Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:24 PM

INPUT INSTRUCTIONS

  title: this is an example of a Monte Carlo simulation of
          Cox mixture regression

  montecarlo: names are t u1-u5 x;
              generate=t(s 10*1) u1-u5(1);
              hazardc = t (1);
              survival=t(all);
              categorical=u1-u5;
              nobs=1000;
              class=c(2);
              genclass=c(2);
              nrep=1;
              save = ex8.17.dat;

  model population:
  %overall%
  x*1;
  t on x*0.3;
  c#1 on x*1.0;

  %c#1%
  [t#1-t#11*1];
  [u1$1-u5$1*1];
  t on x*0.3;

  %c#2%
  [t#1-t#11*0.5];
  [u1$1-u5$1*-1];
  t on x*0.8;

  analysis: type=mixture;

  model:
  %overall%
  t on x*0.3;
  c#1 on x*1.0;

  %c#1%
  [u1$1-u5$1*1];
  t on x*0.3;

  %c#2%
  [u1$1-u5$1*-1];
  t on x*0.8;

  output: tech8;



INPUT READING TERMINATED NORMALLY



this is an example of a Monte Carlo simulation of
Cox mixture regression

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                    0

Number of dependent variables                                    6
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)
   U1          U2          U3          U4          U5

  Time-to-event (survival)

    Non-parametric
     T

Observed independent variables
   X

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
Link                                                         LOGIT
Base Hazard                                   EQUAL ACROSS CLASSES


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              X
              ________
               -0.001


           Covariances
              X
              ________
 X              0.996


           Correlations
              X
              ________
 X              1.000




MODEL FIT INFORMATION

Number of Free Parameters                       15

Loglikelihood

    H0 Value

        Mean                             -3025.790
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -3025.790      -3025.790
           0.980       0.000        -3025.790      -3025.790
           0.950       0.000        -3025.790      -3025.790
           0.900       0.000        -3025.790      -3025.790
           0.800       0.000        -3025.790      -3025.790
           0.700       0.000        -3025.790      -3025.790
           0.500       0.000        -3025.790      -3025.790
           0.300       0.000        -3025.790      -3025.790
           0.200       0.000        -3025.790      -3025.790
           0.100       0.000        -3025.790      -3025.790
           0.050       0.000        -3025.790      -3025.790
           0.020       0.000        -3025.790      -3025.790
           0.010       0.000        -3025.790      -3025.790

Information Criteria

    Akaike (AIC)

        Mean                              6081.579
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         6081.579       6081.579
           0.980       0.000         6081.579       6081.579
           0.950       0.000         6081.579       6081.579
           0.900       0.000         6081.579       6081.579
           0.800       0.000         6081.579       6081.579
           0.700       0.000         6081.579       6081.579
           0.500       0.000         6081.579       6081.579
           0.300       0.000         6081.579       6081.579
           0.200       0.000         6081.579       6081.579
           0.100       0.000         6081.579       6081.579
           0.050       0.000         6081.579       6081.579
           0.020       0.000         6081.579       6081.579
           0.010       0.000         6081.579       6081.579

    Bayesian (BIC)

        Mean                              6155.195
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         6155.195       6155.195
           0.980       0.000         6155.195       6155.195
           0.950       0.000         6155.195       6155.195
           0.900       0.000         6155.195       6155.195
           0.800       0.000         6155.195       6155.195
           0.700       0.000         6155.195       6155.195
           0.500       0.000         6155.195       6155.195
           0.300       0.000         6155.195       6155.195
           0.200       0.000         6155.195       6155.195
           0.100       0.000         6155.195       6155.195
           0.050       0.000         6155.195       6155.195
           0.020       0.000         6155.195       6155.195
           0.010       0.000         6155.195       6155.195

    Sample-Size Adjusted BIC (n* = (n + 2) / 24)

        Mean                              6107.555
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         6107.555       6107.555
           0.980       0.000         6107.555       6107.555
           0.950       0.000         6107.555       6107.555
           0.900       0.000         6107.555       6107.555
           0.800       0.000         6107.555       6107.555
           0.700       0.000         6107.555       6107.555
           0.500       0.000         6107.555       6107.555
           0.300       0.000         6107.555       6107.555
           0.200       0.000         6107.555       6107.555
           0.100       0.000         6107.555       6107.555
           0.050       0.000         6107.555       6107.555
           0.020       0.000         6107.555       6107.555
           0.010       0.000         6107.555       6107.555

Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes

    Pearson Chi-Square

        Mean                                22.661
        Std Dev                              0.000
        Degrees of freedom                      20
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            8.260         22.661
           0.980       1.000            9.237         22.661
           0.950       1.000           10.851         22.661
           0.900       1.000           12.443         22.661
           0.800       1.000           14.578         22.661
           0.700       1.000           16.266         22.661
           0.500       1.000           19.337         22.661
           0.300       0.000           22.775         22.661
           0.200       0.000           25.038         22.661
           0.100       0.000           28.412         22.661
           0.050       0.000           31.410         22.661
           0.020       0.000           35.020         22.661
           0.010       0.000           37.566         22.661

    Likelihood Ratio Chi-Square

        Mean                                22.148
        Std Dev                              0.000
        Degrees of freedom                      20
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            8.260         22.148
           0.980       1.000            9.237         22.148
           0.950       1.000           10.851         22.148
           0.900       1.000           12.443         22.148
           0.800       1.000           14.578         22.148
           0.700       1.000           16.266         22.148
           0.500       1.000           19.337         22.148
           0.300       0.000           22.775         22.148
           0.200       0.000           25.038         22.148
           0.100       0.000           28.412         22.148
           0.050       0.000           31.410         22.148
           0.020       0.000           35.020         22.148
           0.010       0.000           37.566         22.148



FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL

    Latent
   Classes

       1        494.25355          0.49425
       2        505.74645          0.50575


FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES

    Latent
   Classes

       1        494.25355          0.49425
       2        505.74645          0.50575


FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

    Latent
   Classes

       1              497          0.49700
       2              503          0.50300


CLASSIFICATION QUALITY

     Entropy                         0.647


Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)

           1        2

    1   0.895    0.105
    2   0.099    0.901


Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)

           1        2

    1   0.900    0.100
    2   0.104    0.896


Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)

              1        2

    1      2.192    0.000
    2     -2.158    0.000


MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff

Latent Class 1

 T        ON
  X                   0.300     0.4018     0.0000     0.0772     0.0104 1.000 1.000

 Intercepts
  T                   0.000     0.7927     0.0000     0.1468     0.6283 0.000 1.000

 Thresholds
  U1$1                1.000     0.9291     0.0000     0.1257     0.0050 1.000 1.000
  U2$1                1.000     1.0646     0.0000     0.1285     0.0042 1.000 1.000
  U3$1                1.000     1.0441     0.0000     0.1240     0.0019 1.000 1.000
  U4$1                1.000     1.1333     0.0000     0.1332     0.0178 1.000 1.000
  U5$1                1.000     1.0796     0.0000     0.1278     0.0063 1.000 1.000

Latent Class 2

 T        ON
  X                   0.800     0.6621     0.0000     0.1100     0.0190 1.000 1.000

 Intercepts
  T                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Thresholds
  U1$1               -1.000    -0.9735     0.0000     0.1170     0.0007 1.000 1.000
  U2$1               -1.000    -1.0770     0.0000     0.1302     0.0059 1.000 1.000
  U3$1               -1.000    -1.0777     0.0000     0.1305     0.0060 1.000 1.000
  U4$1               -1.000    -0.9591     0.0000     0.1223     0.0017 1.000 1.000
  U5$1               -1.000    -0.8914     0.0000     0.1193     0.0118 1.000 1.000

Categorical Latent Variables

 C#1        ON
  X                   1.000     1.1296     0.0000     0.1124     0.0168 1.000 1.000

 Intercepts
  C#1                 0.000    -0.0245     0.0000     0.1193     0.0006 1.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.998E-01
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR LATENT CLASS 1


           NU
              X
              ________
                    0


           LAMBDA
              X
              ________
 X                  0


           THETA
              X
              ________
 X                  0


           ALPHA
              X
              ________
                    0


           BETA
              X
              ________
 X                  0


           PSI
              X
              ________
 X                  0


     PARAMETER SPECIFICATION FOR LATENT CLASS 2


           NU
              X
              ________
                    0


           LAMBDA
              X
              ________
 X                  0


           THETA
              X
              ________
 X                  0


           ALPHA
              X
              ________
                    0


           BETA
              X
              ________
 X                  0


           PSI
              X
              ________
 X                  0


     PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART


           TAU(U) FOR LATENT CLASS 1
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
                    1             2             3             4             5


           TAU(U) FOR LATENT CLASS 2
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
                    6             7             8             9            10


     PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
                   11             0


           GAMMA(C)
              X
              ________
 C#1               12
 C#2                0


     PARAMETER SPECIFICATION FOR THE CENSORED/NOMINAL/COUNT MODEL PART


           NU(P) FOR LATENT CLASS 1
              T#1           T
              ________      ________
                    0            13


           KAPPA(P) FOR LATENT CLASS 1
              X
              ________
 T#1                0
 T                 14


           NU(P) FOR LATENT CLASS 2
              T#1           T
              ________      ________
                    0             0


           KAPPA(P) FOR LATENT CLASS 2
              X
              ________
 T#1                0
 T                 15


     STARTING VALUES FOR LATENT CLASS 1


           NU
              X
              ________
                0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
                0.000


           BETA
              X
              ________
 X              0.000


           PSI
              X
              ________
 X              0.500


     STARTING VALUES FOR LATENT CLASS 2


           NU
              X
              ________
                0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
                0.000


           BETA
              X
              ________
 X              0.000


           PSI
              X
              ________
 X              0.500


     STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART


           TAU(U) FOR LATENT CLASS 1
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
                1.000         1.000         1.000         1.000         1.000


           TAU(U) FOR LATENT CLASS 2
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
               -1.000        -1.000        -1.000        -1.000        -1.000


     STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
                0.000         0.000


           GAMMA(C)
              X
              ________
 C#1            1.000
 C#2            0.000


     STARTING VALUES FOR THE CENSORED/NOMINAL/COUNT MODEL PART


           NU(P) FOR LATENT CLASS 1
              T#1           T
              ________      ________
              -20.000         0.000


           KAPPA(P) FOR LATENT CLASS 1
              X
              ________
 T#1            0.000
 T              0.300


           NU(P) FOR LATENT CLASS 2
              T#1           T
              ________      ________
              -20.000         0.000


           KAPPA(P) FOR LATENT CLASS 2
              X
              ________
 T#1            0.000
 T              0.800


     POPULATION VALUES FOR LATENT CLASS 1


           NU
              X
              ________
                0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
                0.000


           BETA
              X
              ________
 X              0.000


           PSI
              X
              ________
 X              1.000


     POPULATION VALUES FOR LATENT CLASS 2


           NU
              X
              ________
                0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
                0.000


           BETA
              X
              ________
 X              0.000


           PSI
              X
              ________
 X              1.000


     POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART


           TAU(U) FOR LATENT CLASS 1
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
                1.000         1.000         1.000         1.000         1.000


           TAU(U) FOR LATENT CLASS 2
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
               -1.000        -1.000        -1.000        -1.000        -1.000


     POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
                0.000         0.000


           GAMMA(C)
              X
              ________
 C#1            1.000
 C#2            0.000


     POPULATION VALUES FOR THE CENSORED/NOMINAL/COUNT MODEL PART


           NU(P) FOR LATENT CLASS 1
              T#1           T
              ________      ________
              -20.000         0.000


           KAPPA(P) FOR LATENT CLASS 1
              X
              ________
 T#1            0.000
 T              0.300


           NU(P) FOR LATENT CLASS 2
              T#1           T
              ________      ________
              -20.000         0.000


           KAPPA(P) FOR LATENT CLASS 2
              X
              ________
 T#1            0.000
 T              0.800


     POPULATION VALUES FOR THE BASE HAZARD PARAMETERS


           BASE HAZARD PARAMETERS FOR LATENT CLASS 1
              T#1           T#2           T#3           T#4           T#5
              ________      ________      ________      ________      ________
                1.000         1.000         1.000         1.000         1.000


           BASE HAZARD PARAMETERS FOR LATENT CLASS 1
              T#6           T#7           T#8           T#9           T#10
              ________      ________      ________      ________      ________
                1.000         1.000         1.000         1.000         1.000


           BASE HAZARD PARAMETERS FOR LATENT CLASS 1
              T#11
              ________
                1.000


           BASE HAZARD PARAMETERS FOR LATENT CLASS 2
              T#1           T#2           T#3           T#4           T#5
              ________      ________      ________      ________      ________
                0.500         0.500         0.500         0.500         0.500


           BASE HAZARD PARAMETERS FOR LATENT CLASS 2
              T#6           T#7           T#8           T#9           T#10
              ________      ________      ________      ________      ________
                0.500         0.500         0.500         0.500         0.500


           BASE HAZARD PARAMETERS FOR LATENT CLASS 2
              T#11
              ________
                0.500


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.30567642D+04    0.0000000    0.0000000  EM
              2 -0.30291468D+04   27.6173795    0.0090348  EM
              3 -0.30263359D+04    2.8109081    0.0009280  EM
              4 -0.30259087D+04    0.4271786    0.0001412  EM
              5 -0.30258273D+04    0.0814716    0.0000269  EM
              6 -0.30258065D+04    0.0207237    0.0000068  EM
              7 -0.30257992D+04    0.0073266    0.0000024  EM
              8 -0.30257957D+04    0.0035168    0.0000012  EM
              9 -0.30257936D+04    0.0020606    0.0000007  EM
             10 -0.30257923D+04    0.0013272    0.0000004  EM
             11 -0.30257914D+04    0.0008876    0.0000003  EM
             12 -0.30257908D+04    0.0006018    0.0000002  EM
             13 -0.30257904D+04    0.0004101    0.0000001  EM
             14 -0.30257901D+04    0.0002799    0.0000001  EM
             15 -0.30257899D+04    0.0001912    0.0000001  EM
             16 -0.30257898D+04    0.0001306    0.0000000  EM
             17 -0.30257897D+04    0.0000893    0.0000000  EM
             18 -0.30257897D+04    0.0000610    0.0000000  EM
             19 -0.30257896D+04    0.0000417    0.0000000  EM
             20 -0.30257896D+04    0.0000285    0.0000000  EM
             21 -0.30257896D+04    0.0000195    0.0000000  EM
             22 -0.30257896D+04    0.0000133    0.0000000  EM
             23 -0.30257895D+04    0.0000091    0.0000000  EM
             24 -0.30257895D+04    0.0000062    0.0000000  EM
             25 -0.30257895D+04    0.0000042    0.0000000  EM
             26 -0.30257895D+04    0.0000029    0.0000000  EM
             27 -0.30257895D+04    0.0000020    0.0000000  EM
             28 -0.30257895D+04    0.0000014    0.0000000  EM
             29 -0.30257895D+04    0.0000009    0.0000000  EM
             30 -0.30257895D+04    0.0000006    0.0000000  EM
             31 -0.30257895D+04    0.0000004    0.0000000  EM
             32 -0.30257895D+04    0.0000003    0.0000000  EM
             33 -0.30257895D+04    0.0000002    0.0000000  EM
             34 -0.30257895D+04    0.0000001    0.0000000  EM
             35 -0.30257895D+04    0.0000001    0.0000000  EM
             36 -0.30257895D+04    0.0000001    0.0000000  EM
             37 -0.30257895D+04    0.0000000    0.0000000  EM
             38 -0.30257895D+04    0.0000000    0.0000000  EM
             39 -0.30257895D+04    0.0000000    0.0000000  EM
             40 -0.30257895D+04    0.0000000    0.0000000  FS


SAVEDATA INFORMATION

  Order of variables

    T
    U1
    U2
    U3
    U4
    U5
    X
    _TCENT
    C

  Save file
    ex8.17.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:24:52
        Ending Time:  22:24:53
       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) 1998-2022 Muthen & Muthen

Back to examples