```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;

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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