000         8156.600       8156.600
0.010       0.000         8156.600       8156.600

Sample-Size Adjusted BIC (n* = (n + 2) / 24)

Mean                              8077.248
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         8077.248       8077.248
0.980       0.000         8077.248       8077.248
0.950       0.000         8077.248       8077.248
0.900       0.000         8077.248       8077.248
0.800       0.000         8077.248       8077.248
0.700       0.000         8077.248       8077.248
0.500       0.000         8077.248       8077.248
0.300       0.000         8077.248       8077.248
0.200       0.000         8077.248       8077.248
0.100       0.000         8077.248       8077.248
0.050       0.000         8077.248       8077.248
0.020       0.000         8077.248       8077.248
0.010       0.000         8077.248       8077.248

Chi-Square Test of Model Fit

Degrees of freedom                      20

Mean                                20.023
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000            8.260         20.023
0.980       1.000            9.237         20.023
0.950       1.000           10.851         20.023
0.900       1.000           12.443         20.023
0.800       1.000           14.578         20.023
0.700       1.000           16.266         20.023
0.500       1.000           19.337         20.023
0.300       0.000           22.775         20.023
0.200       0.000           25.038         20.023
0.100       0.000           28.412         20.023
0.050       0.000           31.410         20.023
0.020       0.000           35.020         20.023
0.010       0.000           37.566         20.023

RMSEA (Root Mean Square Error Of Approximation)

Mean                                 0.002
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000            0.002          0.002
0.980       0.000            0.002          0.002
0.950       0.000            0.002          0.002
0.900       0.000            0.002          0.002
0.800       0.000            0.002          0.002
0.700       0.000            0.002          0.002
0.500       0.000            0.002          0.002
0.300       0.000            0.002          0.002
0.200       0.000            0.002          0.002
0.100       0.000            0.002          0.002
0.050       0.000            0.002          0.002
0.020       0.000            0.002          0.002
0.010       0.000            0.002          0.002

SRMR (Standardized Root Mean Square Residual)

Mean                                 0.008
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000            0.008          0.008
0.980       0.000            0.008          0.008
0.950       0.000            0.008          0.008
0.900       0.000            0.008          0.008
0.800       0.000            0.008          0.008
0.700       0.000            0.008          0.008
0.500       0.000            0.008          0.008
0.300       0.000            0.008          0.008
0.200       0.000            0.008          0.008
0.100       0.000            0.008          0.008
0.050       0.000            0.008          0.008
0.020       0.000            0.008          0.008
0.010       0.000            0.008          0.008

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     1.0324     0.0000     0.0297     0.0010 1.000 1.000
Y3                  1.000     1.0220     0.0000     0.0292     0.0005 1.000 1.000

F2       BY
Y4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y5                  1.000     0.9730     0.0000     0.0255     0.0007 1.000 1.000
Y6                  1.000     0.9765     0.0000     0.0273     0.0006 1.000 1.000

F1       ON
X1                  0.500     0.4966     0.0000     0.0262     0.0000 1.000 1.000
X2                  0.600     0.5662     0.0000     0.0310     0.0011 1.000 1.000
X3                  0.700     0.6905     0.0000     0.0432     0.0001 1.000 1.000

F2       ON
X1                  0.700     0.6784     0.0000     0.0262     0.0005 1.000 1.000
X2                  0.600     0.6011     0.0000     0.0297     0.0000 1.000 1.000
X3                  0.500     0.4323     0.0000     0.0404     0.0046 1.000 1.000

F1       WITH
F2                  0.250     0.2282     0.0000     0.0396     0.0005 1.000 1.000

Intercepts
Y1                  0.000     0.0684     0.0000     0.1081     0.0047 1.000 0.000
Y2                  0.000     0.0250     0.0000     0.1101     0.0006 1.000 0.000
Y3                  0.000     0.0457     0.0000     0.1086     0.0021 1.000 0.000
Y4                  0.000     0.1795     0.0000     0.1011     0.0322 1.000 0.000
Y5                  0.000     0.1803     0.0000     0.0962     0.0325 1.000 0.000
Y6                  0.000     0.1474     0.0000     0.0990     0.0217 1.000 0.000

Residual Variances
Y1                  0.500     0.5294     0.0000     0.0460     0.0009 1.000 1.000
Y2                  0.500     0.5124     0.0000     0.0463     0.0002 1.000 1.000
Y3                  0.500     0.4772     0.0000     0.0442     0.0005 1.000 1.000
Y4                  0.500     0.5414     0.0000     0.0465     0.0017 1.000 1.000
Y5                  0.500     0.3989     0.0000     0.0380     0.0102 0.000 1.000
Y6                  0.500     0.5216     0.0000     0.0447     0.0005 1.000 1.000
F1                  0.700     0.7202     0.0000     0.0615     0.0004 1.000 1.000
F2                  0.700     0.6426     0.0000     0.0560     0.0033 1.000 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.364E-02
(ratio of smallest to largest eigenvalue)

TECHNICAL OUTPUT

PARAMETER SPECIFICATION

NU
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
1             2             3             4             5

NU
Y6            X1            X2            X3
________      ________      ________      ________
6             0             0             0

LAMBDA
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
Y1                 0             0             0             0             0
Y2                 7             0             0             0             0
Y3                 8             0             0             0             0
Y4                 0             0             0             0             0
Y5                 0             9             0             0             0
Y6                 0            10             0             0             0
X1                 0             0             0             0             0
X2                 0             0             0             0             0
X3                 0             0             0             0             0

THETA
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1                11
Y2                 0            12
Y3                 0             0            13
Y4                 0             0             0            14
Y5                 0             0             0             0            15
Y6                 0             0             0             0             0
X1                 0             0             0             0             0
X2                 0             0             0             0             0
X3                 0             0             0             0             0

THETA
Y6            X1            X2            X3
________      ________      ________      ________
Y6                16
X1                 0             0
X2                 0             0             0
X3                 0             0             0             0

ALPHA
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
0             0             0             0             0

BETA
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
F1                 0             0            17            18            19
F2                 0             0            20            21            22
X1                 0             0             0             0             0
X2                 0             0             0             0             0
X3                 0             0             0             0             0

PSI
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
F1                23
F2                24            25
X1                 0             0             0
X2                 0             0             0             0
X3                 0             0             0             0             0

STARTING VALUES

NU
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

NU
Y6            X1            X2            X3
________      ________      ________      ________
0.000         0.000         0.000         0.000

LAMBDA
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
Y1             1.000         0.000         0.000         0.000         0.000
Y2             1.035         0.000         0.000         0.000         0.000
Y3             1.021         0.000         0.000         0.000         0.000
Y4             0.000         1.000         0.000         0.000         0.000
Y5             0.000         0.984         0.000         0.000         0.000
Y6             0.000         0.972         0.000         0.000         0.000
X1             0.000         0.000         1.000         0.000         0.000
X2             0.000         0.000         0.000         1.000         0.000
X3             0.000         0.000         0.000         0.000         1.000

THETA
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1             0.500
Y2             0.000         0.500
Y3             0.000         0.000         0.500
Y4             0.000         0.000         0.000         0.500
Y5             0.000         0.000         0.000         0.000         0.500
Y6             0.000         0.000         0.000         0.000         0.000
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000         0.000

THETA
Y6            X1            X2            X3
________      ________      ________      ________
Y6             0.500
X1             0.000         0.000
X2             0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000

ALPHA
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
0.000         0.000        -0.061         1.033         2.090

BETA
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
F1             0.000         0.000         0.500         0.600         0.700
F2             0.000         0.000         0.700         0.600         0.500
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000         0.000

PSI
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
F1             0.700
F2             0.250         0.700
X1             0.000         0.000         2.921
X2             0.000         0.000         0.176         2.082
X3             0.000         0.000        -0.151         0.125         1.042

POPULATION VALUES

NU
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
0.000         0.000         0.000         0.000         0.000

NU
Y6            X1            X2            X3
________      ________      ________      ________
0.000         0.000         0.000         0.000

LAMBDA
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
Y1             1.000         0.000         0.000         0.000         0.000
Y2             1.000         0.000         0.000         0.000         0.000
Y3             1.000         0.000         0.000         0.000         0.000
Y4             0.000         1.000         0.000         0.000         0.000
Y5             0.000         1.000         0.000         0.000         0.000
Y6             0.000         1.000         0.000         0.000         0.000
X1             0.000         0.000         1.000         0.000         0.000
X2             0.000         0.000         0.000         1.000         0.000
X3             0.000         0.000         0.000         0.000         1.000

THETA
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1             0.500
Y2             0.000         0.500
Y3             0.000         0.000         0.500
Y4             0.000         0.000         0.000         0.500
Y5             0.000         0.000         0.000         0.000         0.500
Y6             0.000         0.000         0.000         0.000         0.000
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000         0.000

THETA
Y6            X1            X2            X3
________      ________      ________      ________
Y6             0.500
X1             0.000         0.000
X2             0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000

ALPHA
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
0.000         0.000         0.000         1.000         2.000

BETA
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
F1             0.000         0.000         0.500         0.600         0.700
F2             0.000         0.000         0.700         0.600         0.500
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000         0.000

PSI
F1            F2            X1            X2            X3
________      ________      ________      ________      ________
F1             0.700
F2             0.250         0.700
X1             0.000         0.000         3.000
X2             0.000         0.000         0.000         2.000
X3             0.000         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
X1
X2
X3

Save file
ex5.8.dat

Save file format           Free
Save file record length    10000

Beginning Time:  03:29:13
Ending Time:  03:29:13
Elapsed Time:  00:00:00

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