Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a zero-inflated
Poisson regression carried out as a two-
class model
MONTECARLO:
NAMES = u1 x1 x3;
NOBSERVATIONS = 500;
NREPS = 1;
SEED = 53487;
GENCLASSES = c(2);
CLASSES = c(2);
GENERATE = u1(c);
COUNT = u1;
SAVE = ex7.25.dat;
MODEL POPULATION:
%OVERALL%
[x1-x3@0];
x1-x3@1;
[c#1*-1];
c#1 ON x1*2 x3*1;
%c#1%
[u1@-15];
u1 ON x1@0 x3@0;
%c#2%
[u1*1];
u1 ON x1*.5 x3*.3;
ANALYSIS:
TYPE = MIXTURE;
MODEL:
%OVERALL%
[c#1*-1];
c#1 ON x1*2 x3*1;
%c#1%
[u1@-15];
u1 ON x1@0 x3@0;
%c#2%
[u1*1];
u1 ON x1*.5 x3*.3;
OUTPUT: TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a zero-inflated
Poisson regression carried out as a two-
class model
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 53487
Number of dependent variables 1
Number of independent variables 2
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Count
U1
Observed independent variables
X1 X3
Categorical latent variables
C
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-06
Relative loglikelihood change 0.100D-06
Derivative 0.100D-05
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-05
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-05
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
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
X1 X3
________ ________
0.020 -0.022
Covariances
X1 X3
________ ________
X1 1.070
X3 0.043 0.974
Correlations
X1 X3
________ ________
X1 1.000
X3 0.042 1.000
MODEL FIT INFORMATION
Number of Free Parameters 6
Loglikelihood
H0 Value
Mean -724.663
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -724.663 -724.663
0.980 0.000 -724.663 -724.663
0.950 0.000 -724.663 -724.663
0.900 0.000 -724.663 -724.663
0.800 0.000 -724.663 -724.663
0.700 0.000 -724.663 -724.663
0.500 0.000 -724.663 -724.663
0.300 0.000 -724.663 -724.663
0.200 0.000 -724.663 -724.663
0.100 0.000 -724.663 -724.663
0.050 0.000 -724.663 -724.663
0.020 0.000 -724.663 -724.663
0.010 0.000 -724.663 -724.663
Information Criteria
Akaike (AIC)
Mean 1461.327
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1461.327 1461.327
0.980 0.000 1461.327 1461.327
0.950 0.000 1461.327 1461.327
0.900 0.000 1461.327 1461.327
0.800 0.000 1461.327 1461.327
0.700 0.000 1461.327 1461.327
0.500 0.000 1461.327 1461.327
0.300 0.000 1461.327 1461.327
0.200 0.000 1461.327 1461.327
0.100 0.000 1461.327 1461.327
0.050 0.000 1461.327 1461.327
0.020 0.000 1461.327 1461.327
0.010 0.000 1461.327 1461.327
Bayesian (BIC)
Mean 1486.614
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1486.614 1486.614
0.980 0.000 1486.614 1486.614
0.950 0.000 1486.614 1486.614
0.900 0.000 1486.614 1486.614
0.800 0.000 1486.614 1486.614
0.700 0.000 1486.614 1486.614
0.500 0.000 1486.614 1486.614
0.300 0.000 1486.614 1486.614
0.200 0.000 1486.614 1486.614
0.100 0.000 1486.614 1486.614
0.050 0.000 1486.614 1486.614
0.020 0.000 1486.614 1486.614
0.010 0.000 1486.614 1486.614
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 1467.570
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1467.570 1467.570
0.980 0.000 1467.570 1467.570
0.950 0.000 1467.570 1467.570
0.900 0.000 1467.570 1467.570
0.800 0.000 1467.570 1467.570
0.700 0.000 1467.570 1467.570
0.500 0.000 1467.570 1467.570
0.300 0.000 1467.570 1467.570
0.200 0.000 1467.570 1467.570
0.100 0.000 1467.570 1467.570
0.050 0.000 1467.570 1467.570
0.020 0.000 1467.570 1467.570
0.010 0.000 1467.570 1467.570
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 173.59129 0.34718
2 326.40871 0.65282
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 173.59106 0.34718
2 326.40894 0.65282
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 177 0.35400
2 323 0.64600
CLASSIFICATION QUALITY
Entropy 0.896
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.947 0.053
2 0.019 0.981
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.966 0.034
2 0.029 0.971
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 3.333 0.000
2 -3.519 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
U1 ON
X1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
X3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Intercepts
U1 -15.000 -15.0000 0.0000 0.0000 0.0000 1.000 0.000
Latent Class 2
U1 ON
X1 0.500 0.6338 0.0000 0.0494 0.0179 0.000 1.000
X3 0.300 0.2867 0.0000 0.0356 0.0002 1.000 1.000
Intercepts
U1 1.000 1.0420 0.0000 0.0400 0.0018 1.000 1.000
Categorical Latent Variables
C#1 ON
X1 2.000 2.1891 0.0000 0.2913 0.0358 1.000 1.000
X3 1.000 0.9605 0.0000 0.1722 0.0016 1.000 1.000
Intercepts
C#1 -1.000 -1.2379 0.0000 0.2244 0.0566 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.120E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
X1 X3
________ ________
0 0
LAMBDA
X1 X3
________ ________
X1 0 0
X3 0 0
THETA
X1 X3
________ ________
X1 0
X3 0 0
ALPHA
X1 X3
________ ________
0 0
BETA
X1 X3
________ ________
X1 0 0
X3 0 0
PSI
X1 X3
________ ________
X1 0
X3 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
X1 X3
________ ________
0 0
LAMBDA
X1 X3
________ ________
X1 0 0
X3 0 0
THETA
X1 X3
________ ________
X1 0
X3 0 0
ALPHA
X1 X3
________ ________
0 0
BETA
X1 X3
________ ________
X1 0 0
X3 0 0
PSI
X1 X3
________ ________
X1 0
X3 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 0
GAMMA(C)
X1 X3
________ ________
C#1 2 3
C#2 0 0
PARAMETER SPECIFICATION FOR THE CENSORED/NOMINAL/COUNT MODEL PART
NU(P) FOR LATENT CLASS 1
U1#1 U1
________ ________
0 0
KAPPA(P) FOR LATENT CLASS 1
X1 X3
________ ________
U1#1 0 0
U1 0 0
NU(P) FOR LATENT CLASS 2
U1#1 U1
________ ________
0 4
KAPPA(P) FOR LATENT CLASS 2
X1 X3
________ ________
U1#1 0 0
U1 5 6
STARTING VALUES FOR LATENT CLASS 1
NU
X1 X3
________ ________
0.000 0.000
LAMBDA
X1 X3
________ ________
X1 1.000 0.000
X3 0.000 1.000
THETA
X1 X3
________ ________
X1 0.000
X3 0.000 0.000
ALPHA
X1 X3
________ ________
0.000 0.000
BETA
X1 X3
________ ________
X1 0.000 0.000
X3 0.000 0.000
PSI
X1 X3
________ ________
X1 0.500
X3 0.000 0.500
STARTING VALUES FOR LATENT CLASS 2
NU
X1 X3
________ ________
0.000 0.000
LAMBDA
X1 X3
________ ________
X1 1.000 0.000
X3 0.000 1.000
THETA
X1 X3
________ ________
X1 0.000
X3 0.000 0.000
ALPHA
X1 X3
________ ________
0.000 0.000
BETA
X1 X3
________ ________
X1 0.000 0.000
X3 0.000 0.000
PSI
X1 X3
________ ________
X1 0.500
X3 0.000 0.500
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
-1.000 0.000
GAMMA(C)
X1 X3
________ ________
C#1 2.000 1.000
C#2 0.000 0.000
STARTING VALUES FOR THE CENSORED/NOMINAL/COUNT MODEL PART
NU(P) FOR LATENT CLASS 1
U1#1 U1
________ ________
-20.000 -15.000
KAPPA(P) FOR LATENT CLASS 1
X1 X3
________ ________
U1#1 0.000 0.000
U1 0.000 0.000
NU(P) FOR LATENT CLASS 2
U1#1 U1
________ ________
-20.000 1.000
KAPPA(P) FOR LATENT CLASS 2
X1 X3
________ ________
U1#1 0.000 0.000
U1 0.500 0.300
POPULATION VALUES FOR LATENT CLASS 1
NU
X1 X3
________ ________
0.000 0.000
LAMBDA
X1 X3
________ ________
X1 1.000 0.000
X3 0.000 1.000
THETA
X1 X3
________ ________
X1 0.000
X3 0.000 0.000
ALPHA
X1 X3
________ ________
0.000 0.000
BETA
X1 X3
________ ________
X1 0.000 0.000
X3 0.000 0.000
PSI
X1 X3
________ ________
X1 1.000
X3 0.000 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
X1 X3
________ ________
0.000 0.000
LAMBDA
X1 X3
________ ________
X1 1.000 0.000
X3 0.000 1.000
THETA
X1 X3
________ ________
X1 0.000
X3 0.000 0.000
ALPHA
X1 X3
________ ________
0.000 0.000
BETA
X1 X3
________ ________
X1 0.000 0.000
X3 0.000 0.000
PSI
X1 X3
________ ________
X1 1.000
X3 0.000 1.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
-1.000 0.000
GAMMA(C)
X1 X3
________ ________
C#1 2.000 1.000
C#2 0.000 0.000
POPULATION VALUES FOR THE CENSORED/NOMINAL/COUNT MODEL PART
NU(P) FOR LATENT CLASS 1
U1#1 U1
________ ________
-20.000 -15.000
KAPPA(P) FOR LATENT CLASS 1
X1 X3
________ ________
U1#1 0.000 0.000
U1 0.000 0.000
NU(P) FOR LATENT CLASS 2
U1#1 U1
________ ________
-20.000 1.000
KAPPA(P) FOR LATENT CLASS 2
X1 X3
________ ________
U1#1 0.000 0.000
U1 0.500 0.300
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.73014011D+03 0.0000000 0.0000000 EM
2 -0.72494737D+03 5.1927433 0.0071120 EM
3 -0.72474129D+03 0.2060785 0.0002843 EM
4 -0.72468796D+03 0.0533283 0.0000736 EM
5 -0.72467135D+03 0.0166102 0.0000229 EM
6 -0.72466597D+03 0.0053806 0.0000074 EM
7 -0.72466422D+03 0.0017549 0.0000024 EM
8 -0.72466364D+03 0.0005723 0.0000008 EM
9 -0.72466346D+03 0.0001865 0.0000003 EM
10 -0.72466340D+03 0.0000607 0.0000001 EM
11 -0.72466338D+03 0.0000198 0.0000000 EM
12 -0.72466337D+03 0.0000064 0.0000000 EM
13 -0.72466337D+03 0.0000021 0.0000000 EM
14 -0.72466337D+03 0.0000007 0.0000000 EM
15 -0.72466337D+03 0.0000002 0.0000000 EM
16 -0.72466337D+03 0.0000001 0.0000000 EM
17 -0.72466337D+03 0.0000000 0.0000000 EM
18 -0.72466337D+03 0.0000000 0.0000000 EM
SAVEDATA INFORMATION
Order of variables
U1
X1
X3
C
Save file
ex7.25.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:34
Ending Time: 22:24:34
Elapsed Time: 00:00:00
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