[S] Residual Deviance and log-likelihood

Paul Monaghan (pfm@scmp.scm.liv.ac.uk)
Thu, 19 Feb 1998 13:45:02 +0000 (GMT)


To 'compare' the likelihoods between models for T and log T, the term

- (sum over uncensored observations) log T (*)

should be added to the survreg output for log-likelihood. This is the constant
which Professor Ripley suggested in his recent mail to s-news. The result can
be shown by comparing the likelihood using T under the
Weibull/log-logistic/log-normal model with the likelihood using log T under the
extreme value/logistic/normal model. The latter is given by the survreg fit. I
have studied this in depth, mainly because I wanted to write a program which
fitted a log-logistic proportional hazards model to T, and realised that the
likelihoods were not on the same 'scale' (I cannot think of a better way to #
describe this!)

I think that the amendment (*) is a property of the accelerated life models, and
although I am not certain, would not expect it to hold for models fitted to log T,
where T has a parametric proportional hazards formulation. The 'exception' to this
is of course the Weibull model, which is both proportional hazards and accelerated
life.

Paul Monaghan.
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