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 zero-
inflated Poisson model
montecarlo:
names = u11-u14;
generate = u11-u14(ci);
count = u11-u14(i);
nobs = 500;
nreps = 1;
save = ex6.7.dat;
analysis:
integration = 7;
model population:
i s | u11@0 u12@1 u13@2 u14@3;
[u11-u14@0];
[i*.2 s*.005];
i*.4; s@0;
ii si | u11#1@0 u12#1@1 u13#1@2 u14#1@3;
[u11#1-u14#1*-.5];
[ii@0 si*-.2];
ii*1; si@0;
! inflation slope variance zero for simplicity
si with i-ii@0;
i with ii*-.32;
! correlation is -0.5 between i and ii
s with ii@0;
model:
i s | u11@0 u12@1 u13@2 u14@3;
[u11-u14@0];
[i*.2 s*.005];
i*.4; s@0;
ii si | u11#1@0 u12#1@1 u13#1@2 u14#1@3;
[u11#1-u14#1*-.5] (1);
[ii@0 si*-.2];
ii*1; si@0;
si with i-ii@0;
i with ii*-.32;
s with ii@0;
output:
tech8 tech9;
*** WARNING in MODEL command
All continuous latent variable covariances involving S have been fixed to 0
because the variance of S is fixed at 0.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of a linear growth
model for a count outcome using a zero-
inflated 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 4
Observed dependent variables
Count
U11 U12 U13 U14
Continuous latent variables
I S II SI
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 7
Dimensions of numerical integration 2
Adaptive quadrature ON
Cholesky ON
MODEL FIT INFORMATION
Number of Free Parameters 7
Loglikelihood
H0 Value
Mean -2778.140
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -2778.140 -2778.140
0.980 0.000 -2778.140 -2778.140
0.950 0.000 -2778.140 -2778.140
0.900 0.000 -2778.140 -2778.140
0.800 0.000 -2778.140 -2778.140
0.700 0.000 -2778.140 -2778.140
0.500 0.000 -2778.140 -2778.140
0.300 0.000 -2778.140 -2778.140
0.200 0.000 -2778.140 -2778.140
0.100 0.000 -2778.140 -2778.140
0.050 0.000 -2778.140 -2778.140
0.020 0.000 -2778.140 -2778.140
0.010 0.000 -2778.140 -2778.140
Information Criteria
Akaike (AIC)
Mean 5570.281
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 5570.281 5570.281
0.980 0.000 5570.281 5570.281
0.950 0.000 5570.281 5570.281
0.900 0.000 5570.281 5570.281
0.800 0.000 5570.281 5570.281
0.700 0.000 5570.281 5570.281
0.500 0.000 5570.281 5570.281
0.300 0.000 5570.281 5570.281
0.200 0.000 5570.281 5570.281
0.100 0.000 5570.281 5570.281
0.050 0.000 5570.281 5570.281
0.020 0.000 5570.281 5570.281
0.010 0.000 5570.281 5570.281
Bayesian (BIC)
Mean 5599.783
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 5599.783 5599.783
0.980 0.000 5599.783 5599.783
0.950 0.000 5599.783 5599.783
0.900 0.000 5599.783 5599.783
0.800 0.000 5599.783 5599.783
0.700 0.000 5599.783 5599.783
0.500 0.000 5599.783 5599.783
0.300 0.000 5599.783 5599.783
0.200 0.000 5599.783 5599.783
0.100 0.000 5599.783 5599.783
0.050 0.000 5599.783 5599.783
0.020 0.000 5599.783 5599.783
0.010 0.000 5599.783 5599.783
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 5577.565
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 5577.565 5577.565
0.980 0.000 5577.565 5577.565
0.950 0.000 5577.565 5577.565
0.900 0.000 5577.565 5577.565
0.800 0.000 5577.565 5577.565
0.700 0.000 5577.565 5577.565
0.500 0.000 5577.565 5577.565
0.300 0.000 5577.565 5577.565
0.200 0.000 5577.565 5577.565
0.100 0.000 5577.565 5577.565
0.050 0.000 5577.565 5577.565
0.020 0.000 5577.565 5577.565
0.010 0.000 5577.565 5577.565
Chi-Square Test of Model Fit for the Count Outcomes
Pearson Chi-Square
Mean 1915.459
Std Dev 0.000
Degrees of freedom 9973
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 9647.393 1915.459
0.980 0.000 9685.098 1915.459
0.950 0.000 9741.839 1915.459
0.900 0.000 9792.440 1915.459
0.800 0.000 9853.947 1915.459
0.700 0.000 9898.458 1915.459
0.500 0.000 9972.333 1915.459
0.300 0.000 10046.575 1915.459
0.200 0.000 10091.664 1915.459
0.100 0.000 10154.417 1915.459
0.050 0.000 10206.435 1915.459
0.020 0.000 10265.192 1915.459
0.010 0.000 10304.489 1915.459
Likelihood Ratio Chi-Square
Mean 652.622
Std Dev 0.000
Degrees of freedom 9973
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 9647.393 652.622
0.980 0.000 9685.098 652.622
0.950 0.000 9741.839 652.622
0.900 0.000 9792.440 652.622
0.800 0.000 9853.947 652.622
0.700 0.000 9898.458 652.622
0.500 0.000 9972.333 652.622
0.300 0.000 10046.575 652.622
0.200 0.000 10091.664 652.622
0.100 0.000 10154.417 652.622
0.050 0.000 10206.435 652.622
0.020 0.000 10265.192 652.622
0.010 0.000 10304.489 652.622
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
II |
U11#1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U12#1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U13#1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U14#1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
SI |
U11#1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U12#1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U13#1 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
U14#1 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
SI WITH
I 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
II 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
I WITH
II -0.320 -0.2037 0.0000 0.1169 0.0135 1.000 0.000
S WITH
II 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Means
I 0.200 0.3457 0.0000 0.0685 0.0212 0.000 1.000
S 0.005 -0.0480 0.0000 0.0239 0.0028 0.000 1.000
II 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
SI -0.200 -0.4833 0.0000 0.0932 0.0802 0.000 1.000
Intercepts
U11#1 -0.500 -0.1614 0.0000 0.1487 0.1146 0.000 0.000
U11 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U12#1 -0.500 -0.1614 0.0000 0.1487 0.1146 0.000 0.000
U12 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U13#1 -0.500 -0.1614 0.0000 0.1487 0.1146 0.000 0.000
U13 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U14#1 -0.500 -0.1614 0.0000 0.1487 0.1146 0.000 0.000
U14 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Variances
I 0.400 0.3858 0.0000 0.0595 0.0002 1.000 1.000
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
II 1.000 1.1823 0.0000 0.5337 0.0332 1.000 1.000
SI 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.251E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
U11#1 U11 U12#1 U12 U13#1
________ ________ ________ ________ ________
1 0 1 0 1
NU
U13 U14#1 U14
________ ________ ________
0 1 0
LAMBDA
I S II SI
________ ________ ________ ________
U11#1 0 0 0 0
U11 0 0 0 0
U12#1 0 0 0 0
U12 0 0 0 0
U13#1 0 0 0 0
U13 0 0 0 0
U14#1 0 0 0 0
U14 0 0 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 II SI
________ ________ ________ ________
2 3 0 4
BETA
I S II SI
________ ________ ________ ________
I 0 0 0 0
S 0 0 0 0
II 0 0 0 0
SI 0 0 0 0
PSI
I S II SI
________ ________ ________ ________
I 5
S 0 0
II 6 0 7
SI 0 0 0 0
STARTING VALUES
NU
U11#1 U11 U12#1 U12 U13#1
________ ________ ________ ________ ________
-0.500 0.000 -0.500 0.000 -0.500
NU
U13 U14#1 U14
________ ________ ________
0.000 -0.500 0.000
LAMBDA
I S II SI
________ ________ ________ ________
U11#1 0.000 0.000 1.000 0.000
U11 1.000 0.000 0.000 0.000
U12#1 0.000 0.000 1.000 1.000
U12 1.000 1.000 0.000 0.000
U13#1 0.000 0.000 1.000 2.000
U13 1.000 2.000 0.000 0.000
U14#1 0.000 0.000 1.000 3.000
U14 1.000 3.000 0.000 0.000
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 II SI
________ ________ ________ ________
0.200 0.005 0.000 -0.200
BETA
I S II SI
________ ________ ________ ________
I 0.000 0.000 0.000 0.000
S 0.000 0.000 0.000 0.000
II 0.000 0.000 0.000 0.000
SI 0.000 0.000 0.000 0.000
PSI
I S II SI
________ ________ ________ ________
I 0.400
S 0.000 0.000
II -0.320 0.000 1.000
SI 0.000 0.000 0.000 0.000
POPULATION VALUES
NU
U11#1 U11 U12#1 U12 U13#1
________ ________ ________ ________ ________
-0.500 0.000 -0.500 0.000 -0.500
NU
U13 U14#1 U14
________ ________ ________
0.000 -0.500 0.000
LAMBDA
I S II SI
________ ________ ________ ________
U11#1 0.000 0.000 1.000 0.000
U11 1.000 0.000 0.000 0.000
U12#1 0.000 0.000 1.000 1.000
U12 1.000 1.000 0.000 0.000
U13#1 0.000 0.000 1.000 2.000
U13 1.000 2.000 0.000 0.000
U14#1 0.000 0.000 1.000 3.000
U14 1.000 3.000 0.000 0.000
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 II SI
________ ________ ________ ________
0.200 0.005 0.000 -0.200
BETA
I S II SI
________ ________ ________ ________
I 0.000 0.000 0.000 0.000
S 0.000 0.000 0.000 0.000
II 0.000 0.000 0.000 0.000
SI 0.000 0.000 0.000 0.000
PSI
I S II SI
________ ________ ________ ________
I 0.400
S 0.000 0.000
II -0.320 0.000 1.000
SI 0.000 0.000 0.000 0.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.27881701D+04 0.0000000 0.0000000 EM
2 -0.27786996D+04 9.4705755 0.0033967 FS
3 -0.27781797D+04 0.5198755 0.0001871 FS
4 -0.27781473D+04 0.0324439 0.0000117 FS
5 -0.27781411D+04 0.0061493 0.0000022 FS
6 -0.27781404D+04 0.0006919 0.0000002 FS
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U11
U12
U13
U14
Save file
ex6.7.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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