Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:12 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a linear growth
model for a count outcome using a Poisson
model
DATA: FILE IS ex6.6.dat;
VARIABLE: NAMES ARE u11-u14;
COUNT ARE u11-u14;
MODEL: i s | u11@0 u12@1 u13@2 u14@3;
OUTPUT: TECH1 TECH8;
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 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
Input data file(s)
ex6.6.dat
Input data format FREE
COUNT PROPORTION OF ZERO, MINIMUM AND MAXIMUM VALUES
U11 0.308 0 8
U12 0.320 0 11
U13 0.330 0 19
U14 0.306 0 71
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 5
Loglikelihood
H0 Value -3446.329
H0 Scaling Correction Factor 0.9141
for MLR
Information Criteria
Akaike (AIC) 6902.658
Bayesian (BIC) 6923.732
Sample-Size Adjusted BIC 6907.861
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Count Outcomes**
Pearson Chi-Square
Value 3714.728
Degrees of Freedom 8974
P-Value 1.0000
Likelihood Ratio Chi-Square
Value 1095.265
Degrees of Freedom 8974
P-Value 1.0000
** Of the 9000 cells in the frequency table, 20
were deleted in the calculation of chi-square due to extreme values.
** Large values were truncated at 9.
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
I |
U11 1.000 0.000 999.000 999.000
U12 1.000 0.000 999.000 999.000
U13 1.000 0.000 999.000 999.000
U14 1.000 0.000 999.000 999.000
S |
U11 0.000 0.000 999.000 999.000
U12 1.000 0.000 999.000 999.000
U13 2.000 0.000 999.000 999.000
U14 3.000 0.000 999.000 999.000
S WITH
I 0.022 0.019 1.138 0.255
Means
I 0.204 0.047 4.327 0.000
S 0.039 0.025 1.559 0.119
Intercepts
U11 0.000 0.000 999.000 999.000
U12 0.000 0.000 999.000 999.000
U13 0.000 0.000 999.000 999.000
U14 0.000 0.000 999.000 999.000
Variances
I 0.373 0.052 7.154 0.000
S 0.094 0.012 7.878 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.503E-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
________ ________
1.352 0.392
BETA
I S
________ ________
I 0.000 0.000
S 0.000 0.000
PSI
I S
________ ________
I 1.967
S 0.000 2.080
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.41106741D+04 0.0000000 0.0000000 EM
2 -0.39536496D+04 157.0245182 0.0381992 FS
3 -0.38759349D+04 77.7147670 0.0196565 EM
4 -0.38200731D+04 55.8617847 0.0144125 EM
5 -0.37813327D+04 38.7403643 0.0101413 EM
6 -0.37542455D+04 27.0872313 0.0071634 EM
7 -0.37334131D+04 20.8323939 0.0055490 EM
8 -0.37154960D+04 17.9171193 0.0047991 EM
9 -0.36989258D+04 16.5702132 0.0044598 EM
10 -0.36830616D+04 15.8641845 0.0042889 EM
11 -0.36677002D+04 15.3613202 0.0041708 EM
12 -0.36528038D+04 14.8964664 0.0040615 EM
13 -0.36384024D+04 14.4013483 0.0039425 EM
14 -0.36245251D+04 13.8773351 0.0038141 EM
15 -0.36112222D+04 13.3028611 0.0036702 EM
16 -0.35985160D+04 12.7061945 0.0035185 EM
17 -0.35864429D+04 12.0731188 0.0033550 EM
18 -0.35750103D+04 11.4326561 0.0031877 EM
19 -0.35642346D+04 10.7756918 0.0030142 EM
20 -0.35541105D+04 10.1241162 0.0028405 EM
21 -0.35446368D+04 9.4736675 0.0026656 EM
22 -0.35357988D+04 8.8380381 0.0024934 EM
23 -0.35275824D+04 8.2163726 0.0023238 EM
24 -0.35199663D+04 7.6160872 0.0021590 EM
25 -0.35129284D+04 7.0378809 0.0019994 EM
26 -0.35064431D+04 6.4853128 0.0018461 EM
27 -0.35004838D+04 5.9592714 0.0016995 EM
28 -0.34950226D+04 5.4612087 0.0015601 EM
29 -0.34900311D+04 4.9915654 0.0014282 EM
30 -0.34854804D+04 4.5506512 0.0013039 EM
31 -0.34813421D+04 4.1383290 0.0011873 EM
32 -0.34775878D+04 3.7542281 0.0010784 EM
33 -0.34741901D+04 3.3977248 0.0009770 EM
34 -0.34711221D+04 3.0680078 0.0008831 EM
35 -0.34683580D+04 2.7641041 0.0007963 EM
36 -0.34658731D+04 2.4849177 0.0007165 EM
37 -0.34636438D+04 2.2292559 0.0006432 EM
38 -0.34616480D+04 1.9958567 0.0005762 EM
39 -0.34598646D+04 1.7834148 0.0005152 EM
40 -0.34582740D+04 1.5906023 0.0004597 EM
41 -0.34568579D+04 1.4160860 0.0004095 EM
42 -0.34555993D+04 1.2585475 0.0003641 EM
43 -0.34544826D+04 1.1166949 0.0003232 EM
44 -0.34534934D+04 0.9892756 0.0002864 EM
45 -0.34471191D+04 6.3742866 0.0018458 FS
46 -0.34463775D+04 0.7415830 0.0002151 FS
47 -0.34463317D+04 0.0458161 0.0000133 FS
48 -0.34463243D+04 0.0073372 0.0000021 FS
49 -0.34463292D+04 -0.0048998 -0.0000014 EM
Beginning Time: 23:12:50
Ending Time: 23:12:54
Elapsed Time: 00:00:04
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