Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title: this is an example of a quadratic growth
model for a continuous outcome
montecarlo:
names = y11-y14;
nobs = 500;
nreps = 1;
save = ex6.9.dat;
model population:
i s q | y11@0 y12@1 y13@2 y14@3;
[y11-y14@0];
y11-y14*1;
[i*.5 s*1 q*.5];
i*1; s*.4; q*.2; i with s*.1;
! i and s with q defaults to zero (free)
! this model gives many replications with
! non-pos def cov matrices, with low
! power (see last column) for the s and y14
! variances, suggesting that more time points
! may be needed for this quadratic model
model:
i s q | y11@0 y12@1 y13@2 y14@3;
[y11-y14@0];
y11-y14*1;
[i*.5 s*1 q*.5];
i*1; s*.4; q*.2; i with s*.1;
output:
tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a quadratic growth
model for a continuous outcome
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 4
Number of independent variables 0
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y11 Y12 Y13 Y14
Continuous latent variables
I S Q
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
________ ________ ________ ________
0.516 2.088 4.618 8.240
Covariances
Y11 Y12 Y13 Y14
________ ________ ________ ________
Y11 1.932
Y12 1.174 2.906
Y13 1.303 3.282 7.944
Y14 1.635 4.946 12.455 24.897
Correlations
Y11 Y12 Y13 Y14
________ ________ ________ ________
Y11 1.000
Y12 0.495 1.000
Y13 0.333 0.683 1.000
Y14 0.236 0.582 0.886 1.000
MODEL FIT INFORMATION
Number of Free Parameters 13
Loglikelihood
H0 Value
Mean -3975.519
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3975.519 -3975.519
0.980 0.000 -3975.519 -3975.519
0.950 0.000 -3975.519 -3975.519
0.900 0.000 -3975.519 -3975.519
0.800 0.000 -3975.519 -3975.519
0.700 0.000 -3975.519 -3975.519
0.500 0.000 -3975.519 -3975.519
0.300 0.000 -3975.519 -3975.519
0.200 0.000 -3975.519 -3975.519
0.100 0.000 -3975.519 -3975.519
0.050 0.000 -3975.519 -3975.519
0.020 0.000 -3975.519 -3975.519
0.010 0.000 -3975.519 -3975.519
H1 Value
Mean -3975.281
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3975.281 -3975.281
0.980 0.000 -3975.281 -3975.281
0.950 0.000 -3975.281 -3975.281
0.900 0.000 -3975.281 -3975.281
0.800 0.000 -3975.281 -3975.281
0.700 0.000 -3975.281 -3975.281
0.500 0.000 -3975.281 -3975.281
0.300 0.000 -3975.281 -3975.281
0.200 0.000 -3975.281 -3975.281
0.100 0.000 -3975.281 -3975.281
0.050 0.000 -3975.281 -3975.281
0.020 0.000 -3975.281 -3975.281
0.010 0.000 -3975.281 -3975.281
Information Criteria
Akaike (AIC)
Mean 7977.038
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 7977.038 7977.038
0.980 0.000 7977.038 7977.038
0.950 0.000 7977.038 7977.038
0.900 0.000 7977.038 7977.038
0.800 0.000 7977.038 7977.038
0.700 0.000 7977.038 7977.038
0.500 0.000 7977.038 7977.038
0.300 0.000 7977.038 7977.038
0.200 0.000 7977.038 7977.038
0.100 0.000 7977.038 7977.038
0.050 0.000 7977.038 7977.038
0.020 0.000 7977.038 7977.038
0.010 0.000 7977.038 7977.038
Bayesian (BIC)
Mean 8031.828
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8031.828 8031.828
0.980 0.000 8031.828 8031.828
0.950 0.000 8031.828 8031.828
0.900 0.000 8031.828 8031.828
0.800 0.000 8031.828 8031.828
0.700 0.000 8031.828 8031.828
0.500 0.000 8031.828 8031.828
0.300 0.000 8031.828 8031.828
0.200 0.000 8031.828 8031.828
0.100 0.000 8031.828 8031.828
0.050 0.000 8031.828 8031.828
0.020 0.000 8031.828 8031.828
0.010 0.000 8031.828 8031.828
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 7990.565
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 7990.565 7990.565
0.980 0.000 7990.565 7990.565
0.950 0.000 7990.565 7990.565
0.900 0.000 7990.565 7990.565
0.800 0.000 7990.565 7990.565
0.700 0.000 7990.565 7990.565
0.500 0.000 7990.565 7990.565
0.300 0.000 7990.565 7990.565
0.200 0.000 7990.565 7990.565
0.100 0.000 7990.565 7990.565
0.050 0.000 7990.565 7990.565
0.020 0.000 7990.565 7990.565
0.010 0.000 7990.565 7990.565
Chi-Square Test of Model Fit
Degrees of freedom 1
Mean 0.475
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.000 0.475
0.980 1.000 0.001 0.475
0.950 1.000 0.004 0.475
0.900 1.000 0.016 0.475
0.800 1.000 0.064 0.475
0.700 1.000 0.148 0.475
0.500 1.000 0.455 0.475
0.300 0.000 1.074 0.475
0.200 0.000 1.642 0.475
0.100 0.000 2.706 0.475
0.050 0.000 3.841 0.475
0.020 0.000 5.412 0.475
0.010 0.000 6.635 0.475
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 0.004
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
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
I |
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
S |
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
Q |
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 4.000 4.0000 0.0000 0.0000 0.0000 1.000 0.000
Y14 9.000 9.0000 0.0000 0.0000 0.0000 1.000 0.000
I WITH
S 0.100 -0.1734 0.0000 0.3003 0.0747 1.000 0.000
Q WITH
I 0.000 0.1010 0.0000 0.0796 0.0102 1.000 0.000
S 0.000 -0.1787 0.0000 0.1172 0.0319 1.000 0.000
Means
I 0.500 0.5214 0.0000 0.0618 0.0005 1.000 1.000
S 1.000 1.0348 0.0000 0.0769 0.0012 1.000 1.000
Q 0.500 0.5121 0.0000 0.0311 0.0001 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
Variances
I 1.000 1.2462 0.0000 0.2728 0.0606 1.000 1.000
S 0.400 0.9982 0.0000 0.3581 0.3579 1.000 1.000
Q 0.200 0.2815 0.0000 0.0603 0.0066 1.000 1.000
Residual Variances
Y11 1.000 0.6855 0.0000 0.2647 0.0989 1.000 1.000
Y12 1.000 0.8822 0.0000 0.1145 0.0139 1.000 1.000
Y13 1.000 0.9460 0.0000 0.1827 0.0029 1.000 1.000
Y14 1.000 0.7379 0.0000 0.9445 0.0687 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.241E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
NU
Y11 Y12 Y13 Y14
________ ________ ________ ________
0 0 0 0
LAMBDA
I S Q
________ ________ ________
Y11 0 0 0
Y12 0 0 0
Y13 0 0 0
Y14 0 0 0
THETA
Y11 Y12 Y13 Y14
________ ________ ________ ________
Y11 1
Y12 0 2
Y13 0 0 3
Y14 0 0 0 4
ALPHA
I S Q
________ ________ ________
5 6 7
BETA
I S Q
________ ________ ________
I 0 0 0
S 0 0 0
Q 0 0 0
PSI
I S Q
________ ________ ________
I 8
S 9 10
Q 11 12 13
STARTING VALUES
NU
Y11 Y12 Y13 Y14
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
I S Q
________ ________ ________
Y11 1.000 0.000 0.000
Y12 1.000 1.000 1.000
Y13 1.000 2.000 4.000
Y14 1.000 3.000 9.000
THETA
Y11 Y12 Y13 Y14
________ ________ ________ ________
Y11 1.000
Y12 0.000 1.000
Y13 0.000 0.000 1.000
Y14 0.000 0.000 0.000 1.000
ALPHA
I S Q
________ ________ ________
0.500 1.000 0.500
BETA
I S Q
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 0.000
Q 0.000 0.000 0.000
PSI
I S Q
________ ________ ________
I 1.000
S 0.100 0.400
Q 0.000 0.000 0.200
POPULATION VALUES
NU
Y11 Y12 Y13 Y14
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
I S Q
________ ________ ________
Y11 1.000 0.000 0.000
Y12 1.000 1.000 1.000
Y13 1.000 2.000 4.000
Y14 1.000 3.000 9.000
THETA
Y11 Y12 Y13 Y14
________ ________ ________ ________
Y11 1.000
Y12 0.000 1.000
Y13 0.000 0.000 1.000
Y14 0.000 0.000 0.000 1.000
ALPHA
I S Q
________ ________ ________
0.500 1.000 0.500
BETA
I S Q
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 0.000
Q 0.000 0.000 0.000
PSI
I S Q
________ ________ ________
I 1.000
S 0.100 0.400
Q 0.000 0.000 0.200
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y11
Y12
Y13
Y14
Save file
ex6.9.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:27
Ending Time: 22:24:27
Elapsed Time: 00:00:00
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