Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title: this is an example of a mixture regression
analysis for a count variable using a
zero-inflated Poisson model using
automatic starting values with random
starts
montecarlo:
names = u x1 x2;
seed = 53487;
nobs = 500;
nreps = 1;
generate = u(ci);
count = u(i);
genclasses = c(2);
classes = c(2);
save = ex7.2.dat;
analysis:
type = mixture;
model population:
%overall%
[x1-x2@0];
x1-x2@1;
u on x1*.5 x2*.3;
[u*1];
u#1 on x1*2 x2*1;
[u#1*-1] ;
c#1 on x1*1;
%c#1%
[u*2];
u on x2*0;
model:
%overall%
u on x1*.5 x2*.3;
[u*1];
u#1 on x1*2 x2*1;
[u#1*-1] (1);
c#1 on x1*1;
%c#1%
[u*2];
u on x2*0;
output:
tech8;
INPUT READING TERMINATED NORMALLY
this is an example of a mixture regression
analysis for a count variable using a
zero-inflated Poisson model using
automatic starting values with random
starts
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
U
Observed independent variables
X1 X2
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 X2
________ ________
0.020 -0.022
Covariances
X1 X2
________ ________
X1 1.070
X2 0.043 0.974
Correlations
X1 X2
________ ________
X1 1.000
X2 0.042 1.000
MODEL FIT INFORMATION
Number of Free Parameters 10
Loglikelihood
H0 Value
Mean -902.299
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -902.299 -902.299
0.980 0.000 -902.299 -902.299
0.950 0.000 -902.299 -902.299
0.900 0.000 -902.299 -902.299
0.800 0.000 -902.299 -902.299
0.700 0.000 -902.299 -902.299
0.500 0.000 -902.299 -902.299
0.300 0.000 -902.299 -902.299
0.200 0.000 -902.299 -902.299
0.100 0.000 -902.299 -902.299
0.050 0.000 -902.299 -902.299
0.020 0.000 -902.299 -902.299
0.010 0.000 -902.299 -902.299
Information Criteria
Akaike (AIC)
Mean 1824.598
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1824.598 1824.598
0.980 0.000 1824.598 1824.598
0.950 0.000 1824.598 1824.598
0.900 0.000 1824.598 1824.598
0.800 0.000 1824.598 1824.598
0.700 0.000 1824.598 1824.598
0.500 0.000 1824.598 1824.598
0.300 0.000 1824.598 1824.598
0.200 0.000 1824.598 1824.598
0.100 0.000 1824.598 1824.598
0.050 0.000 1824.598 1824.598
0.020 0.000 1824.598 1824.598
0.010 0.000 1824.598 1824.598
Bayesian (BIC)
Mean 1866.744
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1866.744 1866.744
0.980 0.000 1866.744 1866.744
0.950 0.000 1866.744 1866.744
0.900 0.000 1866.744 1866.744
0.800 0.000 1866.744 1866.744
0.700 0.000 1866.744 1866.744
0.500 0.000 1866.744 1866.744
0.300 0.000 1866.744 1866.744
0.200 0.000 1866.744 1866.744
0.100 0.000 1866.744 1866.744
0.050 0.000 1866.744 1866.744
0.020 0.000 1866.744 1866.744
0.010 0.000 1866.744 1866.744
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 1835.003
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1835.003 1835.003
0.980 0.000 1835.003 1835.003
0.950 0.000 1835.003 1835.003
0.900 0.000 1835.003 1835.003
0.800 0.000 1835.003 1835.003
0.700 0.000 1835.003 1835.003
0.500 0.000 1835.003 1835.003
0.300 0.000 1835.003 1835.003
0.200 0.000 1835.003 1835.003
0.100 0.000 1835.003 1835.003
0.050 0.000 1835.003 1835.003
0.020 0.000 1835.003 1835.003
0.010 0.000 1835.003 1835.003
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 226.59891 0.45320
2 273.40109 0.54680
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 226.59877 0.45320
2 273.40123 0.54680
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 238 0.47600
2 262 0.52400
CLASSIFICATION QUALITY
Entropy 0.409
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.767 0.233
2 0.168 0.832
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.806 0.194
2 0.203 0.797
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.422 0.000
2 -1.369 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
U ON
X1 0.500 0.5615 0.0000 0.0544 0.0038 1.000 1.000
X2 0.000 0.0248 0.0000 0.0386 0.0006 1.000 0.000
U#1 ON
X1 2.000 1.6538 0.0000 0.2092 0.1199 1.000 1.000
X2 1.000 0.8059 0.0000 0.1433 0.0377 1.000 1.000
Intercepts
U#1 -1.000 -0.8498 0.0000 0.1654 0.0226 1.000 1.000
U 2.000 2.0786 0.0000 0.0544 0.0062 1.000 1.000
Latent Class 2
U ON
X1 0.500 0.5615 0.0000 0.0544 0.0038 1.000 1.000
X2 0.300 0.3827 0.0000 0.0671 0.0068 1.000 1.000
U#1 ON
X1 2.000 1.6538 0.0000 0.2092 0.1199 1.000 1.000
X2 1.000 0.8059 0.0000 0.1433 0.0377 1.000 1.000
Intercepts
U#1 -1.000 -0.8498 0.0000 0.1654 0.0226 1.000 1.000
U 1.000 1.0274 0.0000 0.0766 0.0008 1.000 1.000
Categorical Latent Variables
C#1 ON
X1 1.000 0.9181 0.0000 0.2756 0.0067 1.000 1.000
Intercepts
C#1 0.000 -0.2471 0.0000 0.2124 0.0611 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.837E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
X1 X2
________ ________
0 0
LAMBDA
X1 X2
________ ________
X1 0 0
X2 0 0
THETA
X1 X2
________ ________
X1 0
X2 0 0
ALPHA
X1 X2
________ ________
0 0
BETA
X1 X2
________ ________
X1 0 0
X2 0 0
PSI
X1 X2
________ ________
X1 0
X2 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
X1 X2
________ ________
0 0
LAMBDA
X1 X2
________ ________
X1 0 0
X2 0 0
THETA
X1 X2
________ ________
X1 0
X2 0 0
ALPHA
X1 X2
________ ________
0 0
BETA
X1 X2
________ ________
X1 0 0
X2 0 0
PSI
X1 X2
________ ________
X1 0
X2 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 0
GAMMA(C)
X1 X2
________ ________
C#1 2 0
C#2 0 0
PARAMETER SPECIFICATION FOR THE CENSORED/NOMINAL/COUNT MODEL PART
NU(P) FOR LATENT CLASS 1
U#1 U
________ ________
3 4
KAPPA(P) FOR LATENT CLASS 1
X1 X2
________ ________
U#1 5 6
U 7 8
NU(P) FOR LATENT CLASS 2
U#1 U
________ ________
3 9
KAPPA(P) FOR LATENT CLASS 2
X1 X2
________ ________
U#1 5 6
U 7 10
STARTING VALUES FOR LATENT CLASS 1
NU
X1 X2
________ ________
0.000 0.000
LAMBDA
X1 X2
________ ________
X1 1.000 0.000
X2 0.000 1.000
THETA
X1 X2
________ ________
X1 0.000
X2 0.000 0.000
ALPHA
X1 X2
________ ________
0.000 0.000
BETA
X1 X2
________ ________
X1 0.000 0.000
X2 0.000 0.000
PSI
X1 X2
________ ________
X1 0.500
X2 0.000 0.500
STARTING VALUES FOR LATENT CLASS 2
NU
X1 X2
________ ________
0.000 0.000
LAMBDA
X1 X2
________ ________
X1 1.000 0.000
X2 0.000 1.000
THETA
X1 X2
________ ________
X1 0.000
X2 0.000 0.000
ALPHA
X1 X2
________ ________
0.000 0.000
BETA
X1 X2
________ ________
X1 0.000 0.000
X2 0.000 0.000
PSI
X1 X2
________ ________
X1 0.500
X2 0.000 0.500
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
GAMMA(C)
X1 X2
________ ________
C#1 1.000 0.000
C#2 0.000 0.000
STARTING VALUES FOR THE CENSORED/NOMINAL/COUNT MODEL PART
NU(P) FOR LATENT CLASS 1
U#1 U
________ ________
-1.000 2.000
KAPPA(P) FOR LATENT CLASS 1
X1 X2
________ ________
U#1 2.000 1.000
U 0.500 0.000
NU(P) FOR LATENT CLASS 2
U#1 U
________ ________
-1.000 1.000
KAPPA(P) FOR LATENT CLASS 2
X1 X2
________ ________
U#1 2.000 1.000
U 0.500 0.300
POPULATION VALUES FOR LATENT CLASS 1
NU
X1 X2
________ ________
0.000 0.000
LAMBDA
X1 X2
________ ________
X1 1.000 0.000
X2 0.000 1.000
THETA
X1 X2
________ ________
X1 0.000
X2 0.000 0.000
ALPHA
X1 X2
________ ________
0.000 0.000
BETA
X1 X2
________ ________
X1 0.000 0.000
X2 0.000 0.000
PSI
X1 X2
________ ________
X1 1.000
X2 0.000 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
X1 X2
________ ________
0.000 0.000
LAMBDA
X1 X2
________ ________
X1 1.000 0.000
X2 0.000 1.000
THETA
X1 X2
________ ________
X1 0.000
X2 0.000 0.000
ALPHA
X1 X2
________ ________
0.000 0.000
BETA
X1 X2
________ ________
X1 0.000 0.000
X2 0.000 0.000
PSI
X1 X2
________ ________
X1 1.000
X2 0.000 1.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
GAMMA(C)
X1 X2
________ ________
C#1 1.000 0.000
C#2 0.000 0.000
POPULATION VALUES FOR THE CENSORED/NOMINAL/COUNT MODEL PART
NU(P) FOR LATENT CLASS 1
U#1 U
________ ________
-1.000 2.000
KAPPA(P) FOR LATENT CLASS 1
X1 X2
________ ________
U#1 2.000 1.000
U 0.500 0.000
NU(P) FOR LATENT CLASS 2
U#1 U
________ ________
-1.000 1.000
KAPPA(P) FOR LATENT CLASS 2
X1 X2
________ ________
U#1 2.000 1.000
U 0.500 0.300
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.90883707D+03 0.0000000 0.0000000 EM
2 -0.90323047D+03 5.6065950 0.0061690 EM
3 -0.90279340D+03 0.4370704 0.0004839 EM
4 -0.90261232D+03 0.1810828 0.0002006 EM
5 -0.90250313D+03 0.1091911 0.0001210 EM
6 -0.90243313D+03 0.0699986 0.0000776 EM
7 -0.90238752D+03 0.0456139 0.0000505 EM
8 -0.90235759D+03 0.0299221 0.0000332 EM
9 -0.90233789D+03 0.0197072 0.0000218 EM
10 -0.90232487D+03 0.0130193 0.0000144 EM
11 -0.90231624D+03 0.0086239 0.0000096 EM
12 -0.90231052D+03 0.0057265 0.0000063 EM
13 -0.90230671D+03 0.0038115 0.0000042 EM
14 -0.90230416D+03 0.0025429 0.0000028 EM
15 -0.90230246D+03 0.0017006 0.0000019 EM
16 -0.90230132D+03 0.0011401 0.0000013 EM
17 -0.90230056D+03 0.0007664 0.0000008 EM
18 -0.90230004D+03 0.0005166 0.0000006 EM
19 -0.90229969D+03 0.0003493 0.0000004 EM
20 -0.90229945D+03 0.0002369 0.0000003 EM
21 -0.90229929D+03 0.0001612 0.0000002 EM
22 -0.90229918D+03 0.0001102 0.0000001 EM
23 -0.90229911D+03 0.0000756 0.0000001 EM
24 -0.90229905D+03 0.0000521 0.0000001 EM
25 -0.90229902D+03 0.0000360 0.0000000 EM
26 -0.90229899D+03 0.0000250 0.0000000 EM
27 -0.90229898D+03 0.0000175 0.0000000 EM
28 -0.90229896D+03 0.0000123 0.0000000 EM
29 -0.90229895D+03 0.0000087 0.0000000 EM
30 -0.90229895D+03 0.0000062 0.0000000 EM
31 -0.90229894D+03 0.0000044 0.0000000 EM
32 -0.90229894D+03 0.0000031 0.0000000 EM
33 -0.90229894D+03 0.0000023 0.0000000 EM
34 -0.90229894D+03 0.0000016 0.0000000 EM
35 -0.90229894D+03 0.0000012 0.0000000 EM
36 -0.90229893D+03 0.0000033 0.0000000 FS
37 -0.90229893D+03 0.0000000 0.0000000 FS
38 -0.90229893D+03 0.0000000 0.0000000 EM
SAVEDATA INFORMATION
Order of variables
U
X1
X2
C
Save file
ex7.2.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:32
Ending Time: 22:24:33
Elapsed Time: 00:00:01
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