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 count outcome using a Poisson
model
montecarlo:
names = u11-u14;
generate = u11-u14(c);
count = u11-u14;
nobs = 500;
nreps = 1;
save = ex6.6.dat;
model population:
i s | u11@0 u12@1 u13@2 u14@3;
[u11-u14@0];
[i*.2 s*.005];
i*.4; s*.1; i with s*0;
model:
i s | u11@0 u12@1 u13@2 u14@3;
[u11-u14@0];
[i*.2 s*.005];
i*.4; s*.1; i with s*0;
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a linear growth
model for a count outcome using a Poisson
model
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 2
Observed dependent variables
Count
U11 U12 U13 U14
Continuous latent variables
I S
Estimator MLR
Information matrix OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 100
Convergence criterion 0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations 500
Convergence criteria
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Maximum value for logit thresholds 15
Minimum value for logit thresholds -15
Minimum expected cell size for chi-square 0.100D-01
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 15
Dimensions of numerical integration 2
Adaptive quadrature ON
Cholesky ON
MODEL FIT INFORMATION
Number of Free Parameters 5
Loglikelihood
H0 Value
Mean -3446.329
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3446.329 -3446.329
0.980 0.000 -3446.329 -3446.329
0.950 0.000 -3446.329 -3446.329
0.900 0.000 -3446.329 -3446.329
0.800 0.000 -3446.329 -3446.329
0.700 0.000 -3446.329 -3446.329
0.500 0.000 -3446.329 -3446.329
0.300 0.000 -3446.329 -3446.329
0.200 0.000 -3446.329 -3446.329
0.100 0.000 -3446.329 -3446.329
0.050 0.000 -3446.329 -3446.329
0.020 0.000 -3446.329 -3446.329
0.010 0.000 -3446.329 -3446.329
Information Criteria
Akaike (AIC)
Mean 6902.657
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6902.657 6902.657
0.980 0.000 6902.657 6902.657
0.950 0.000 6902.657 6902.657
0.900 0.000 6902.657 6902.657
0.800 0.000 6902.657 6902.657
0.700 0.000 6902.657 6902.657
0.500 0.000 6902.657 6902.657
0.300 0.000 6902.657 6902.657
0.200 0.000 6902.657 6902.657
0.100 0.000 6902.657 6902.657
0.050 0.000 6902.657 6902.657
0.020 0.000 6902.657 6902.657
0.010 0.000 6902.657 6902.657
Bayesian (BIC)
Mean 6923.730
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6923.730 6923.730
0.980 0.000 6923.730 6923.730
0.950 0.000 6923.730 6923.730
0.900 0.000 6923.730 6923.730
0.800 0.000 6923.730 6923.730
0.700 0.000 6923.730 6923.730
0.500 0.000 6923.730 6923.730
0.300 0.000 6923.730 6923.730
0.200 0.000 6923.730 6923.730
0.100 0.000 6923.730 6923.730
0.050 0.000 6923.730 6923.730
0.020 0.000 6923.730 6923.730
0.010 0.000 6923.730 6923.730
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 6907.860
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6907.860 6907.860
0.980 0.000 6907.860 6907.860
0.950 0.000 6907.860 6907.860
0.900 0.000 6907.860 6907.860
0.800 0.000 6907.860 6907.860
0.700 0.000 6907.860 6907.860
0.500 0.000 6907.860 6907.860
0.300 0.000 6907.860 6907.860
0.200 0.000 6907.860 6907.860
0.100 0.000 6907.860 6907.860
0.050 0.000 6907.860 6907.860
0.020 0.000 6907.860 6907.860
0.010 0.000 6907.860 6907.860
Chi-Square Test of Model Fit for the Count Outcomes
Pearson Chi-Square
Mean 3715.328
Std Dev 0.000
Degrees of freedom 8974
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8665.283 3715.328
0.980 0.000 8701.009 3715.328
0.950 0.000 8754.782 3715.328
0.900 0.000 8802.744 3715.328
0.800 0.000 8861.058 3715.328
0.700 0.000 8903.266 3715.328
0.500 0.000 8973.333 3715.328
0.300 0.000 9043.768 3715.328
0.200 0.000 9086.553 3715.328
0.100 0.000 9146.112 3715.328
0.050 0.000 9195.492 3715.328
0.020 0.000 9251.282 3715.328
0.010 0.000 9288.599 3715.328
Likelihood Ratio Chi-Square
Mean 1095.234
Std Dev 0.000
Degrees of freedom 8974
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8665.283 1095.234
0.980 0.000 8701.009 1095.234
0.950 0.000 8754.782 1095.234
0.900 0.000 8802.744 1095.234
0.800 0.000 8861.058 1095.234
0.700 0.000 8903.266 1095.234
0.500 0.000 8973.333 1095.234
0.300 0.000 9043.768 1095.234
0.200 0.000 9086.553 1095.234
0.100 0.000 9146.112 1095.234
0.050 0.000 9195.492 1095.234
0.020 0.000 9251.282 1095.234
0.010 0.000 9288.599 1095.234
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
I |
U11 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U12 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U13 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U14 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S |
U11 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U12 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U13 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
U14 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
I WITH
S 0.000 0.0220 0.0000 0.0193 0.0005 1.000 0.000
Means
I 0.200 0.2038 0.0000 0.0471 0.0000 1.000 1.000
S 0.005 0.0390 0.0000 0.0250 0.0012 1.000 0.000
Intercepts
U11 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U12 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U13 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U14 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
I 0.400 0.3725 0.0000 0.0521 0.0008 1.000 1.000
S 0.100 0.0943 0.0000 0.0120 0.0000 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.502E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
U11#1 U11 U12#1 U12 U13#1
________ ________ ________ ________ ________
0 0 0 0 0
NU
U13 U14#1 U14
________ ________ ________
0 0 0
LAMBDA
I S
________ ________
U11#1 0 0
U11 0 0
U12#1 0 0
U12 0 0
U13#1 0 0
U13 0 0
U14#1 0 0
U14 0 0
THETA
U11#1 U11 U12#1 U12 U13#1
________ ________ ________ ________ ________
U11#1 0
U11 0 0
U12#1 0 0 0
U12 0 0 0 0
U13#1 0 0 0 0 0
U13 0 0 0 0 0
U14#1 0 0 0 0 0
U14 0 0 0 0 0
THETA
U13 U14#1 U14
________ ________ ________
U13 0
U14#1 0 0
U14 0 0 0
ALPHA
I S
________ ________
1 2
BETA
I S
________ ________
I 0 0
S 0 0
PSI
I S
________ ________
I 3
S 4 5
STARTING VALUES
NU
U11#1 U11 U12#1 U12 U13#1
________ ________ ________ ________ ________
-20.000 0.000 -20.000 0.000 -20.000
NU
U13 U14#1 U14
________ ________ ________
0.000 -20.000 0.000
LAMBDA
I S
________ ________
U11#1 0.000 0.000
U11 1.000 0.000
U12#1 0.000 0.000
U12 1.000 1.000
U13#1 0.000 0.000
U13 1.000 2.000
U14#1 0.000 0.000
U14 1.000 3.000
THETA
U11#1 U11 U12#1 U12 U13#1
________ ________ ________ ________ ________
U11#1 0.000
U11 0.000 0.000
U12#1 0.000 0.000 0.000
U12 0.000 0.000 0.000 0.000
U13#1 0.000 0.000 0.000 0.000 0.000
U13 0.000 0.000 0.000 0.000 0.000
U14#1 0.000 0.000 0.000 0.000 0.000
U14 0.000 0.000 0.000 0.000 0.000
THETA
U13 U14#1 U14
________ ________ ________
U13 0.000
U14#1 0.000 0.000
U14 0.000 0.000 0.000
ALPHA
I S
________ ________
0.200 0.005
BETA
I S
________ ________
I 0.000 0.000
S 0.000 0.000
PSI
I S
________ ________
I 0.400
S 0.000 0.100
POPULATION VALUES
NU
U11#1 U11 U12#1 U12 U13#1
________ ________ ________ ________ ________
-20.000 0.000 -20.000 0.000 -20.000
NU
U13 U14#1 U14
________ ________ ________
0.000 -20.000 0.000
LAMBDA
I S
________ ________
U11#1 0.000 0.000
U11 1.000 0.000
U12#1 0.000 0.000
U12 1.000 1.000
U13#1 0.000 0.000
U13 1.000 2.000
U14#1 0.000 0.000
U14 1.000 3.000
THETA
U11#1 U11 U12#1 U12 U13#1
________ ________ ________ ________ ________
U11#1 0.000
U11 0.000 0.000
U12#1 0.000 0.000 0.000
U12 0.000 0.000 0.000 0.000
U13#1 0.000 0.000 0.000 0.000 0.000
U13 0.000 0.000 0.000 0.000 0.000
U14#1 0.000 0.000 0.000 0.000 0.000
U14 0.000 0.000 0.000 0.000 0.000
THETA
U13 U14#1 U14
________ ________ ________
U13 0.000
U14#1 0.000 0.000
U14 0.000 0.000 0.000
ALPHA
I S
________ ________
0.200 0.005
BETA
I S
________ ________
I 0.000 0.000
S 0.000 0.000
PSI
I S
________ ________
I 0.400
S 0.000 0.100
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.34489730D+04 0.0000000 0.0000000 EM
2 -0.34470743D+04 1.8986788 0.0005505 FS
3 -0.34463634D+04 0.7109007 0.0002062 FS
4 -0.34463244D+04 0.0390098 0.0000113 FS
5 -0.34463285D+04 -0.0041590 -0.0000012 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U11
U12
U13
U14
Save file
ex6.6.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:26
Ending Time: 22:24:26
Elapsed Time: 00:00:00
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