Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 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)
Parametric (time intervals)
T (20)
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
________
0.056
Covariances
X
________
X 1.031
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
________ ________ ________ ________
8 9 10 11
NU
T#1 T U1 U2 U3
________ ________ ________ ________ ________
0 0 0 0 0
NU
U4 X
________ ________
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
________ ________ ________ ________
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
________ ________ ________ ________ ________
12 13 14 15 16
BASE HAZARD PARAMETERS
T#6 T#7 T#8 T#9 T#10
________ ________ ________ ________ ________
17 18 19 20 21
BASE HAZARD PARAMETERS
T#11 T#12 T#13 T#14 T#15
________ ________ ________ ________ ________
22 23 24 25 26
BASE HAZARD PARAMETERS
T#16 T#17 T#18 T#19 T#20
________ ________ ________ ________ ________
27 28 29 30 31
BASE HAZARD PARAMETERS
T#21
________
32
STARTING VALUES
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
T#1 T U1 U2 U3
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U4 X
________ ________
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
________ ________ ________ ________
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
________ ________ ________ ________ ________
0.050 0.050 0.050 0.050 0.050
BASE HAZARD PARAMETERS
T#6 T#7 T#8 T#9 T#10
________ ________ ________ ________ ________
0.050 0.050 0.050 0.050 0.050
BASE HAZARD PARAMETERS
T#11 T#12 T#13 T#14 T#15
________ ________ ________ ________ ________
0.050 0.050 0.050 0.050 0.050
BASE HAZARD PARAMETERS
T#16 T#17 T#18 T#19 T#20
________ ________ ________ ________ ________
0.050 0.050 0.050 0.050 0.050
BASE HAZARD PARAMETERS
T#21
________
0.050
POPULATION VALUES
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
T#1 T U1 U2 U3
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U4 X
________ ________
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
________ ________ ________ ________
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
________ ________ ________ ________ ________
0.050 0.050 0.050 0.050 0.050
BASE HAZARD PARAMETERS
T#6 T#7 T#8 T#9 T#10
________ ________ ________ ________ ________
0.050 0.050 0.050 0.050 0.050
BASE HAZARD PARAMETERS
T#11 T#12 T#13 T#14 T#15
________ ________ ________ ________ ________
0.050 0.050 0.050 0.050 0.050
BASE HAZARD PARAMETERS
T#16 T#17 T#18 T#19 T#20
________ ________ ________ ________ ________
0.050 0.050 0.050 0.050 0.050
BASE HAZARD PARAMETERS
T#21
________
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: 22:24:19
Ending Time: 22:24:20
Elapsed Time: 00:00:01
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