Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
TITLE:
this is an example of a linear growth
model for a continuous outcome with first-
order auto correlated residuals using non-
linear constraints
MONTECARLO:
NAMES = y1-y4;
NOBS = 1000;
NREPS = 1;
SAVE = ex6.17.dat;
MODEL POPULATION:
i s | y1@0 y2@1 y3@2 y4@3;
[i*0 s*1];
i*1 s*.2;
y1-y4*1;
y1-y3 PWITH y2-y4*.3;
y1-y2 PWITH y3-y4*.09;
y1 WITH y4*.027;
MODEL:
i s | y1@0 y2@1 y3@2 y4@3;
[i*0 s*1];
i*1 s*.2;
y1-y4*1 (resvar);
y1-y3 PWITH y2-y4*.3 (p1);
y1-y2 PWITH y3-y4*.09 (p2);
y1 WITH y4*.027 (p3);
MODEL CONSTRAINT:
NEW(corr*0.3);
p1 = resvar*corr;
p2 = resvar*corr**2;
p3 = resvar*corr**3;
OUTPUT:
TECH9;
INPUT READING TERMINATED NORMALLY
this is an example of a linear growth
model for a continuous outcome with first-
order auto correlated residuals using non-
linear constraints
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
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 2
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Continuous latent variables
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
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.016 1.027 2.001 3.053
Covariances
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.897
Y2 1.302 2.295
Y3 1.045 1.835 2.982
Y4 1.039 1.772 2.698 4.006
Correlations
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.000
Y2 0.624 1.000
Y3 0.439 0.701 1.000
Y4 0.377 0.584 0.781 1.000
MODEL FIT INFORMATION
Number of Free Parameters 7
Loglikelihood
H0 Value
Mean -6593.460
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -6593.460 -6593.460
0.980 0.000 -6593.460 -6593.460
0.950 0.000 -6593.460 -6593.460
0.900 0.000 -6593.460 -6593.460
0.800 0.000 -6593.460 -6593.460
0.700 0.000 -6593.460 -6593.460
0.500 0.000 -6593.460 -6593.460
0.300 0.000 -6593.460 -6593.460
0.200 0.000 -6593.460 -6593.460
0.100 0.000 -6593.460 -6593.460
0.050 0.000 -6593.460 -6593.460
0.020 0.000 -6593.460 -6593.460
0.010 0.000 -6593.460 -6593.460
H1 Value
Mean -6592.226
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -6592.226 -6592.226
0.980 0.000 -6592.226 -6592.226
0.950 0.000 -6592.226 -6592.226
0.900 0.000 -6592.226 -6592.226
0.800 0.000 -6592.226 -6592.226
0.700 0.000 -6592.226 -6592.226
0.500 0.000 -6592.226 -6592.226
0.300 0.000 -6592.226 -6592.226
0.200 0.000 -6592.226 -6592.226
0.100 0.000 -6592.226 -6592.226
0.050 0.000 -6592.226 -6592.226
0.020 0.000 -6592.226 -6592.226
0.010 0.000 -6592.226 -6592.226
Information Criteria
Akaike (AIC)
Mean 13200.921
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 13200.921 13200.921
0.980 0.000 13200.921 13200.921
0.950 0.000 13200.921 13200.921
0.900 0.000 13200.921 13200.921
0.800 0.000 13200.921 13200.921
0.700 0.000 13200.921 13200.921
0.500 0.000 13200.921 13200.921
0.300 0.000 13200.921 13200.921
0.200 0.000 13200.921 13200.921
0.100 0.000 13200.921 13200.921
0.050 0.000 13200.921 13200.921
0.020 0.000 13200.921 13200.921
0.010 0.000 13200.921 13200.921
Bayesian (BIC)
Mean 13235.275
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 13235.275 13235.275
0.980 0.000 13235.275 13235.275
0.950 0.000 13235.275 13235.275
0.900 0.000 13235.275 13235.275
0.800 0.000 13235.275 13235.275
0.700 0.000 13235.275 13235.275
0.500 0.000 13235.275 13235.275
0.300 0.000 13235.275 13235.275
0.200 0.000 13235.275 13235.275
0.100 0.000 13235.275 13235.275
0.050 0.000 13235.275 13235.275
0.020 0.000 13235.275 13235.275
0.010 0.000 13235.275 13235.275
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 13213.043
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 13213.043 13213.043
0.980 0.000 13213.043 13213.043
0.950 0.000 13213.043 13213.043
0.900 0.000 13213.043 13213.043
0.800 0.000 13213.043 13213.043
0.700 0.000 13213.043 13213.043
0.500 0.000 13213.043 13213.043
0.300 0.000 13213.043 13213.043
0.200 0.000 13213.043 13213.043
0.100 0.000 13213.043 13213.043
0.050 0.000 13213.043 13213.043
0.020 0.000 13213.043 13213.043
0.010 0.000 13213.043 13213.043
Chi-Square Test of Model Fit
Degrees of freedom 7
Mean 2.469
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 1.239 2.469
0.980 1.000 1.564 2.469
0.950 1.000 2.167 2.469
0.900 0.000 2.833 2.469
0.800 0.000 3.822 2.469
0.700 0.000 4.671 2.469
0.500 0.000 6.346 2.469
0.300 0.000 8.383 2.469
0.200 0.000 9.803 2.469
0.100 0.000 12.017 2.469
0.050 0.000 14.067 2.469
0.020 0.000 16.622 2.469
0.010 0.000 18.475 2.469
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 0.006
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 |
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S |
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
S WITH
I 0.000 0.1389 0.0000 0.0518 0.0193 0.000 1.000
Y1 WITH
Y2 0.300 0.7337 0.0000 0.2092 0.1881 0.000 1.000
Y3 0.090 0.3684 0.0000 0.1537 0.0775 1.000 1.000
Y4 0.027 0.1849 0.0000 0.1016 0.0249 1.000 0.000
Y2 WITH
Y3 0.300 0.7337 0.0000 0.2092 0.1881 0.000 1.000
Y4 0.090 0.3684 0.0000 0.1537 0.0775 1.000 1.000
Y3 WITH
Y4 0.300 0.7337 0.0000 0.2092 0.1881 0.000 1.000
Means
I 0.000 0.0112 0.0000 0.0423 0.0001 1.000 0.000
S 1.000 1.0111 0.0000 0.0206 0.0001 1.000 1.000
Intercepts
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
I 1.000 0.4236 0.0000 0.2528 0.3322 0.000 0.000
S 0.200 0.1420 0.0000 0.0343 0.0034 1.000 1.000
Residual Variances
Y1 1.000 1.4615 0.0000 0.2252 0.2130 0.000 1.000
Y2 1.000 1.4615 0.0000 0.2252 0.2130 0.000 1.000
Y3 1.000 1.4615 0.0000 0.2252 0.2130 0.000 1.000
Y4 1.000 1.4615 0.0000 0.2252 0.2130 0.000 1.000
New/Additional Parameters
CORR 0.300 0.5020 0.0000 0.0666 0.0408 0.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.159E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0 0 0 0
LAMBDA
I S
________ ________
Y1 0 0
Y2 0 0
Y3 0 0
Y4 0 0
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1
Y2 2 1
Y3 3 2 1
Y4 4 3 2 1
ALPHA
I S
________ ________
5 6
BETA
I S
________ ________
I 0 0
S 0 0
PSI
I S
________ ________
I 7
S 8 9
PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS
New/Additional Parameters
CORR
________
10
STARTING VALUES
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
I S
________ ________
Y1 1.000 0.000
Y2 1.000 1.000
Y3 1.000 2.000
Y4 1.000 3.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.000
Y2 0.300 1.000
Y3 0.090 0.300 1.000
Y4 0.027 0.090 0.300 1.000
ALPHA
I S
________ ________
0.000 1.000
BETA
I S
________ ________
I 0.000 0.000
S 0.000 0.000
PSI
I S
________ ________
I 1.000
S 0.000 0.200
STARTING VALUES FOR THE ADDITIONAL PARAMETERS
New/Additional Parameters
CORR
________
0.300
POPULATION VALUES
NU
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
I S
________ ________
Y1 1.000 0.000
Y2 1.000 1.000
Y3 1.000 2.000
Y4 1.000 3.000
THETA
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.000
Y2 0.300 1.000
Y3 0.090 0.300 1.000
Y4 0.027 0.090 0.300 1.000
ALPHA
I S
________ ________
0.000 1.000
BETA
I S
________ ________
I 0.000 0.000
S 0.000 0.000
PSI
I S
________ ________
I 1.000
S 0.000 0.200
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Save file
ex6.17.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:17
Ending Time: 22:24:17
Elapsed Time: 00:00:00
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