```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;

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

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
(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

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

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

DENOM0        DENOM1        P10           P11           P20
________      ________      ________      ________      ________
1                 11            12            13            14            15

P21           P30           P31           TERM11        TERM10
________      ________      ________      ________      ________
1                 16            17            18            19            20

TERM01        TERM00        PNDE          TNIE          TOTAL
________      ________      ________      ________      ________
1                 21            22            23            24            25

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

DENOM0        DENOM1        P10           P11           P20
________      ________      ________      ________      ________
1              0.500         0.500         0.500         0.500         0.500

P21           P30           P31           TERM11        TERM10
________      ________      ________      ________      ________
1              0.500         0.500         0.500         0.500         0.500

TERM01        TERM00        PNDE          TNIE          TOTAL
________      ________      ________      ________      ________
1              0.500         0.500         0.500         0.500         0.500

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

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2015 Muthen & Muthen

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