Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:47 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a Monte Carlo simulation study for a two-level
          continuous-time survival analysis using Cox regression with a random
          intercept and a frailty
  MONTECARLO:
  	NAMES = t x w;
  	NOBSERVATIONS = 1000;
  	NREPS = 100;
  	GENERATE = t(s 20*1);
  	NCSIZES = 3;
  	CSIZES = 40 (5) 50 (10) 20 (15);
  	HAZARDC = t (.5);
  	SURVIVAL = t (ALL);
  	WITHIN = x;
  	BETWEEN = w;
  MODEL POPULATION:
  	%WITHIN%
  	x@1;
  	t ON x*.5;
  	%BETWEEN%
  	w@1;
  	[t#1-t#21*1];
  	t ON w*.2;
  	t*0.5;
  ANALYSIS:	TYPE = TWOLEVEL;
  	BASEHAZARD = OFF;
  MODEL:	%WITHIN%
  	t ON x*.5;
  	%BETWEEN%
  	t ON w*.2;
  	t*0.5;



INPUT READING TERMINATED NORMALLY



this is an example of a Monte Carlo simulation study for a two-level
continuous-time survival analysis using Cox regression with a random
intercept and a frailty

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of replications
    Requested                                                  100
    Completed                                                  100
Value of seed                                                    0

Number of dependent variables                                    1
Number of independent variables                                  2
Number of continuous latent variables                            0

Observed dependent variables

  Time-to-event (survival)
   T

Observed independent variables
   X           W

Variables with special functions

  Within variables
   X

  Between variables
   W


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
Base Hazard                                                    OFF
Cholesky                                                        ON


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Cluster information

       Size (s)    Number of clusters of Size s

          5            40
         10            50
         15            20


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              X             W
              ________      ________
 1              0.008        -0.092


           Covariances
              X             W
              ________      ________
 X              1.023
 W              0.009         1.167


           Correlations
              X             W
              ________      ________
 X              1.000
 W              0.008         1.000




MODEL FIT INFORMATION

Number of Free Parameters                        3

Loglikelihood

    H0 Value

        Mean                                96.089
        Std Dev                             44.693
        Number of successful computations      100

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990           -7.881        -11.717
           0.980       0.990            4.302          7.186
           0.950       0.950           22.573         18.102
           0.900       0.890           38.810         31.137
           0.800       0.790           58.475         54.610
           0.700       0.700           72.652         70.691
           0.500       0.520           96.089         97.092
           0.300       0.310          119.527        120.290
           0.200       0.170          133.703        129.395
           0.100       0.090          153.368        148.974
           0.050       0.050          169.606        169.055
           0.020       0.040          187.876        191.153
           0.010       0.010          200.060        196.213

Information Criteria

    Akaike (AIC)

        Mean                              -186.179
        Std Dev                             89.387
        Number of successful computations      100

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990         -394.120       -414.150
           0.980       0.960         -369.753       -386.426
           0.950       0.950         -333.211       -343.869
           0.900       0.910         -300.737       -300.771
           0.800       0.830         -261.407       -254.272
           0.700       0.690         -233.053       -237.716
           0.500       0.480         -186.179       -193.103
           0.300       0.300         -139.304       -140.764
           0.200       0.210         -110.951       -110.331
           0.100       0.110          -71.620        -68.276
           0.050       0.050          -39.146        -41.328
           0.020       0.010           -2.605         -8.703
           0.010       0.010           21.762         -8.372

    Bayesian (BIC)

        Mean                              -171.455
        Std Dev                             89.387
        Number of successful computations      100

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990         -379.396       -399.427
           0.980       0.960         -355.029       -371.702
           0.950       0.950         -318.488       -329.145
           0.900       0.910         -286.014       -286.048
           0.800       0.830         -246.683       -239.549
           0.700       0.690         -218.330       -222.993
           0.500       0.480         -171.455       -178.380
           0.300       0.300         -124.581       -126.041
           0.200       0.210          -96.227        -95.608
           0.100       0.110          -56.897        -53.553
           0.050       0.050          -24.423        -26.605
           0.020       0.010           12.119          6.020
           0.010       0.010           36.486          6.352

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

        Mean                              -180.984
        Std Dev                             89.387
        Number of successful computations      100

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.990         -388.924       -408.955
           0.980       0.960         -364.558       -381.231
           0.950       0.950         -328.016       -338.674
           0.900       0.910         -295.542       -295.576
           0.800       0.830         -256.212       -249.077
           0.700       0.690         -227.858       -232.521
           0.500       0.480         -180.984       -187.908
           0.300       0.300         -134.109       -135.569
           0.200       0.210         -105.755       -105.136
           0.100       0.110          -66.425        -63.081
           0.050       0.050          -33.951        -36.133
           0.020       0.010            2.590         -3.508
           0.010       0.010           26.957         -3.177



MODEL RESULTS

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

 T          ON
  X                0.500     0.5019     0.0523     0.0456     0.0027 0.900 1.000

Between Level

 T          ON
  W                0.200     0.2064     0.0835     0.0789     0.0069 0.940 0.730

 Residual Variances
  T                0.500     0.4960     0.1002     0.0993     0.0100 0.920 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.274E+00
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              T#1           T             X             W
              ________      ________      ________      ________
 1                  0             0             0             0


           LAMBDA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1                0             0             0             0
 T                  0             0             0             0
 X                  0             0             0             0
 W                  0             0             0             0


           THETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1                0
 T                  0             0
 X                  0             0             0
 W                  0             0             0             0


           ALPHA
              T#1           T             X             W
              ________      ________      ________      ________
 1                  0             0             0             0


           BETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1                0             0             0             0
 T                  0             0             1             0
 X                  0             0             0             0
 W                  0             0             0             0


           PSI
              T#1           T             X             W
              ________      ________      ________      ________
 T#1                0
 T                  0             0
 X                  0             0             0
 W                  0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN


           NU
              T#1           T             X             W
              ________      ________      ________      ________
 1                  0             0             0             0


           LAMBDA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1                0             0             0             0
 T                  0             0             0             0
 X                  0             0             0             0
 W                  0             0             0             0


           THETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1                0
 T                  0             0
 X                  0             0             0
 W                  0             0             0             0


           ALPHA
              T#1           T             X             W
              ________      ________      ________      ________
 1                  0             0             0             0


           BETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1                0             0             0             0
 T                  0             0             0             2
 X                  0             0             0             0
 W                  0             0             0             0


           PSI
              T#1           T             X             W
              ________      ________      ________      ________
 T#1                0
 T                  0             3
 X                  0             0             0
 W                  0             0             0             0


     STARTING VALUES FOR WITHIN


           NU
              T#1           T             X             W
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            1.000         0.000         0.000         0.000
 T              0.000         1.000         0.000         0.000
 X              0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         1.000


           THETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000
 T              0.000         0.000
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


           ALPHA
              T#1           T             X             W
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           BETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000         0.000         0.000         0.000
 T              0.000         0.000         0.500         0.000
 X              0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


           PSI
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000
 T              0.000         0.000
 X              0.000         0.000         0.500
 W              0.000         0.000         0.000         0.000


     STARTING VALUES FOR BETWEEN


           NU
              T#1           T             X             W
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            1.000         0.000         0.000         0.000
 T              0.000         1.000         0.000         0.000
 X              0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         1.000


           THETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000
 T              0.000         0.000
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


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


           BETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000         0.000         0.000         0.000
 T              0.000         0.000         0.000         0.200
 X              0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


           PSI
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000
 T              0.000         0.500
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000         0.500


     POPULATION VALUES FOR WITHIN


           NU
              T#1           T             X             W
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            1.000         0.000         0.000         0.000
 T              0.000         1.000         0.000         0.000
 X              0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         1.000


           THETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000
 T              0.000         0.000
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


           ALPHA
              T#1           T             X             W
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           BETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000         0.000         0.000         0.000
 T              0.000         0.000         0.500         0.000
 X              0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


           PSI
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000
 T              0.000         0.000
 X              0.000         0.000         1.000
 W              0.000         0.000         0.000         0.000


     POPULATION VALUES FOR BETWEEN


           NU
              T#1           T             X             W
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            1.000         0.000         0.000         0.000
 T              0.000         1.000         0.000         0.000
 X              0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         1.000


           THETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000
 T              0.000         0.000
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


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


           BETA
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000         0.000         0.000         0.000
 T              0.000         0.000         0.000         0.200
 X              0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


           PSI
              T#1           T             X             W
              ________      ________      ________      ________
 T#1            0.000
 T              0.000         0.500
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000         1.000


     POPULATION VALUES FOR THE BASE HAZARD PARAMETERS FOR WITHIN


           BASE HAZARD PARAMETERS
              T#1           T#2           T#3           T#4           T#5
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BASE HAZARD PARAMETERS
              T#6           T#7           T#8           T#9           T#10
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BASE HAZARD PARAMETERS
              T#11          T#12          T#13          T#14          T#15
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BASE HAZARD PARAMETERS
              T#16          T#17          T#18          T#19          T#20
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BASE HAZARD PARAMETERS
              T#21
              ________
 1              0.000


     POPULATION VALUES FOR THE BASE HAZARD PARAMETERS FOR BETWEEN


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


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


           BASE HAZARD PARAMETERS
              T#11          T#12          T#13          T#14          T#15
              ________      ________      ________      ________      ________
 1              1.000         1.000         1.000         1.000         1.000


           BASE HAZARD PARAMETERS
              T#16          T#17          T#18          T#19          T#20
              ________      ________      ________      ________      ________
 1              1.000         1.000         1.000         1.000         1.000


           BASE HAZARD PARAMETERS
              T#21
              ________
 1              1.000


     Beginning Time:  22:47:26
        Ending Time:  22:48:06
       Elapsed Time:  00:00:40



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