Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title: this is an example of parallel process
linear growth models for two continuous
outcomes with regressions among the random
effects
montecarlo:
names = y11-y14 y21-y24;
nobs = 500;
nreps = 1;
save = ex6.13.dat;
model population:
i1 s1 | y11@0 y12@1 y13@2 y14@3;
[i1*.5 s1*1];
i1*1; s1*.2;
i2 s2 | y21@0 y22@1 y23@2 y24@3;
[i2*.5 s2*1];
i2*1; s2*.2;
s2 on i1*.6;
s1 on i2*.3;
s1 with s2*.1;
y11-y24*.5;
model:
i1 s1 | y11@0 y12@1 y13@2 y14@3;
[i1*.5 s1*1];
i1*1; s1*.2;
i2 s2 | y21@0 y22@1 y23@2 y24@3;
[i2*.5 s2*1];
i2*1; s2*.2;
s2 on i1*.6;
s1 on i2*.3;
s1 with s2*.1;
y11-y24*.5;
output:
tech9;
INPUT READING TERMINATED NORMALLY
this is an example of parallel process
linear growth models for two continuous
outcomes with regressions among the random
effects
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 8
Number of independent variables 0
Number of continuous latent variables 4
Observed dependent variables
Continuous
Y11 Y12 Y13 Y14 Y21 Y22
Y23 Y24
Continuous latent variables
I1 S1 I2 S2
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 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
0.534 1.686 2.845 4.006 0.503
Means
Y22 Y23 Y24
________ ________ ________
1.840 3.110 4.515
Covariances
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
Y11 1.443
Y12 1.031 1.937
Y13 0.923 1.719 2.876
Y14 1.019 2.014 3.007 4.479
Y21 0.044 0.325 0.653 1.067 1.456
Y22 0.604 1.054 1.446 1.846 1.016
Y23 1.204 1.834 2.229 2.831 1.057
Y24 1.767 2.442 2.950 3.575 1.044
Covariances
Y22 Y23 Y24
________ ________ ________
Y22 2.054
Y23 2.197 3.829
Y24 2.628 4.383 6.310
Correlations
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
Y11 1.000
Y12 0.617 1.000
Y13 0.453 0.728 1.000
Y14 0.401 0.684 0.838 1.000
Y21 0.030 0.193 0.319 0.418 1.000
Y22 0.351 0.528 0.595 0.609 0.587
Y23 0.512 0.674 0.672 0.684 0.448
Y24 0.586 0.699 0.692 0.672 0.344
Correlations
Y22 Y23 Y24
________ ________ ________
Y22 1.000
Y23 0.783 1.000
Y24 0.730 0.892 1.000
MODEL FIT INFORMATION
Number of Free Parameters 20
Loglikelihood
H0 Value
Mean -5990.576
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -5990.576 -5990.576
0.980 0.000 -5990.576 -5990.576
0.950 0.000 -5990.576 -5990.576
0.900 0.000 -5990.576 -5990.576
0.800 0.000 -5990.576 -5990.576
0.700 0.000 -5990.576 -5990.576
0.500 0.000 -5990.576 -5990.576
0.300 0.000 -5990.576 -5990.576
0.200 0.000 -5990.576 -5990.576
0.100 0.000 -5990.576 -5990.576
0.050 0.000 -5990.576 -5990.576
0.020 0.000 -5990.576 -5990.576
0.010 0.000 -5990.576 -5990.576
H1 Value
Mean -5974.993
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -5974.993 -5974.993
0.980 0.000 -5974.993 -5974.993
0.950 0.000 -5974.993 -5974.993
0.900 0.000 -5974.993 -5974.993
0.800 0.000 -5974.993 -5974.993
0.700 0.000 -5974.993 -5974.993
0.500 0.000 -5974.993 -5974.993
0.300 0.000 -5974.993 -5974.993
0.200 0.000 -5974.993 -5974.993
0.100 0.000 -5974.993 -5974.993
0.050 0.000 -5974.993 -5974.993
0.020 0.000 -5974.993 -5974.993
0.010 0.000 -5974.993 -5974.993
Information Criteria
Akaike (AIC)
Mean 12021.152
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12021.152 12021.152
0.980 0.000 12021.152 12021.152
0.950 0.000 12021.152 12021.152
0.900 0.000 12021.152 12021.152
0.800 0.000 12021.152 12021.152
0.700 0.000 12021.152 12021.152
0.500 0.000 12021.152 12021.152
0.300 0.000 12021.152 12021.152
0.200 0.000 12021.152 12021.152
0.100 0.000 12021.152 12021.152
0.050 0.000 12021.152 12021.152
0.020 0.000 12021.152 12021.152
0.010 0.000 12021.152 12021.152
Bayesian (BIC)
Mean 12105.445
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12105.445 12105.445
0.980 0.000 12105.445 12105.445
0.950 0.000 12105.445 12105.445
0.900 0.000 12105.445 12105.445
0.800 0.000 12105.445 12105.445
0.700 0.000 12105.445 12105.445
0.500 0.000 12105.445 12105.445
0.300 0.000 12105.445 12105.445
0.200 0.000 12105.445 12105.445
0.100 0.000 12105.445 12105.445
0.050 0.000 12105.445 12105.445
0.020 0.000 12105.445 12105.445
0.010 0.000 12105.445 12105.445
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 12041.963
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 12041.963 12041.963
0.980 0.000 12041.963 12041.963
0.950 0.000 12041.963 12041.963
0.900 0.000 12041.963 12041.963
0.800 0.000 12041.963 12041.963
0.700 0.000 12041.963 12041.963
0.500 0.000 12041.963 12041.963
0.300 0.000 12041.963 12041.963
0.200 0.000 12041.963 12041.963
0.100 0.000 12041.963 12041.963
0.050 0.000 12041.963 12041.963
0.020 0.000 12041.963 12041.963
0.010 0.000 12041.963 12041.963
Chi-Square Test of Model Fit
Degrees of freedom 24
Mean 31.167
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 10.856 31.167
0.980 1.000 11.992 31.167
0.950 1.000 13.848 31.167
0.900 1.000 15.659 31.167
0.800 1.000 18.062 31.167
0.700 1.000 19.943 31.167
0.500 1.000 23.337 31.167
0.300 1.000 27.096 31.167
0.200 1.000 29.553 31.167
0.100 0.000 33.196 31.167
0.050 0.000 36.415 31.167
0.020 0.000 40.270 31.167
0.010 0.000 42.980 31.167
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.024
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
CFI/TLI
CFI
Mean 0.998
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 0.997
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 0.017
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
I1 |
Y11 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y12 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y13 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y14 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S1 |
Y11 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y12 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y13 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
Y14 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
I2 |
Y21 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y22 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y23 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y24 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S2 |
Y21 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y22 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y23 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
Y24 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
S2 ON
I1 0.600 0.6017 0.0000 0.0291 0.0000 1.000 1.000
S1 ON
I2 0.300 0.3294 0.0000 0.0250 0.0009 1.000 1.000
S1 WITH
S2 0.100 0.0812 0.0000 0.0186 0.0004 1.000 1.000
I2 WITH
I1 0.000 0.0254 0.0000 0.0573 0.0006 1.000 0.000
Means
I1 0.500 0.5314 0.0000 0.0518 0.0010 1.000 1.000
I2 0.500 0.4960 0.0000 0.0518 0.0000 1.000 1.000
Intercepts
Y11 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y12 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y13 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y14 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y21 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y22 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y23 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y24 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S1 1.000 0.9940 0.0000 0.0293 0.0000 1.000 1.000
S2 1.000 1.0106 0.0000 0.0323 0.0001 1.000 1.000
Variances
I1 1.000 0.9883 0.0000 0.0826 0.0001 1.000 1.000
I2 1.000 1.0178 0.0000 0.0840 0.0003 1.000 1.000
Residual Variances
Y11 0.500 0.4970 0.0000 0.0549 0.0000 1.000 1.000
Y12 0.500 0.5271 0.0000 0.0416 0.0007 1.000 1.000
Y13 0.500 0.5471 0.0000 0.0485 0.0022 1.000 1.000
Y14 0.500 0.4933 0.0000 0.0813 0.0000 1.000 1.000
Y21 0.500 0.4532 0.0000 0.0568 0.0022 1.000 1.000
Y22 0.500 0.4887 0.0000 0.0404 0.0001 1.000 1.000
Y23 0.500 0.4488 0.0000 0.0428 0.0026 1.000 1.000
Y24 0.500 0.4664 0.0000 0.0758 0.0011 1.000 1.000
S1 0.200 0.2178 0.0000 0.0220 0.0003 1.000 1.000
S2 0.200 0.1791 0.0000 0.0259 0.0004 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.876E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
NU
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
0 0 0 0 0
NU
Y22 Y23 Y24
________ ________ ________
0 0 0
LAMBDA
I1 S1 I2 S2
________ ________ ________ ________
Y11 0 0 0 0
Y12 0 0 0 0
Y13 0 0 0 0
Y14 0 0 0 0
Y21 0 0 0 0
Y22 0 0 0 0
Y23 0 0 0 0
Y24 0 0 0 0
THETA
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
Y11 1
Y12 0 2
Y13 0 0 3
Y14 0 0 0 4
Y21 0 0 0 0 5
Y22 0 0 0 0 0
Y23 0 0 0 0 0
Y24 0 0 0 0 0
THETA
Y22 Y23 Y24
________ ________ ________
Y22 6
Y23 0 7
Y24 0 0 8
ALPHA
I1 S1 I2 S2
________ ________ ________ ________
9 10 11 12
BETA
I1 S1 I2 S2
________ ________ ________ ________
I1 0 0 0 0
S1 0 0 13 0
I2 0 0 0 0
S2 14 0 0 0
PSI
I1 S1 I2 S2
________ ________ ________ ________
I1 15
S1 0 16
I2 17 0 18
S2 0 19 0 20
STARTING VALUES
NU
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y22 Y23 Y24
________ ________ ________
0.000 0.000 0.000
LAMBDA
I1 S1 I2 S2
________ ________ ________ ________
Y11 1.000 0.000 0.000 0.000
Y12 1.000 1.000 0.000 0.000
Y13 1.000 2.000 0.000 0.000
Y14 1.000 3.000 0.000 0.000
Y21 0.000 0.000 1.000 0.000
Y22 0.000 0.000 1.000 1.000
Y23 0.000 0.000 1.000 2.000
Y24 0.000 0.000 1.000 3.000
THETA
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
Y11 0.500
Y12 0.000 0.500
Y13 0.000 0.000 0.500
Y14 0.000 0.000 0.000 0.500
Y21 0.000 0.000 0.000 0.000 0.500
Y22 0.000 0.000 0.000 0.000 0.000
Y23 0.000 0.000 0.000 0.000 0.000
Y24 0.000 0.000 0.000 0.000 0.000
THETA
Y22 Y23 Y24
________ ________ ________
Y22 0.500
Y23 0.000 0.500
Y24 0.000 0.000 0.500
ALPHA
I1 S1 I2 S2
________ ________ ________ ________
0.500 1.000 0.500 1.000
BETA
I1 S1 I2 S2
________ ________ ________ ________
I1 0.000 0.000 0.000 0.000
S1 0.000 0.000 0.300 0.000
I2 0.000 0.000 0.000 0.000
S2 0.600 0.000 0.000 0.000
PSI
I1 S1 I2 S2
________ ________ ________ ________
I1 1.000
S1 0.000 0.200
I2 0.000 0.000 1.000
S2 0.000 0.100 0.000 0.200
POPULATION VALUES
NU
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y22 Y23 Y24
________ ________ ________
0.000 0.000 0.000
LAMBDA
I1 S1 I2 S2
________ ________ ________ ________
Y11 1.000 0.000 0.000 0.000
Y12 1.000 1.000 0.000 0.000
Y13 1.000 2.000 0.000 0.000
Y14 1.000 3.000 0.000 0.000
Y21 0.000 0.000 1.000 0.000
Y22 0.000 0.000 1.000 1.000
Y23 0.000 0.000 1.000 2.000
Y24 0.000 0.000 1.000 3.000
THETA
Y11 Y12 Y13 Y14 Y21
________ ________ ________ ________ ________
Y11 0.500
Y12 0.000 0.500
Y13 0.000 0.000 0.500
Y14 0.000 0.000 0.000 0.500
Y21 0.000 0.000 0.000 0.000 0.500
Y22 0.000 0.000 0.000 0.000 0.000
Y23 0.000 0.000 0.000 0.000 0.000
Y24 0.000 0.000 0.000 0.000 0.000
THETA
Y22 Y23 Y24
________ ________ ________
Y22 0.500
Y23 0.000 0.500
Y24 0.000 0.000 0.500
ALPHA
I1 S1 I2 S2
________ ________ ________ ________
0.500 1.000 0.500 1.000
BETA
I1 S1 I2 S2
________ ________ ________ ________
I1 0.000 0.000 0.000 0.000
S1 0.000 0.000 0.300 0.000
I2 0.000 0.000 0.000 0.000
S2 0.600 0.000 0.000 0.000
PSI
I1 S1 I2 S2
________ ________ ________ ________
I1 1.000
S1 0.000 0.200
I2 0.000 0.000 1.000
S2 0.000 0.100 0.000 0.200
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y11
Y12
Y13
Y14
Y21
Y22
Y23
Y24
Save file
ex6.13.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:15
Ending Time: 22:24:16
Elapsed Time: 00:00:01
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