Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title: this is an example of a multiple indicator
linear growth model for continuous outcomes
montecarlo:
names = y11 y21 y31 y12 y22 y32 y13 y23 y33;
nobs = 500;
nreps = 1;
save = ex6.14.dat;
model montecarlo:
f1 BY y11@1
y21*1 (1)
y31*1 (2);
f2 BY y12@1
y22*1 (1)
y32*1 (2);
f3 BY y13@1
y23*1 (1)
y33*1 (2);
[y11*-.5 y12*-.5 y13*-.5] (3);
[y21*0 y22*0 y23*0] (4);
[y31*.5 y32*.5 y33*.5] (5);
y11-y33*.5;
i s | f1@0 f2@1 f3@2;
[i@0 s*1];
i*1 s*.2;
f1-f3*.4;
model:
f1 BY y11@1
y21*1 (1)
y31*1 (2);
f2 BY y12@1
y22*1 (1)
y32*1 (2);
f3 BY y13@1
y23*1 (1)
y33*1 (2);
[y11*-.5 y12*-.5 y13*-.5] (3);
[y21*0 y22*0 y23*0] (4);
[y31*.5 y32*.5 y33*.5] (5);
y11-y33*.5;
i s | f1@0 f2@1 f3@2;
[i@0 s*1];
i*1 s*.2;
f1-f3*.4;
INPUT READING TERMINATED NORMALLY
this is an example of a multiple indicator
linear growth model for continuous outcomes
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 9
Number of independent variables 0
Number of continuous latent variables 5
Observed dependent variables
Continuous
Y11 Y21 Y31 Y12 Y22 Y32
Y13 Y23 Y33
Continuous latent variables
F1 F2 F3 I S
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
Y11 Y21 Y31 Y12 Y22
________ ________ ________ ________ ________
-0.549 -0.014 0.549 0.512 1.035
Means
Y32 Y13 Y23 Y33
________ ________ ________ ________
1.536 1.556 2.018 2.489
Covariances
Y11 Y21 Y31 Y12 Y22
________ ________ ________ ________ ________
Y11 1.850
Y21 1.455 2.044
Y31 1.301 1.480 1.876
Y12 0.950 0.995 0.949 2.096
Y22 0.997 1.058 0.991 1.641 2.225
Y32 1.010 1.031 0.998 1.614 1.695
Y13 0.953 0.983 0.886 1.408 1.445
Y23 0.885 0.920 0.804 1.238 1.313
Y33 0.876 0.981 0.836 1.225 1.296
Covariances
Y32 Y13 Y23 Y33
________ ________ ________ ________
Y32 2.153
Y13 1.442 2.677
Y23 1.310 2.060 2.339
Y33 1.332 1.950 1.879 2.336
Correlations
Y11 Y21 Y31 Y12 Y22
________ ________ ________ ________ ________
Y11 1.000
Y21 0.748 1.000
Y31 0.698 0.756 1.000
Y12 0.483 0.481 0.479 1.000
Y22 0.492 0.496 0.485 0.760 1.000
Y32 0.506 0.491 0.496 0.760 0.775
Y13 0.428 0.420 0.395 0.595 0.592
Y23 0.425 0.421 0.384 0.559 0.576
Y33 0.421 0.449 0.399 0.553 0.568
Correlations
Y32 Y13 Y23 Y33
________ ________ ________ ________
Y32 1.000
Y13 0.601 1.000
Y23 0.583 0.823 1.000
Y33 0.594 0.780 0.804 1.000
MODEL FIT INFORMATION
Number of Free Parameters 21
Loglikelihood
H0 Value
Mean -6357.999
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -6357.999 -6357.999
0.980 0.000 -6357.999 -6357.999
0.950 0.000 -6357.999 -6357.999
0.900 0.000 -6357.999 -6357.999
0.800 0.000 -6357.999 -6357.999
0.700 0.000 -6357.999 -6357.999
0.500 0.000 -6357.999 -6357.999
0.300 0.000 -6357.999 -6357.999
0.200 0.000 -6357.999 -6357.999
0.100 0.000 -6357.999 -6357.999
0.050 0.000 -6357.999 -6357.999
0.020 0.000 -6357.999 -6357.999
0.010 0.000 -6357.999 -6357.999
H1 Value
Mean -6339.524
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -6339.524 -6339.524
0.980 0.000 -6339.524 -6339.524
0.950 0.000 -6339.524 -6339.524
0.900 0.000 -6339.524 -6339.524
0.800 0.000 -6339.524 -6339.524
0.700 0.000 -6339.524 -6339.524
0.500 0.000 -6339.524 -6339.524
0.300 0.000 -6339.524 -6339.524
0.200 0.000 -6339.524 -6339.524
0.100 0.000 -6339.524 -6339.524
0.050 0.000 -6339.524 -6339.524
0.020 0.000 -6339.524 -6339.524
0.010 0.000 -6339.524 -6339.524
Information Criteria
Akaike (AIC)
Mean 12757.998
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12757.998 12757.998
0.980 0.000 12757.998 12757.998
0.950 0.000 12757.998 12757.998
0.900 0.000 12757.998 12757.998
0.800 0.000 12757.998 12757.998
0.700 0.000 12757.998 12757.998
0.500 0.000 12757.998 12757.998
0.300 0.000 12757.998 12757.998
0.200 0.000 12757.998 12757.998
0.100 0.000 12757.998 12757.998
0.050 0.000 12757.998 12757.998
0.020 0.000 12757.998 12757.998
0.010 0.000 12757.998 12757.998
Bayesian (BIC)
Mean 12846.504
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12846.504 12846.504
0.980 0.000 12846.504 12846.504
0.950 0.000 12846.504 12846.504
0.900 0.000 12846.504 12846.504
0.800 0.000 12846.504 12846.504
0.700 0.000 12846.504 12846.504
0.500 0.000 12846.504 12846.504
0.300 0.000 12846.504 12846.504
0.200 0.000 12846.504 12846.504
0.100 0.000 12846.504 12846.504
0.050 0.000 12846.504 12846.504
0.020 0.000 12846.504 12846.504
0.010 0.000 12846.504 12846.504
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 12779.849
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12779.849 12779.849
0.980 0.000 12779.849 12779.849
0.950 0.000 12779.849 12779.849
0.900 0.000 12779.849 12779.849
0.800 0.000 12779.849 12779.849
0.700 0.000 12779.849 12779.849
0.500 0.000 12779.849 12779.849
0.300 0.000 12779.849 12779.849
0.200 0.000 12779.849 12779.849
0.100 0.000 12779.849 12779.849
0.050 0.000 12779.849 12779.849
0.020 0.000 12779.849 12779.849
0.010 0.000 12779.849 12779.849
Chi-Square Test of Model Fit
Degrees of freedom 33
Mean 36.949
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 17.074 36.949
0.980 1.000 18.527 36.949
0.950 1.000 20.867 36.949
0.900 1.000 23.110 36.949
0.800 1.000 26.042 36.949
0.700 1.000 28.307 36.949
0.500 1.000 32.336 36.949
0.300 1.000 36.731 36.949
0.200 0.000 39.572 36.949
0.100 0.000 43.745 36.949
0.050 0.000 47.400 36.949
0.020 0.000 51.743 36.949
0.010 0.000 54.776 36.949
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.015
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
CFI/TLI
CFI
Mean 0.999
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 0.999
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 0.023
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 0.000
0.010 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
I |
F1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S |
F1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
F1 BY
Y11 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y21 1.000 1.0033 0.0000 0.0178 0.0000 1.000 1.000
Y31 1.000 0.9599 0.0000 0.0180 0.0016 0.000 1.000
F2 BY
Y12 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y22 1.000 1.0033 0.0000 0.0178 0.0000 1.000 1.000
Y32 1.000 0.9599 0.0000 0.0180 0.0016 0.000 1.000
F3 BY
Y13 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y23 1.000 1.0033 0.0000 0.0178 0.0000 1.000 1.000
Y33 1.000 0.9599 0.0000 0.0180 0.0016 0.000 1.000
S WITH
I 0.000 -0.1016 0.0000 0.0657 0.0103 1.000 0.000
Means
I 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S 1.000 1.0233 0.0000 0.0333 0.0005 1.000 1.000
Intercepts
Y11 -0.500 -0.5191 0.0000 0.0589 0.0004 1.000 1.000
Y21 0.000 -0.0173 0.0000 0.0586 0.0003 1.000 0.000
Y31 0.500 0.5404 0.0000 0.0569 0.0016 1.000 1.000
Y12 -0.500 -0.5191 0.0000 0.0589 0.0004 1.000 1.000
Y22 0.000 -0.0173 0.0000 0.0586 0.0003 1.000 0.000
Y32 0.500 0.5404 0.0000 0.0569 0.0016 1.000 1.000
Y13 -0.500 -0.5191 0.0000 0.0589 0.0004 1.000 1.000
Y23 0.000 -0.0173 0.0000 0.0586 0.0003 1.000 0.000
Y33 0.500 0.5404 0.0000 0.0569 0.0016 1.000 1.000
F1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
F3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
I 1.000 1.1246 0.0000 0.1291 0.0155 1.000 1.000
S 0.200 0.2694 0.0000 0.0603 0.0048 1.000 1.000
Residual Variances
Y11 0.500 0.5193 0.0000 0.0473 0.0004 1.000 1.000
Y21 0.500 0.4662 0.0000 0.0448 0.0011 1.000 1.000
Y31 0.500 0.5435 0.0000 0.0468 0.0019 1.000 1.000
Y12 0.500 0.5196 0.0000 0.0459 0.0004 1.000 1.000
Y22 0.500 0.5097 0.0000 0.0456 0.0001 1.000 1.000
Y32 0.500 0.4965 0.0000 0.0437 0.0000 1.000 1.000
Y13 0.500 0.5417 0.0000 0.0482 0.0017 1.000 1.000
Y23 0.500 0.3779 0.0000 0.0395 0.0149 0.000 1.000
Y33 0.500 0.5357 0.0000 0.0457 0.0013 1.000 1.000
F1 0.400 0.3287 0.0000 0.1110 0.0051 1.000 1.000
F2 0.400 0.5008 0.0000 0.0663 0.0102 1.000 1.000
F3 0.400 0.2099 0.0000 0.1261 0.0361 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.237E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
NU
Y11 Y21 Y31 Y12 Y22
________ ________ ________ ________ ________
1 2 3 1 2
NU
Y32 Y13 Y23 Y33
________ ________ ________ ________
3 1 2 3
LAMBDA
F1 F2 F3 I S
________ ________ ________ ________ ________
Y11 0 0 0 0 0
Y21 4 0 0 0 0
Y31 5 0 0 0 0
Y12 0 0 0 0 0
Y22 0 4 0 0 0
Y32 0 5 0 0 0
Y13 0 0 0 0 0
Y23 0 0 4 0 0
Y33 0 0 5 0 0
THETA
Y11 Y21 Y31 Y12 Y22
________ ________ ________ ________ ________
Y11 6
Y21 0 7
Y31 0 0 8
Y12 0 0 0 9
Y22 0 0 0 0 10
Y32 0 0 0 0 0
Y13 0 0 0 0 0
Y23 0 0 0 0 0
Y33 0 0 0 0 0
THETA
Y32 Y13 Y23 Y33
________ ________ ________ ________
Y32 11
Y13 0 12
Y23 0 0 13
Y33 0 0 0 14
ALPHA
F1 F2 F3 I S
________ ________ ________ ________ ________
0 0 0 0 15
BETA
F1 F2 F3 I S
________ ________ ________ ________ ________
F1 0 0 0 0 0
F2 0 0 0 0 0
F3 0 0 0 0 0
I 0 0 0 0 0
S 0 0 0 0 0
PSI
F1 F2 F3 I S
________ ________ ________ ________ ________
F1 16
F2 0 17
F3 0 0 18
I 0 0 0 19
S 0 0 0 20 21
STARTING VALUES
NU
Y11 Y21 Y31 Y12 Y22
________ ________ ________ ________ ________
-0.500 0.000 0.500 -0.500 0.000
NU
Y32 Y13 Y23 Y33
________ ________ ________ ________
0.500 -0.500 0.000 0.500
LAMBDA
F1 F2 F3 I S
________ ________ ________ ________ ________
Y11 1.000 0.000 0.000 0.000 0.000
Y21 1.138 0.000 0.000 0.000 0.000
Y31 1.017 0.000 0.000 0.000 0.000
Y12 0.000 1.000 0.000 0.000 0.000
Y22 0.000 1.050 0.000 0.000 0.000
Y32 0.000 1.033 0.000 0.000 0.000
Y13 0.000 0.000 1.000 0.000 0.000
Y23 0.000 0.000 0.963 0.000 0.000
Y33 0.000 0.000 0.912 0.000 0.000
THETA
Y11 Y21 Y31 Y12 Y22
________ ________ ________ ________ ________
Y11 0.500
Y21 0.000 0.500
Y31 0.000 0.000 0.500
Y12 0.000 0.000 0.000 0.500
Y22 0.000 0.000 0.000 0.000 0.500
Y32 0.000 0.000 0.000 0.000 0.000
Y13 0.000 0.000 0.000 0.000 0.000
Y23 0.000 0.000 0.000 0.000 0.000
Y33 0.000 0.000 0.000 0.000 0.000
THETA
Y32 Y13 Y23 Y33
________ ________ ________ ________
Y32 0.500
Y13 0.000 0.500
Y23 0.000 0.000 0.500
Y33 0.000 0.000 0.000 0.500
ALPHA
F1 F2 F3 I S
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 1.000
BETA
F1 F2 F3 I S
________ ________ ________ ________ ________
F1 0.000 0.000 0.000 1.000 0.000
F2 0.000 0.000 0.000 1.000 1.000
F3 0.000 0.000 0.000 1.000 2.000
I 0.000 0.000 0.000 0.000 0.000
S 0.000 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 I S
________ ________ ________ ________ ________
F1 0.400
F2 0.000 0.400
F3 0.000 0.000 0.400
I 0.000 0.000 0.000 1.000
S 0.000 0.000 0.000 0.000 0.200
POPULATION VALUES
NU
Y11 Y21 Y31 Y12 Y22
________ ________ ________ ________ ________
-0.500 0.000 0.500 -0.500 0.000
NU
Y32 Y13 Y23 Y33
________ ________ ________ ________
0.500 -0.500 0.000 0.500
LAMBDA
F1 F2 F3 I S
________ ________ ________ ________ ________
Y11 1.000 0.000 0.000 0.000 0.000
Y21 1.000 0.000 0.000 0.000 0.000
Y31 1.000 0.000 0.000 0.000 0.000
Y12 0.000 1.000 0.000 0.000 0.000
Y22 0.000 1.000 0.000 0.000 0.000
Y32 0.000 1.000 0.000 0.000 0.000
Y13 0.000 0.000 1.000 0.000 0.000
Y23 0.000 0.000 1.000 0.000 0.000
Y33 0.000 0.000 1.000 0.000 0.000
THETA
Y11 Y21 Y31 Y12 Y22
________ ________ ________ ________ ________
Y11 0.500
Y21 0.000 0.500
Y31 0.000 0.000 0.500
Y12 0.000 0.000 0.000 0.500
Y22 0.000 0.000 0.000 0.000 0.500
Y32 0.000 0.000 0.000 0.000 0.000
Y13 0.000 0.000 0.000 0.000 0.000
Y23 0.000 0.000 0.000 0.000 0.000
Y33 0.000 0.000 0.000 0.000 0.000
THETA
Y32 Y13 Y23 Y33
________ ________ ________ ________
Y32 0.500
Y13 0.000 0.500
Y23 0.000 0.000 0.500
Y33 0.000 0.000 0.000 0.500
ALPHA
F1 F2 F3 I S
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 1.000
BETA
F1 F2 F3 I S
________ ________ ________ ________ ________
F1 0.000 0.000 0.000 1.000 0.000
F2 0.000 0.000 0.000 1.000 1.000
F3 0.000 0.000 0.000 1.000 2.000
I 0.000 0.000 0.000 0.000 0.000
S 0.000 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 I S
________ ________ ________ ________ ________
F1 0.400
F2 0.000 0.400
F3 0.000 0.000 0.400
I 0.000 0.000 0.000 1.000
S 0.000 0.000 0.000 0.000 0.200
SAVEDATA INFORMATION
Order of variables
Y11
Y21
Y31
Y12
Y22
Y32
Y13
Y23
Y33
Save file
ex6.14.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:16
Ending Time: 22:24:16
Elapsed Time: 00:00:00
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