Mplus VERSION 7.4
MUTHEN & MUTHEN
06/02/2016 5:21 PM
INPUT INSTRUCTIONS
title:
Nominal M, Binary Y
Using a latent class variable to represent M
data:
file = nombin9expanded.txt;
variable:
names = x m y;
usev = y x;
categorical = y;
classes = c(3);
knownclass = c(m=1 m=2 m=3);
analysis:
type = mixture;
estimator = ml;
bootstrap = 1000;
model:
%overall%
[c#1] (gamma01);
[c#2] (gamma02);
c#1 on x (gamma11);
c#2 on x (gamma12);
y on x;
%c#1%
[y$1] (beta01);
y on x (beta11);
%c#2%
[y$1] (beta02);
y on x (beta12);
%c#3%
[y$1] (beta03);
y on x (beta13);
model constraint:
new(denom0 denom1 p10 p11 p20 p21 p30 p31 term11 term10 term01 term00
pnde tnie total pnie orpnde ortnie orpnie);
! mediator probabilities:
! index is x0 for multinomial denominator
denom0=exp(gamma01)+exp(gamma02)+1;
denom1=exp(gamma01+gamma11)+exp(gamma02+gamma12)+1;
! first index is class, second x0 for probabilities
p10=exp(gamma01)/denom0;
p11=exp(gamma01+gamma11)/denom1;
p20=exp(gamma02)/denom0;
p21=exp(gamma02+gamma12)/denom1;
p30=1/denom0;
p31=1/denom1;
! outcome probabilities:
! first index is x1, second x0, summing over class
term11=(1/(1+exp(beta01-beta11)))*p11+(1/(1+exp(beta02-beta12)))*p21
+(1/(1+exp(beta03-beta13)))*p31;
term10=(1/(1+exp(beta01-beta11)))*p10+(1/(1+exp(beta02-beta12)))*p20
+(1/(1+exp(beta03-beta13)))*p30;
term01=(1/(1+exp(beta01)))*p11+(1/(1+exp(beta02)))*p21
+(1/(1+exp(beta03)))*p31;
term00=(1/(1+exp(beta01)))*p10+(1/(1+exp(beta02)))*p20
+(1/(1+exp(beta03)))*p30;
! effects:
pnde=term10-term00;
tnie=term11-term10;
total=term11-term00;
pnie=term01-term00;
orpnde=(term10/(1-term10))/(term00/(1-term00));
ortnie=(term11/(1-term11))/(term10/(1-term10));
orpnie=(term01/(1-term01))/(term00/(1-term00));
output:
tech1 tech8 cinterval(bootstrap);
plot:
type = plot3;
INPUT READING TERMINATED NORMALLY
Nominal M, Binary Y
Using a latent class variable to represent M
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 480
Number of dependent variables 1
Number of independent variables 1
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
Y
Observed independent variables
X
Categorical latent variables
C
Knownclass C
Estimator ML
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
Number of bootstrap draws
Requested 1000
Completed 1000
Optimization algorithm EMA
Link LOGIT
Input data file(s)
nombin9expanded.txt
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
Y
Category 1 0.615 295.000
Category 2 0.385 185.000
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 10
Loglikelihood
H0 Value -738.734
Information Criteria
Akaike (AIC) 1497.468
Bayesian (BIC) 1539.206
Sample-Size Adjusted BIC 1507.467
(n* = (n + 2) / 24)
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 140.00000 0.29167
2 180.00000 0.37500
3 160.00000 0.33333
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1 (1)
Y ON
X -0.336 0.536 -0.628 0.530
Thresholds
Y$1 1.609 0.387 4.163 0.000
Latent Class 2 (2)
Y ON
X -0.636 0.406 -1.567 0.117
Thresholds
Y$1 1.099 0.266 4.135 0.000
Latent Class 3 (3)
Y ON
X 0.223 0.448 0.498 0.619
Thresholds
Y$1 -1.386 0.250 -5.549 0.000
Categorical Latent Variables
C#1 ON
X 0.799 0.240 3.324 0.001
C#2 ON
X 0.734 0.229 3.203 0.001
Intercepts
C#1 -0.511 0.170 -3.014 0.003
C#2 -0.223 0.151 -1.476 0.140
New/Additional Parameters
DENOM0 2.400 0.194 12.357 0.000
DENOM1 4.000 0.472 8.482 0.000
P10 0.250 0.028 8.793 0.000
P11 0.333 0.030 11.167 0.000
P20 0.333 0.030 11.051 0.000
P21 0.417 0.033 12.802 0.000
P30 0.417 0.032 12.847 0.000
P31 0.250 0.028 8.873 0.000
TERM11 0.312 0.030 10.290 0.000
TERM10 0.428 0.034 12.565 0.000
TERM01 0.360 0.032 11.374 0.000
TERM00 0.458 0.032 14.462 0.000
PNDE -0.030 0.037 -0.818 0.413
TNIE -0.116 0.032 -3.660 0.000
TOTAL -0.146 0.044 -3.278 0.001
PNIE -0.099 0.027 -3.614 0.000
ORPNDE 0.886 0.135 6.578 0.000
ORTNIE 0.606 0.085 7.163 0.000
ORPNIE 0.664 0.077 8.668 0.000
LOGISTIC REGRESSION ODDS RATIO RESULTS
Latent Class 1 (1)
Y ON
X 0.714
Latent Class 2 (2)
Y ON
X 0.529
Latent Class 3 (3)
Y ON
X 1.250
Categorical Latent Variables
C#1 ON
X 2.222
C#2 ON
X 2.083
CONFIDENCE INTERVALS OF MODEL RESULTS
Lower .5% Lower 2.5% Lower 5% Estimate Upper 5% Upper 2.5% Upper .5%
Latent Class 1 (1)
Y ON
X -1.939 -1.455 -1.181 -0.336 0.523 0.738 1.099
Thresholds
Y$1 0.816 1.025 1.118 1.609 2.358 2.546 2.944
Latent Class 2 (2)
Y ON
X -1.912 -1.482 -1.313 -0.636 -0.028 0.128 0.372
Thresholds
Y$1 0.480 0.619 0.693 1.099 1.578 1.689 1.836
Latent Class 3 (3)
Y ON
X -0.894 -0.636 -0.450 0.223 0.975 1.173 1.556
Thresholds
Y$1 -2.179 -1.920 -1.823 -1.386 -1.025 -0.969 -0.803
Categorical Latent Variables
C#1 ON
X 0.165 0.328 0.417 0.799 1.198 1.271 1.402
C#2 ON
X 0.176 0.281 0.358 0.734 1.119 1.186 1.323
Intercepts
C#1 -1.012 -0.838 -0.800 -0.511 -0.229 -0.168 -0.064
C#2 -0.599 -0.511 -0.465 -0.223 0.041 0.074 0.152
New/Additional Parameters
DENOM0 2.009 2.108 2.142 2.400 2.780 2.850 3.000
DENOM1 3.013 3.293 3.391 4.000 4.911 5.096 5.533
P10 0.177 0.197 0.204 0.250 0.300 0.306 0.321
P11 0.248 0.274 0.285 0.333 0.382 0.392 0.407
P20 0.258 0.276 0.286 0.333 0.384 0.393 0.414
P21 0.329 0.355 0.364 0.417 0.470 0.477 0.500
P30 0.329 0.350 0.359 0.417 0.467 0.474 0.493
P31 0.177 0.196 0.204 0.250 0.295 0.303 0.325
TERM11 0.234 0.250 0.262 0.312 0.361 0.371 0.397
TERM10 0.345 0.362 0.372 0.428 0.482 0.492 0.510
TERM01 0.279 0.293 0.304 0.360 0.411 0.417 0.433
TERM00 0.371 0.395 0.403 0.458 0.509 0.516 0.537
PNDE -0.121 -0.100 -0.088 -0.030 0.031 0.042 0.064
TNIE -0.196 -0.180 -0.167 -0.116 -0.063 -0.054 -0.041
TOTAL -0.262 -0.233 -0.214 -0.146 -0.070 -0.057 -0.031
PNIE -0.173 -0.154 -0.145 -0.099 -0.054 -0.047 -0.031
ORPNDE 0.610 0.663 0.697 0.886 1.136 1.189 1.301
ORTNIE 0.424 0.460 0.478 0.606 0.759 0.791 0.836
ORPNIE 0.483 0.520 0.543 0.664 0.801 0.825 0.879
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1 (1)
NU
X
________
1 0
LAMBDA
X
________
X 0
THETA
X
________
X 0
ALPHA
X
________
1 0
BETA
X
________
X 0
PSI
X
________
X 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2 (2)
NU
X
________
1 0
LAMBDA
X
________
X 0
THETA
X
________
X 0
ALPHA
X
________
1 0
BETA
X
________
X 0
PSI
X
________
X 0
PARAMETER SPECIFICATION FOR LATENT CLASS 3 (3)
NU
X
________
1 0
LAMBDA
X
________
X 0
THETA
X
________
X 0
ALPHA
X
________
1 0
BETA
X
________
X 0
PSI
X
________
X 0
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1 (1)
Y$1
________
1 1
TAU(U) FOR LATENT CLASS 2 (2)
Y$1
________
1 3
TAU(U) FOR LATENT CLASS 3 (3)
Y$1
________
1 5
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3
________ ________ ________
1 7 8 0
GAMMA(C)
X
________
C#1 9
C#2 10
C#3 0
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR GROWTH MODEL PART
LAMBDA(F) FOR LATENT CLASS 1 (1)
Y
________
Y 0
ALPHA(F) FOR LATENT CLASS 1 (1)
Y
________
1 0
GAMMA(F) FOR LATENT CLASS 1 (1)
X
________
Y 2
LAMBDA(F) FOR LATENT CLASS 2 (2)
Y
________
Y 0
ALPHA(F) FOR LATENT CLASS 2 (2)
Y
________
1 0
GAMMA(F) FOR LATENT CLASS 2 (2)
X
________
Y 4
LAMBDA(F) FOR LATENT CLASS 3 (3)
Y
________
Y 0
ALPHA(F) FOR LATENT CLASS 3 (3)
Y
________
1 0
GAMMA(F) FOR LATENT CLASS 3 (3)
X
________
Y 6
PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS
NEW/ADDITIONAL PARAMETERS
DENOM0 DENOM1 P10 P11 P20
________ ________ ________ ________ ________
1 11 12 13 14 15
NEW/ADDITIONAL PARAMETERS
P21 P30 P31 TERM11 TERM10
________ ________ ________ ________ ________
1 16 17 18 19 20
NEW/ADDITIONAL PARAMETERS
TERM01 TERM00 PNDE TNIE TOTAL
________ ________ ________ ________ ________
1 21 22 23 24 25
NEW/ADDITIONAL PARAMETERS
PNIE ORPNDE ORTNIE ORPNIE
________ ________ ________ ________
1 26 27 28 29
STARTING VALUES FOR LATENT CLASS 1 (1)
NU
X
________
1 0.000
LAMBDA
X
________
X 1.000
THETA
X
________
X 0.000
ALPHA
X
________
1 0.000
BETA
X
________
X 0.000
PSI
X
________
X 0.125
STARTING VALUES FOR LATENT CLASS 2 (2)
NU
X
________
1 0.000
LAMBDA
X
________
X 1.000
THETA
X
________
X 0.000
ALPHA
X
________
1 0.000
BETA
X
________
X 0.000
PSI
X
________
X 0.125
STARTING VALUES FOR LATENT CLASS 3 (3)
NU
X
________
1 0.000
LAMBDA
X
________
X 1.000
THETA
X
________
X 0.000
ALPHA
X
________
1 0.000
BETA
X
________
X 0.000
PSI
X
________
X 0.125
STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1 (1)
Y$1
________
1 -0.533
TAU(U) FOR LATENT CLASS 2 (2)
Y$1
________
1 0.467
TAU(U) FOR LATENT CLASS 3 (3)
Y$1
________
1 1.467
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3
________ ________ ________
1 0.000 0.000 0.000
GAMMA(C)
X
________
C#1 0.000
C#2 0.000
C#3 0.000
STARTING VALUES FOR LATENT CLASS INDICATOR GROWTH MODEL PART
LAMBDA(F) FOR CLASS LATENT CLASS 1 (1)
Y
________
Y 1.000
ALPHA(F) FOR LATENT CLASS 1 (1)
Y
________
1 0.000
GAMMA(F) FOR LATENT CLASS 1 (1)
X
________
Y 0.000
LAMBDA(F) FOR CLASS LATENT CLASS 2 (2)
Y
________
Y 1.000
ALPHA(F) FOR LATENT CLASS 2 (2)
Y
________
1 0.000
GAMMA(F) FOR LATENT CLASS 2 (2)
X
________
Y 0.000
LAMBDA(F) FOR CLASS LATENT CLASS 3 (3)
Y
________
Y 1.000
ALPHA(F) FOR LATENT CLASS 3 (3)
Y
________
1 0.000
GAMMA(F) FOR LATENT CLASS 3 (3)
X
________
Y 0.000
STARTING VALUES FOR THE ADDITIONAL PARAMETERS
NEW/ADDITIONAL PARAMETERS
DENOM0 DENOM1 P10 P11 P20
________ ________ ________ ________ ________
1 0.500 0.500 0.500 0.500 0.500
NEW/ADDITIONAL PARAMETERS
P21 P30 P31 TERM11 TERM10
________ ________ ________ ________ ________
1 0.500 0.500 0.500 0.500 0.500
NEW/ADDITIONAL PARAMETERS
TERM01 TERM00 PNDE TNIE TOTAL
________ ________ ________ ________ ________
1 0.500 0.500 0.500 0.500 0.500
NEW/ADDITIONAL PARAMETERS
PNIE ORPNDE ORTNIE ORPNIE
________ ________ ________ ________
1 0.500 0.500 0.500 0.500
TECHNICAL 8 OUTPUT
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.98379625D+03 0.0000000 0.0000000 140.000 180.000 EM
160.000
2 -0.75276318D+03 231.0330725 0.2348383 140.000 180.000 EM
160.000
3 -0.74684703D+03 5.9161481 0.0078592 140.000 180.000 EM
160.000
4 -0.73889727D+03 7.9497603 0.0106444 140.000 180.000 EM
160.000
5 -0.73873416D+03 0.1631121 0.0002208 140.000 180.000 EM
160.000
6 -0.73873396D+03 0.0002011 0.0000003 140.000 180.000 EM
160.000
7 -0.73873396D+03 0.0000000 0.0000000 140.000 180.000 EM
160.000
PLOT INFORMATION
The following plots are available:
Histograms (sample values)
Scatterplots (sample values)
Sample proportions and estimated probabilities
Bootstrap distributions
Estimated probabilities for a categorical latent variable as a
function of its covariates
DIAGRAM INFORMATION
Mplus diagrams are currently not available for Mixture analysis.
No diagram output was produced.
Beginning Time: 17:21:50
Ending Time: 17:21:51
Elapsed Time: 00:00:01
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