Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:12 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a continuous-time
survival analysis using a parametric
proportional hazards model with a factor
influencing survival
DATA: FILE = ex6.22.dat;
VARIABLE: NAMES = t u1-u4 x tc;
SURVIVAL = t (20*1);
TIMECENSORED = tc;
CATEGORICAL = u1-u4;
ANALYSIS: ALGORITHM = INTEGRATION;
BASEHAZARD = ON;
MODEL: f BY u1-u4;
[t#1-t#21];
t ON x f;
f ON x;
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a continuous-time
survival analysis using a parametric
proportional hazards model with a factor
influencing survival
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
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
Variables with special functions
Time-censoring variables
TC
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
Input data file(s)
ex6.22.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.505 505.000
Category 2 0.495 495.000
U2
Category 1 0.505 505.000
Category 2 0.495 495.000
U3
Category 1 0.486 486.000
Category 2 0.514 514.000
U4
Category 1 0.517 517.000
Category 2 0.483 483.000
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
X 0.056 -0.051 -2.941 0.10% -0.754 -0.187 0.038
1000.000 1.031 0.012 3.254 0.10% 0.305 0.934
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 32
Loglikelihood
H0 Value -4644.938
H0 Scaling Correction Factor 0.9988
for MLR
Information Criteria
Akaike (AIC) 9353.876
Bayesian (BIC) 9510.924
Sample-Size Adjusted BIC 9409.291
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F BY
U1 1.000 0.000 999.000 999.000
U2 0.839 0.139 6.053 0.000
U3 1.067 0.199 5.352 0.000
U4 0.853 0.153 5.581 0.000
F ON
X 0.212 0.063 3.364 0.001
T ON
F 0.038 0.036 1.057 0.291
T ON
X 0.085 0.043 1.982 0.047
Thresholds
U1$1 0.038 0.092 0.418 0.676
U2$1 0.035 0.084 0.416 0.677
U3$1 -0.074 0.095 -0.784 0.433
U4$1 0.100 0.085 1.176 0.239
Residual Variances
F 2.465 0.597 4.130 0.000
Base Hazard Parameters
T#1 0.049 0.007 6.861 0.000
T#2 0.060 0.008 7.191 0.000
T#3 0.049 0.008 6.238 0.000
T#4 0.050 0.008 6.012 0.000
T#5 0.035 0.007 4.781 0.000
T#6 0.055 0.010 5.738 0.000
T#7 0.046 0.009 5.005 0.000
T#8 0.049 0.010 4.890 0.000
T#9 0.050 0.011 4.672 0.000
T#10 0.057 0.012 4.775 0.000
T#11 0.048 0.011 4.251 0.000
T#12 0.047 0.012 4.027 0.000
T#13 0.073 0.016 4.670 0.000
T#14 0.040 0.012 3.319 0.001
T#15 0.040 0.013 3.158 0.002
T#16 0.058 0.016 3.573 0.000
T#17 0.053 0.016 3.314 0.001
T#18 0.048 0.016 3.019 0.003
T#19 0.065 0.020 3.317 0.001
T#20 0.053 0.019 2.802 0.005
T#21 0.047 0.006 8.281 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.115E-03
(ratio of smallest to largest eigenvalue)
RESULTS IN PROBABILITY SCALE
Estimate
U1
Category 1 0.505
Category 2 0.495
U2
Category 1 0.505
Category 2 0.495
U3
Category 1 0.486
Category 2 0.514
U4
Category 1 0.517
Category 2 0.483
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
________ ________ ________ ________
0.020 0.020 -0.056 0.068
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 0.000
T#1 0.000 0.000 0.000 0.000
T 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000
PSI
F T#1 T X
________ ________ ________ ________
F 0.050
T#1 0.000 0.000
T 0.000 0.000 0.000
X 0.000 0.000 0.000 0.515
STARTING VALUES FOR THE BASE HAZARD PARAMETERS
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
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.13147066D+05 0.0000000 0.0000000 EM
2 -0.47982293D+04 8348.8367075 0.6350342 EM
3 -0.47607506D+04 37.4787160 0.0078109 EM
4 -0.47267041D+04 34.0464563 0.0071515 EM
5 -0.47078917D+04 18.8124525 0.0039800 EM
6 -0.47008234D+04 7.0682326 0.0015014 EM
7 -0.46985488D+04 2.2746135 0.0004839 EM
8 -0.46976600D+04 0.8888471 0.0001892 EM
9 -0.46971191D+04 0.5408349 0.0001151 EM
10 -0.46966688D+04 0.4503482 0.0000959 EM
11 -0.46962464D+04 0.4223771 0.0000899 EM
12 -0.46958343D+04 0.4121102 0.0000878 EM
13 -0.46954257D+04 0.4085767 0.0000870 EM
14 -0.46950173D+04 0.4084354 0.0000870 EM
15 -0.46946070D+04 0.4103041 0.0000874 EM
16 -0.46941935D+04 0.4134542 0.0000881 EM
17 -0.46937761D+04 0.4174506 0.0000889 EM
18 -0.46933541D+04 0.4220224 0.0000899 EM
19 -0.46929271D+04 0.4269899 0.0000910 EM
20 -0.46924948D+04 0.4322350 0.0000921 EM
21 -0.46920572D+04 0.4376821 0.0000933 EM
22 -0.46916139D+04 0.4432719 0.0000945 EM
23 -0.46911649D+04 0.4489643 0.0000957 EM
24 -0.46907102D+04 0.4547348 0.0000969 EM
25 -0.46902496D+04 0.4605562 0.0000982 EM
26 -0.46897832D+04 0.4664102 0.0000994 EM
27 -0.46893109D+04 0.4722873 0.0001007 EM
28 -0.46888328D+04 0.4781691 0.0001020 EM
29 -0.46883487D+04 0.4840434 0.0001032 EM
30 -0.46878588D+04 0.4899095 0.0001045 EM
31 -0.46873631D+04 0.4957389 0.0001057 EM
32 -0.46868615D+04 0.5015346 0.0001070 EM
33 -0.46863543D+04 0.5072800 0.0001082 EM
34 -0.46858413D+04 0.5129754 0.0001095 EM
35 -0.46853227D+04 0.5185913 0.0001107 EM
36 -0.46847986D+04 0.5241303 0.0001119 EM
37 -0.46842690D+04 0.5295741 0.0001130 EM
38 -0.46837341D+04 0.5349195 0.0001142 EM
39 -0.46831939D+04 0.5401401 0.0001153 EM
40 -0.46826487D+04 0.5452449 0.0001164 EM
41 -0.46820985D+04 0.5501908 0.0001175 EM
42 -0.46815435D+04 0.5549974 0.0001185 EM
43 -0.46809839D+04 0.5596179 0.0001195 EM
44 -0.46804198D+04 0.5640710 0.0001205 EM
45 -0.46798515D+04 0.5683095 0.0001214 EM
46 -0.46792791D+04 0.5723514 0.0001223 EM
47 -0.46787030D+04 0.5761493 0.0001231 EM
48 -0.46781233D+04 0.5797206 0.0001239 EM
49 -0.46775402D+04 0.5830182 0.0001246 EM
50 -0.46769542D+04 0.5860587 0.0001253 EM
51 -0.46763654D+04 0.5888037 0.0001259 EM
52 -0.46757741D+04 0.5912457 0.0001264 EM
53 -0.46751808D+04 0.5933707 0.0001269 EM
54 -0.46745856D+04 0.5951640 0.0001273 EM
55 -0.46739890D+04 0.5966121 0.0001276 EM
56 -0.46733913D+04 0.5977015 0.0001279 EM
57 -0.46727929D+04 0.5984195 0.0001280 EM
58 -0.46721941D+04 0.5987542 0.0001281 EM
59 -0.46715954D+04 0.5986944 0.0001281 EM
60 -0.46702085D+04 1.3869099 0.0002969 QN
61 -0.46688305D+04 1.3780203 0.0002951 EM
62 -0.46680868D+04 0.7436484 0.0001593 EM
63 -0.46674708D+04 0.6159991 0.0001320 EM
64 -0.46668818D+04 0.5890326 0.0001262 EM
65 -0.46663011D+04 0.5806668 0.0001244 EM
66 -0.46657257D+04 0.5754004 0.0001233 EM
67 -0.46651554D+04 0.5703750 0.0001222 EM
68 -0.46645903D+04 0.5650641 0.0001211 EM
69 -0.46640309D+04 0.5593712 0.0001199 EM
70 -0.46634777D+04 0.5532818 0.0001186 EM
71 -0.46629309D+04 0.5467990 0.0001173 EM
72 -0.46609614D+04 1.9694520 0.0004224 QN
73 -0.46595235D+04 1.4378999 0.0003085 EM
74 -0.46587509D+04 0.7726089 0.0001658 EM
75 -0.46581448D+04 0.6061018 0.0001301 EM
76 -0.46576098D+04 0.5349781 0.0001148 EM
77 -0.46571162D+04 0.4936031 0.0001060 EM
78 -0.46566511D+04 0.4651334 0.0000999 EM
79 -0.46562075D+04 0.4436057 0.0000953 EM
80 -0.46557813D+04 0.4261569 0.0000915 EM
81 -0.46553701D+04 0.4112119 0.0000883 EM
82 -0.46549723D+04 0.3978256 0.0000855 EM
83 -0.46545868D+04 0.3854329 0.0000828 EM
84 -0.46542132D+04 0.3736765 0.0000803 EM
85 -0.46538508D+04 0.3623527 0.0000779 EM
86 -0.46534995D+04 0.3513278 0.0000755 EM
87 -0.46531590D+04 0.3405371 0.0000732 EM
88 -0.46528290D+04 0.3299231 0.0000709 EM
89 -0.46525096D+04 0.3194668 0.0000687 EM
90 -0.46522004D+04 0.3091687 0.0000665 EM
91 -0.46519014D+04 0.2990254 0.0000643 EM
92 -0.46516123D+04 0.2890300 0.0000621 EM
93 -0.46513331D+04 0.2791962 0.0000600 EM
94 -0.46510636D+04 0.2695288 0.0000579 EM
95 -0.46508036D+04 0.2600423 0.0000559 EM
96 -0.46505528D+04 0.2507368 0.0000539 EM
97 -0.46503112D+04 0.2416239 0.0000520 EM
98 -0.46500785D+04 0.2327083 0.0000500 EM
99 -0.46498545D+04 0.2239816 0.0000482 EM
100 -0.46496390D+04 0.2155144 0.0000463 EM
101 -0.46494318D+04 0.2072291 0.0000446 EM
102 -0.46492326D+04 0.1991630 0.0000428 EM
103 -0.46490413D+04 0.1913179 0.0000412 EM
104 -0.46488576D+04 0.1836958 0.0000395 EM
105 -0.46486813D+04 0.1762978 0.0000379 EM
106 -0.46485122D+04 0.1691241 0.0000364 EM
107 -0.46483500D+04 0.1621744 0.0000349 EM
108 -0.46481946D+04 0.1554476 0.0000334 EM
109 -0.46480456D+04 0.1489422 0.0000320 EM
110 -0.46479030D+04 0.1426559 0.0000307 EM
111 -0.46452490D+04 2.6539113 0.0005710 QN
112 -0.46451556D+04 0.0933985 0.0000201 EM
113 -0.46451318D+04 0.0238436 0.0000051 EM
114 -0.46451169D+04 0.0148689 0.0000032 EM
115 -0.46451056D+04 0.0112858 0.0000024 EM
116 -0.46450962D+04 0.0094513 0.0000020 EM
117 -0.46450878D+04 0.0083532 0.0000018 EM
118 -0.46450802D+04 0.0076175 0.0000016 EM
119 -0.46450732D+04 0.0070748 0.0000015 EM
120 -0.46450665D+04 0.0066403 0.0000014 EM
121 -0.46450602D+04 0.0062698 0.0000013 EM
122 -0.46450543D+04 0.0059398 0.0000013 EM
123 -0.46450487D+04 0.0056376 0.0000012 EM
124 -0.46450433D+04 0.0053564 0.0000012 EM
125 -0.46450382D+04 0.0050921 0.0000011 EM
126 -0.46449385D+04 0.0997590 0.0000215 QN
127 -0.46449381D+04 0.0003152 0.0000001 EM
Beginning Time: 23:12:25
Ending Time: 23:12:28
Elapsed Time: 00:00:03
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