[R] Parameters of Weibull regression
Christian Hennig
fm3a004 at math.uni-hamburg.de
Mon Mar 14 13:22:53 CET 2005
Dear list, dear Frank,
I try to fit a Weibull survival regression model with package Design:
sclear <- psm(sobj~V1+V2,dist="weibull")
sobj is a one-dimensional survival object (no event indicators), V1 and V2
are factors.
I get the following result:
Parametric Survival Model: Weibull Distribution
psm(formula = sobj ~ V1 + V2, dist = "weibull")
Obs Events Model L.R. d.f. P R2
120 120 30.96 3 0 0.23
Value Std. Error z p
(Intercept) 2.6161 0.0639 40.94 0.00e+00
V1=2 0.3098 0.0748 4.14 3.47e-05
V1=3 0.0911 0.0741 1.23 2.19e-01
V2=2 -0.2212 0.0613 -3.61 3.09e-04
Log(scale) -1.1060 0.0704 -15.70 1.52e-55
Scale= 0.331
I wonder how to relate the estimated parameters to the Weibull regression
model. Here is the model specification from Harrel, Regression Modeling
Strategies, p. 422:
S(t|X)=exp[-\alpha*t^\gamma exp(X\beta)]
This is the model without intercept, and it is indicated that \alpha can be
replaced by exp(\beta_0) in the model with intercept.
Now I am puzzled by the fact that \alpha (or \alpha exp(X\beta))
is usually referred to as
"scale parameter" in the context of the Weibull distribution. If this would
be the case, I could get the Weibull scale from the \beta/\beta_0 estimators
and I would need an estimator for \gamma. But only one further estimator is
given which is called "scale". This is definitely not the \gamma estimator,
because if I compute, say, median estimators, I get a result outside the
value range. From survplot I know that the model fit of the survival
function is OK, so in principle it seems that I did the right thing.
But how do I relate the output to the parameters
\alpha,\gamma,\beta in the model?
Thanks,
Christian
***********************************************************************
Christian Hennig
Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg
hennig at math.uni-hamburg.de, http://www.math.uni-hamburg.de/home/hennig/
>From 1 April 2005: Department of Statistical Science, UCL, London
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ich empfehle www.boag-online.de
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