```Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:23 PM

INPUT INSTRUCTIONS

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

montecarlo:
names = y1-y6;
nobs = 500;
nreps = 1;
save = ex5.20.dat;

model montecarlo:
f1 by y1@1 y2-y3*1;
f2 by y4@1 y5-y6*.8;
y1-y3*.5; ! reliability 0.67
y4-y6*.32; ! reliability 0.67
f1-f2*1;

model:
f1 by y1
y2-y3(lam2-lam3);
f2 by y4
y5-y6*.8 (lam5-lam6);
f1*1 (vf1);
f2*1 (vf2);
y1-y3*.5 (ve1-ve3); ! reliability 0.67
y4-y6*.32 (ve4-ve6); ! reliability 0.67

model constraint:
new(rel2*.67 rel5*.67 stan3*.82 stan6*.82);
rel2 = lam2**2*vf1/(lam2**2*vf1 + ve2);
rel5 = lam5**2*vf2/(lam5**2*vf2 + ve5);
rel5 = rel2;
stan3 = lam3*sqrt(vf1)/sqrt(lam3**2*vf1 + ve3);
stan6 = lam6*sqrt(vf2)/sqrt(lam6**2*vf2 + ve6);
0 = stan6 - stan3;
ve2 > ve5;
ve4 > 0;

output:
tech9;

this is an example of a CFA 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                                  0
Number of continuous latent variables                            2

Observed dependent variables

Continuous
Y1          Y2          Y3          Y4          Y5          Y6

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
________      ________      ________      ________      ________
-0.019         0.015         0.022        -0.018        -0.015

Means
Y6
________
0.022

Covariances
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1             1.478
Y2             1.009         1.477
Y3             0.950         1.011         1.458
Y4            -0.001        -0.042        -0.015         1.353
Y5            -0.025        -0.049        -0.044         0.812         0.988
Y6             0.014        -0.024         0.024         0.755         0.657

Covariances
Y6
________
Y6             0.949

Correlations
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1             1.000
Y2             0.683         1.000
Y3             0.647         0.689         1.000
Y4            -0.001        -0.030        -0.011         1.000
Y5            -0.021        -0.040        -0.037         0.702         1.000
Y6             0.012        -0.020         0.021         0.666         0.679

Correlations
Y6
________
Y6             1.000

MODEL FIT INFORMATION

Number of Free Parameters                       17

Loglikelihood

H0 Value

Mean                             -3898.949
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        -3898.949      -3898.949
0.980       0.000        -3898.949      -3898.949
0.950       0.000        -3898.949      -3898.949
0.900       0.000        -3898.949      -3898.949
0.800       0.000        -3898.949      -3898.949
0.700       0.000        -3898.949      -3898.949
0.500       0.000        -3898.949      -3898.949
0.300       0.000        -3898.949      -3898.949
0.200       0.000        -3898.949      -3898.949
0.100       0.000        -3898.949      -3898.949
0.050       0.000        -3898.949      -3898.949
0.020       0.000        -3898.949      -3898.949
0.010       0.000        -3898.949      -3898.949

H1 Value

Mean                             -3896.904
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        -3896.904      -3896.904
0.980       0.000        -3896.904      -3896.904
0.950       0.000        -3896.904      -3896.904
0.900       0.000        -3896.904      -3896.904
0.800       0.000        -3896.904      -3896.904
0.700       0.000        -3896.904      -3896.904
0.500       0.000        -3896.904      -3896.904
0.300       0.000        -3896.904      -3896.904
0.200       0.000        -3896.904      -3896.904
0.100       0.000        -3896.904      -3896.904
0.050       0.000        -3896.904      -3896.904
0.020       0.000        -3896.904      -3896.904
0.010       0.000        -3896.904      -3896.904

Information Criteria

Akaike (AIC)

Mean                              7831.898
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         7831.898       7831.898
0.980       0.000         7831.898       7831.898
0.950       0.000         7831.898       7831.898
0.900       0.000         7831.898       7831.898
0.800       0.000         7831.898       7831.898
0.700       0.000         7831.898       7831.898
0.500       0.000         7831.898       7831.898
0.300       0.000         7831.898       7831.898
0.200       0.000         7831.898       7831.898
0.100       0.000         7831.898       7831.898
0.050       0.000         7831.898       7831.898
0.020       0.000         7831.898       7831.898
0.010       0.000         7831.898       7831.898

Bayesian (BIC)

Mean                              7903.547
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         7903.547       7903.547
0.980       0.000         7903.547       7903.547
0.950       0.000         7903.547       7903.547
0.900       0.000         7903.547       7903.547
0.800       0.000         7903.547       7903.547
0.700       0.000         7903.547       7903.547
0.500       0.000         7903.547       7903.547
0.300       0.000         7903.547       7903.547
0.200       0.000         7903.547       7903.547
0.100       0.000         7903.547       7903.547
0.050       0.000         7903.547       7903.547
0.020       0.000         7903.547       7903.547
0.010       0.000         7903.547       7903.547

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

Mean                              7849.588
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         7849.588       7849.588
0.980       0.000         7849.588       7849.588
0.950       0.000         7849.588       7849.588
0.900       0.000         7849.588       7849.588
0.800       0.000         7849.588       7849.588
0.700       0.000         7849.588       7849.588
0.500       0.000         7849.588       7849.588
0.300       0.000         7849.588       7849.588
0.200       0.000         7849.588       7849.588
0.100       0.000         7849.588       7849.588
0.050       0.000         7849.588       7849.588
0.020       0.000         7849.588       7849.588
0.010       0.000         7849.588       7849.588

Chi-Square Test of Model Fit

Degrees of freedom                      10

Mean                                 4.090
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000            2.558          4.090
0.980       1.000            3.059          4.090
0.950       1.000            3.940          4.090
0.900       0.000            4.865          4.090
0.800       0.000            6.179          4.090
0.700       0.000            7.267          4.090
0.500       0.000            9.342          4.090
0.300       0.000           11.781          4.090
0.200       0.000           13.442          4.090
0.100       0.000           15.987          4.090
0.050       0.000           18.307          4.090
0.020       0.000           21.161          4.090
0.010       0.000           23.209          4.090

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                                 0.012
Std Dev                              0.000
Number of successful computations        1

Cumulative Distribution Function
Value    Function Value
0.990       1.000
0.980       1.000
0.950       1.000
0.900       1.000
0.800       1.000
0.700       1.000
0.500       1.000
0.300       1.000
0.200       1.000
0.100       1.000
0.050       1.000
0.020       1.000
0.010       0.000

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     1.0602     0.0000     0.0521     0.0036 1.000 1.000
Y3                  1.000     0.9983     0.0000     0.0507     0.0000 1.000 1.000

F2       BY
Y4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y5                  0.800     0.8756     0.0000     0.0411     0.0057 1.000 1.000
Y6                  0.800     0.8132     0.0000     0.0395     0.0002 1.000 1.000

F2       WITH
F1                  0.000    -0.0241     0.0000     0.0486     0.0006 1.000 0.000

Intercepts
Y1                  0.000    -0.0193     0.0000     0.0542     0.0004 1.000 0.000
Y2                  0.000     0.0145     0.0000     0.0542     0.0002 1.000 0.000
Y3                  0.000     0.0224     0.0000     0.0538     0.0005 1.000 0.000
Y4                  0.000    -0.0182     0.0000     0.0522     0.0003 1.000 0.000
Y5                  0.000    -0.0152     0.0000     0.0446     0.0002 1.000 0.000
Y6                  0.000     0.0217     0.0000     0.0437     0.0005 1.000 0.000

Variances
F1                  1.000     0.9421     0.0000     0.0921     0.0033 1.000 1.000
F2                  1.000     0.9370     0.0000     0.0871     0.0040 1.000 1.000

Residual Variances
Y1                  0.500     0.5287     0.0000     0.0483     0.0008 1.000 1.000
Y2                  0.500     0.4078     0.0000     0.0368     0.0085 0.000 1.000
Y3                  0.500     0.5093     0.0000     0.0390     0.0001 1.000 1.000
Y4                  0.320     0.4237     0.0000     0.0418     0.0107 0.000 1.000
Y5                  0.320     0.2767     0.0000     0.0248     0.0019 1.000 1.000
Y6                  0.320     0.3361     0.0000     0.0255     0.0003 1.000 1.000

REL2                0.670     0.7220     0.0000     0.0240     0.0027 0.000 1.000
REL5                0.670     0.7220     0.0000     0.0240     0.0027 0.000 1.000
STAN3               0.820     0.8052     0.0000     0.0153     0.0002 1.000 1.000
STAN6               0.820     0.8052     0.0000     0.0153     0.0002 1.000 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.205E-03
(ratio of smallest to largest eigenvalue)

TECHNICAL OUTPUT

PARAMETER SPECIFICATION

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

NU
Y6
________
6

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

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

THETA
Y6
________
Y6                16

ALPHA
F1            F2
________      ________
0             0

BETA
F1            F2
________      ________
F1                 0             0
F2                 0             0

PSI
F1            F2
________      ________
F1                17
F2                18            19

PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS

REL2          REL5          STAN3         STAN6
________      ________      ________      ________
20            21            22            23

STARTING VALUES

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

NU
Y6
________
0.000

LAMBDA
F1            F2
________      ________
Y1             1.000         0.000
Y2             1.065         0.000
Y3             1.003         0.000
Y4             0.000         1.000
Y5             0.000         0.800
Y6             0.000         0.800

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         0.320
Y5             0.000         0.000         0.000         0.000         0.320
Y6             0.000         0.000         0.000         0.000         0.000

THETA
Y6
________
Y6             0.320

ALPHA
F1            F2
________      ________
0.000         0.000

BETA
F1            F2
________      ________
F1             0.000         0.000
F2             0.000         0.000

PSI
F1            F2
________      ________
F1             1.000
F2             0.000         1.000

STARTING VALUES FOR THE ADDITIONAL PARAMETERS

REL2          REL5          STAN3         STAN6
________      ________      ________      ________
0.670         0.670         0.820         0.820

POPULATION VALUES

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

NU
Y6
________
0.000

LAMBDA
F1            F2
________      ________
Y1             1.000         0.000
Y2             1.000         0.000
Y3             1.000         0.000
Y4             0.000         1.000
Y5             0.000         0.800
Y6             0.000         0.800

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         0.320
Y5             0.000         0.000         0.000         0.000         0.320
Y6             0.000         0.000         0.000         0.000         0.000

THETA
Y6
________
Y6             0.320

ALPHA
F1            F2
________      ________
0.000         0.000

BETA
F1            F2
________      ________
F1             0.000         0.000
F2             0.000         0.000

PSI
F1            F2
________      ________
F1             1.000
F2             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

Save file
ex5.20.dat

Save file format           Free
Save file record length    10000

Beginning Time:  22:23:05
Ending Time:  22:23:05
Elapsed Time:  00:00:00

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