Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:06 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)
Non-parametric
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
________ ________
0.008 -0.092
Covariances
X W
________ ________
X 1.022
W 0.009 1.166
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 0.040 187.876 191.154
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 -386.425
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 -180.983
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 -381.230
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 -180.983 -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 2.591 -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 0.4959 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
________ ________ ________
0 0 0
LAMBDA
T#1 T X
________ ________ ________
T#1 0 0 0
T 0 0 0
X 0 0 0
THETA
T#1 T X
________ ________ ________
T#1 0
T 0 0
X 0 0 0
ALPHA
T#1 T X
________ ________ ________
0 0 0
BETA
T#1 T X
________ ________ ________
T#1 0 0 0
T 0 0 1
X 0 0 0
PSI
T#1 T X
________ ________ ________
T#1 0
T 0 0
X 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
T#1 T W
________ ________ ________
0 0 0
LAMBDA
T#1 T W
________ ________ ________
T#1 0 0 0
T 0 0 0
W 0 0 0
THETA
T#1 T W
________ ________ ________
T#1 0
T 0 0
W 0 0 0
ALPHA
T#1 T W
________ ________ ________
0 0 0
BETA
T#1 T W
________ ________ ________
T#1 0 0 0
T 0 0 2
W 0 0 0
PSI
T#1 T W
________ ________ ________
T#1 0
T 0 3
W 0 0 0
STARTING VALUES FOR WITHIN
NU
T#1 T X
________ ________ ________
0.000 0.000 0.000
LAMBDA
T#1 T X
________ ________ ________
T#1 1.000 0.000 0.000
T 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
T#1 T X
________ ________ ________
T#1 0.000
T 0.000 0.000
X 0.000 0.000 0.000
ALPHA
T#1 T X
________ ________ ________
0.000 0.000 0.000
BETA
T#1 T X
________ ________ ________
T#1 0.000 0.000 0.000
T 0.000 0.000 0.500
X 0.000 0.000 0.000
PSI
T#1 T X
________ ________ ________
T#1 0.000
T 0.000 0.000
X 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN
NU
T#1 T W
________ ________ ________
0.000 0.000 0.000
LAMBDA
T#1 T W
________ ________ ________
T#1 1.000 0.000 0.000
T 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
T#1 T W
________ ________ ________
T#1 0.000
T 0.000 0.000
W 0.000 0.000 0.000
ALPHA
T#1 T W
________ ________ ________
-20.000 0.000 0.000
BETA
T#1 T W
________ ________ ________
T#1 0.000 0.000 0.000
T 0.000 0.000 0.200
W 0.000 0.000 0.000
PSI
T#1 T W
________ ________ ________
T#1 0.000
T 0.000 0.500
W 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
NU
T#1 T X
________ ________ ________
0.000 0.000 0.000
LAMBDA
T#1 T X
________ ________ ________
T#1 1.000 0.000 0.000
T 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
T#1 T X
________ ________ ________
T#1 0.000
T 0.000 0.000
X 0.000 0.000 0.000
ALPHA
T#1 T X
________ ________ ________
0.000 0.000 0.000
BETA
T#1 T X
________ ________ ________
T#1 0.000 0.000 0.000
T 0.000 0.000 0.500
X 0.000 0.000 0.000
PSI
T#1 T X
________ ________ ________
T#1 0.000
T 0.000 0.000
X 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN
NU
T#1 T W
________ ________ ________
0.000 0.000 0.000
LAMBDA
T#1 T W
________ ________ ________
T#1 1.000 0.000 0.000
T 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
T#1 T W
________ ________ ________
T#1 0.000
T 0.000 0.000
W 0.000 0.000 0.000
ALPHA
T#1 T W
________ ________ ________
-20.000 0.000 0.000
BETA
T#1 T W
________ ________ ________
T#1 0.000 0.000 0.000
T 0.000 0.000 0.200
W 0.000 0.000 0.000
PSI
T#1 T W
________ ________ ________
T#1 0.000
T 0.000 0.500
W 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
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BASE HAZARD PARAMETERS
T#6 T#7 T#8 T#9 T#10
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BASE HAZARD PARAMETERS
T#11 T#12 T#13 T#14 T#15
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BASE HAZARD PARAMETERS
T#16 T#17 T#18 T#19 T#20
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BASE HAZARD PARAMETERS
T#21
________
0.000
POPULATION VALUES FOR THE BASE HAZARD PARAMETERS FOR BETWEEN
BASE HAZARD PARAMETERS
T#1 T#2 T#3 T#4 T#5
________ ________ ________ ________ ________
1.000 1.000 1.000 1.000 1.000
BASE HAZARD PARAMETERS
T#6 T#7 T#8 T#9 T#10
________ ________ ________ ________ ________
1.000 1.000 1.000 1.000 1.000
BASE HAZARD PARAMETERS
T#11 T#12 T#13 T#14 T#15
________ ________ ________ ________ ________
1.000 1.000 1.000 1.000 1.000
BASE HAZARD PARAMETERS
T#16 T#17 T#18 T#19 T#20
________ ________ ________ ________ ________
1.000 1.000 1.000 1.000 1.000
BASE HAZARD PARAMETERS
T#21
________
1.000
Beginning Time: 23:06:02
Ending Time: 23:06:23
Elapsed Time: 00:00:21
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