Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:02 PM

INPUT INSTRUCTIONS

  title:	this is an example of a continuous-time survival analysis
      using a parametric model and a latent variable influencing
      survival
  montecarlo:
  	names = t x u1-u4;
  	generate = t(s 20*1) u1-u4(1);
  	hazardc = t (.05);
      survival = t(20*1);
      categorical = u1-u4;
  	nobs = 1000;
  	nreps = 1;
  	save = ex6.22.dat;

  model population:
      x@0;
      x@1;
      f by u1-u4*1;
      f@2;
      [u1$1-u4$1*0];
      [t#1-t#21*.05];
      t on x*.1 f*.05;
      f on x*.2;

  analysis:
      basehazard = on;

  model:
      f by u1@1 u2-u4*1;
      f*2;
      [u1$1-u4$1*0];
      [t#1-t#21*.05];
      t on x*.1 f*.05;
      f on x*.2;

  output:
  	tech8 tech9;




INPUT READING TERMINATED NORMALLY



this is an example of a continuous-time survival analysis
using a parametric model and a latent variable influencing
survival

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                                    5
Number of independent variables                                  1
Number of continuous latent variables                            1

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4

  Time-to-event (survival)
   T

Observed independent variables
   X

Continuous latent variables
   F


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-02
    Relative loglikelihood change                        0.100D-05
    Derivative                                           0.100D-02
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-02
  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-02
  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
Integration Specifications
  Type                                                    STANDARD
  Number of integration points                                  15
  Dimensions of numerical integration                            1
  Adaptive quadrature                                           ON
Link                                                         LOGIT
Base Hazard                                                     ON
Cholesky                                                       OFF


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              X
              ________
 1              0.056


           Covariances
              X
              ________
 X              1.032


           Correlations
              X
              ________
 X              1.000




MODEL FIT INFORMATION

Number of Free Parameters                       32

Loglikelihood

    H0 Value

        Mean                             -4644.938
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -4644.938      -4644.938
           0.980       0.000        -4644.938      -4644.938
           0.950       0.000        -4644.938      -4644.938
           0.900       0.000        -4644.938      -4644.938
           0.800       0.000        -4644.938      -4644.938
           0.700       0.000        -4644.938      -4644.938
           0.500       0.000        -4644.938      -4644.938
           0.300       0.000        -4644.938      -4644.938
           0.200       0.000        -4644.938      -4644.938
           0.100       0.000        -4644.938      -4644.938
           0.050       0.000        -4644.938      -4644.938
           0.020       0.000        -4644.938      -4644.938
           0.010       0.000        -4644.938      -4644.938

Information Criteria

    Akaike (AIC)

        Mean                              9353.876
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         9353.876       9353.876
           0.980       0.000         9353.876       9353.876
           0.950       0.000         9353.876       9353.876
           0.900       0.000         9353.876       9353.876
           0.800       0.000         9353.876       9353.876
           0.700       0.000         9353.876       9353.876
           0.500       0.000         9353.876       9353.876
           0.300       0.000         9353.876       9353.876
           0.200       0.000         9353.876       9353.876
           0.100       0.000         9353.876       9353.876
           0.050       0.000         9353.876       9353.876
           0.020       0.000         9353.876       9353.876
           0.010       0.000         9353.876       9353.876

    Bayesian (BIC)

        Mean                              9510.924
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         9510.924       9510.924
           0.980       0.000         9510.924       9510.924
           0.950       0.000         9510.924       9510.924
           0.900       0.000         9510.924       9510.924
           0.800       0.000         9510.924       9510.924
           0.700       0.000         9510.924       9510.924
           0.500       0.000         9510.924       9510.924
           0.300       0.000         9510.924       9510.924
           0.200       0.000         9510.924       9510.924
           0.100       0.000         9510.924       9510.924
           0.050       0.000         9510.924       9510.924
           0.020       0.000         9510.924       9510.924
           0.010       0.000         9510.924       9510.924

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

        Mean                              9409.290
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         9409.290       9409.290
           0.980       0.000         9409.290       9409.290
           0.950       0.000         9409.290       9409.290
           0.900       0.000         9409.290       9409.290
           0.800       0.000         9409.290       9409.290
           0.700       0.000         9409.290       9409.290
           0.500       0.000         9409.290       9409.290
           0.300       0.000         9409.290       9409.290
           0.200       0.000         9409.290       9409.290
           0.100       0.000         9409.290       9409.290
           0.050       0.000         9409.290       9409.290
           0.020       0.000         9409.290       9409.290
           0.010       0.000         9409.290       9409.290



MODEL RESULTS

                           ESTIMATES              S. E.     M. S. E.  95%  % Sig
              Population   Average   Std. Dev.   Average             Cover Coeff
 F        BY
  U1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U2               1.000     0.8394     0.0000     0.1385     0.0258 1.000 1.000
  U3               1.000     1.0661     0.0000     0.1982     0.0044 1.000 1.000
  U4               1.000     0.8544     0.0000     0.1531     0.0212 1.000 1.000

 F          ON
  X                0.200     0.2123     0.0000     0.0631     0.0002 1.000 1.000

 T          ON
  F                0.050     0.0384     0.0000     0.0363     0.0001 1.000 0.000

 T          ON
  X                0.100     0.0853     0.0000     0.0430     0.0002 1.000 1.000

 Thresholds
  U1$1             0.000     0.0380     0.0000     0.0920     0.0014 1.000 0.000
  U2$1             0.000     0.0349     0.0000     0.0845     0.0012 1.000 0.000
  U3$1             0.000    -0.0746     0.0000     0.0947     0.0056 1.000 0.000
  U4$1             0.000     0.0999     0.0000     0.0853     0.0100 1.000 0.000

 Residual Variances
  F                2.000     2.4620     0.0000     0.5942     0.2134 1.000 1.000

Base Hazard Parameters
  T#1              0.050     0.0485     0.0000     0.0071     0.0000 1.000 1.000
  T#2              0.050     0.0597     0.0000     0.0083     0.0001 1.000 1.000
  T#3              0.050     0.0494     0.0000     0.0079     0.0000 1.000 1.000
  T#4              0.050     0.0504     0.0000     0.0084     0.0000 1.000 1.000
  T#5              0.050     0.0353     0.0000     0.0074     0.0002 0.000 1.000
  T#6              0.050     0.0549     0.0000     0.0096     0.0000 1.000 1.000
  T#7              0.050     0.0456     0.0000     0.0091     0.0000 1.000 1.000
  T#8              0.050     0.0486     0.0000     0.0099     0.0000 1.000 1.000
  T#9              0.050     0.0495     0.0000     0.0106     0.0000 1.000 1.000
  T#10             0.050     0.0568     0.0000     0.0119     0.0000 1.000 1.000
  T#11             0.050     0.0483     0.0000     0.0114     0.0000 1.000 1.000
  T#12             0.050     0.0467     0.0000     0.0116     0.0000 1.000 1.000
  T#13             0.050     0.0728     0.0000     0.0156     0.0005 1.000 1.000
  T#14             0.050     0.0401     0.0000     0.0121     0.0001 1.000 1.000
  T#15             0.050     0.0404     0.0000     0.0128     0.0001 1.000 1.000
  T#16             0.050     0.0578     0.0000     0.0162     0.0001 1.000 1.000
  T#17             0.050     0.0535     0.0000     0.0161     0.0000 1.000 1.000
  T#18             0.050     0.0485     0.0000     0.0161     0.0000 1.000 1.000
  T#19             0.050     0.0652     0.0000     0.0197     0.0002 1.000 1.000
  T#20             0.050     0.0533     0.0000     0.0190     0.0000 1.000 1.000
  T#21             0.050     0.0467     0.0000     0.0056     0.0000 1.000 1.000

QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.115E-03
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1                  8             9            10            11


           NU
              T#1           T             U1            U2            U3
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           NU
              U4            X
              ________      ________
 1                  0             0


           LAMBDA
              F             T#1           T             X
              ________      ________      ________      ________
 T#1                0             0             0             0
 T                  0             0             0             0
 U1                 0             0             0             0
 U2                 1             0             0             0
 U3                 2             0             0             0
 U4                 3             0             0             0
 X                  0             0             0             0


           THETA
              T#1           T             U1            U2            U3
              ________      ________      ________      ________      ________
 T#1                0
 T                  0             0
 U1                 0             0             0
 U2                 0             0             0             0
 U3                 0             0             0             0             0
 U4                 0             0             0             0             0
 X                  0             0             0             0             0


           THETA
              U4            X
              ________      ________
 U4                 0
 X                  0             0


           ALPHA
              F             T#1           T             X
              ________      ________      ________      ________
 1                  0             0             0             0


           BETA
              F             T#1           T             X
              ________      ________      ________      ________
 F                  0             0             0             4
 T#1                0             0             0             0
 T                  5             0             0             6
 X                  0             0             0             0


           PSI
              F             T#1           T             X
              ________      ________      ________      ________
 F                  7
 T#1                0             0
 T                  0             0             0
 X                  0             0             0             0


     PARAMETER SPECIFICATION FOR THE BASE HAZARD PARAMETERS


           BASE HAZARD PARAMETERS
              T#1           T#2           T#3           T#4           T#5
              ________      ________      ________      ________      ________
 1                 12            13            14            15            16


           BASE HAZARD PARAMETERS
              T#6           T#7           T#8           T#9           T#10
              ________      ________      ________      ________      ________
 1                 17            18            19            20            21


           BASE HAZARD PARAMETERS
              T#11          T#12          T#13          T#14          T#15
              ________      ________      ________      ________      ________
 1                 22            23            24            25            26


           BASE HAZARD PARAMETERS
              T#16          T#17          T#18          T#19          T#20
              ________      ________      ________      ________      ________
 1                 27            28            29            30            31


           BASE HAZARD PARAMETERS
              T#21
              ________
 1                 32


     STARTING VALUES


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           NU
              T#1           T             U1            U2            U3
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              U4            X
              ________      ________
 1              0.000         0.000


           LAMBDA
              F             T#1           T             X
              ________      ________      ________      ________
 T#1            0.000         1.000         0.000         0.000
 T              0.000         0.000         1.000         0.000
 U1             1.000         0.000         0.000         0.000
 U2             1.000         0.000         0.000         0.000
 U3             1.000         0.000         0.000         0.000
 U4             1.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         1.000


           THETA
              T#1           T             U1            U2            U3
              ________      ________      ________      ________      ________
 T#1            0.000
 T              0.000         0.000
 U1             0.000         0.000         1.000
 U2             0.000         0.000         0.000         1.000
 U3             0.000         0.000         0.000         0.000         1.000
 U4             0.000         0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000         0.000


           THETA
              U4            X
              ________      ________
 U4             1.000
 X              0.000         0.000


           ALPHA
              F             T#1           T             X
              ________      ________      ________      ________
 1              0.000       -20.000         0.000         0.000


           BETA
              F             T#1           T             X
              ________      ________      ________      ________
 F              0.000         0.000         0.000         0.200
 T#1            0.000         0.000         0.000         0.000
 T              0.050         0.000         0.000         0.100
 X              0.000         0.000         0.000         0.000


           PSI
              F             T#1           T             X
              ________      ________      ________      ________
 F              2.000
 T#1            0.000         0.000
 T              0.000         0.000         0.000
 X              0.000         0.000         0.000         0.500


     STARTING VALUES FOR THE BASE HAZARD PARAMETERS


           BASE HAZARD PARAMETERS
              T#1           T#2           T#3           T#4           T#5
              ________      ________      ________      ________      ________
 1              0.050         0.050         0.050         0.050         0.050


           BASE HAZARD PARAMETERS
              T#6           T#7           T#8           T#9           T#10
              ________      ________      ________      ________      ________
 1              0.050         0.050         0.050         0.050         0.050


           BASE HAZARD PARAMETERS
              T#11          T#12          T#13          T#14          T#15
              ________      ________      ________      ________      ________
 1              0.050         0.050         0.050         0.050         0.050


           BASE HAZARD PARAMETERS
              T#16          T#17          T#18          T#19          T#20
              ________      ________      ________      ________      ________
 1              0.050         0.050         0.050         0.050         0.050


           BASE HAZARD PARAMETERS
              T#21
              ________
 1              0.050


     POPULATION VALUES


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           NU
              T#1           T             U1            U2            U3
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              U4            X
              ________      ________
 1              0.000         0.000


           LAMBDA
              F             T#1           T             X
              ________      ________      ________      ________
 T#1            0.000         1.000         0.000         0.000
 T              0.000         0.000         1.000         0.000
 U1             1.000         0.000         0.000         0.000
 U2             1.000         0.000         0.000         0.000
 U3             1.000         0.000         0.000         0.000
 U4             1.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         1.000


           THETA
              T#1           T             U1            U2            U3
              ________      ________      ________      ________      ________
 T#1            0.000
 T              0.000         0.000
 U1             0.000         0.000         0.000
 U2             0.000         0.000         0.000         0.000
 U3             0.000         0.000         0.000         0.000         0.000
 U4             0.000         0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000         0.000


           THETA
              U4            X
              ________      ________
 U4             0.000
 X              0.000         0.000


           ALPHA
              F             T#1           T             X
              ________      ________      ________      ________
 1              0.000       -20.000         0.000         0.000


           BETA
              F             T#1           T             X
              ________      ________      ________      ________
 F              0.000         0.000         0.000         0.200
 T#1            0.000         0.000         0.000         0.000
 T              0.050         0.000         0.000         0.100
 X              0.000         0.000         0.000         0.000


           PSI
              F             T#1           T             X
              ________      ________      ________      ________
 F              2.000
 T#1            0.000         0.000
 T              0.000         0.000         0.000
 X              0.000         0.000         0.000         1.000


     POPULATION VALUES FOR THE BASE HAZARD PARAMETERS


           BASE HAZARD PARAMETERS
              T#1           T#2           T#3           T#4           T#5
              ________      ________      ________      ________      ________
 1              0.050         0.050         0.050         0.050         0.050


           BASE HAZARD PARAMETERS
              T#6           T#7           T#8           T#9           T#10
              ________      ________      ________      ________      ________
 1              0.050         0.050         0.050         0.050         0.050


           BASE HAZARD PARAMETERS
              T#11          T#12          T#13          T#14          T#15
              ________      ________      ________      ________      ________
 1              0.050         0.050         0.050         0.050         0.050


           BASE HAZARD PARAMETERS
              T#16          T#17          T#18          T#19          T#20
              ________      ________      ________      ________      ________
 1              0.050         0.050         0.050         0.050         0.050


           BASE HAZARD PARAMETERS
              T#21
              ________
 1              0.050


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.46535525D+04    0.0000000    0.0000000  EM
              2 -0.46464854D+04    7.0671924    0.0015187  EM
              3 -0.46455579D+04    0.9274355    0.0001996  EM
              4 -0.46453719D+04    0.1859825    0.0000400  EM
              5 -0.46452794D+04    0.0925119    0.0000199  EM
              6 -0.46452268D+04    0.0526516    0.0000113  EM
              7 -0.46451943D+04    0.0324854    0.0000070  EM
              8 -0.46451723D+04    0.0219768    0.0000047  EM
              9 -0.46451560D+04    0.0163248    0.0000035  EM
             10 -0.46451428D+04    0.0131594    0.0000028  EM
             11 -0.46451315D+04    0.0112856    0.0000024  EM
             12 -0.46451215D+04    0.0100923    0.0000022  EM
             13 -0.46451122D+04    0.0092641    0.0000020  EM
             14 -0.46451036D+04    0.0086366    0.0000019  EM
             15 -0.46450954D+04    0.0081236    0.0000017  EM
             16 -0.46450877D+04    0.0076795    0.0000017  EM
             17 -0.46450805D+04    0.0072801    0.0000016  EM
             18 -0.46450736D+04    0.0069123    0.0000015  EM
             19 -0.46450670D+04    0.0065687    0.0000014  EM
             20 -0.46450607D+04    0.0062452    0.0000013  EM
             21 -0.46450548D+04    0.0059392    0.0000013  EM
             22 -0.46450492D+04    0.0056490    0.0000012  EM
             23 -0.46450438D+04    0.0053734    0.0000012  EM
             24 -0.46450387D+04    0.0051116    0.0000011  EM
             25 -0.46450338D+04    0.0048626    0.0000010  EM
             26 -0.46450292D+04    0.0046259    0.0000010  EM
             27 -0.46450248D+04    0.0044007    0.0000009  EM
             28 -0.46450206D+04    0.0041866    0.0000009  EM
             29 -0.46450166D+04    0.0039829    0.0000009  EM
             30 -0.46450128D+04    0.0037892    0.0000008  EM
             31 -0.46450092D+04    0.0036049    0.0000008  EM
             32 -0.46450058D+04    0.0034296    0.0000007  EM
             33 -0.46450025D+04    0.0032629    0.0000007  EM
             34 -0.46449994D+04    0.0031044    0.0000007  EM
             35 -0.46449965D+04    0.0029535    0.0000006  EM
             36 -0.46449937D+04    0.0028101    0.0000006  EM
             37 -0.46449416D+04    0.0520974    0.0000112  FS
             38 -0.46449384D+04    0.0031979    0.0000007  FS
             39 -0.46449380D+04    0.0003200    0.0000001  FS


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    T
    U1
    U2
    U3
    U4
    X
    _TCENT

  Save file
    ex6.22.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:02:56
        Ending Time:  22:02:57
       Elapsed Time:  00:00:01



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