Re: [S] Residual Deviance and log-likelihood in survreg

Prof Brian Ripley (ripley@stats.ox.ac.uk)
Wed, 18 Feb 1998 16:29:25 GMT


On Fri, 13 Feb 1998 I wrote:

> It would not be for a glm fit, either. The definition of residual
> deviance used here is
>
> 2[log L(saturated model) - log L(this model)]
>
> (For a glm fit we also need to worry about scale factors: `deviance' is
> certainly more complicated than -2 log L. Indeed, as a likelihood of
> continuous data is only defined up to a multiplicative constant, the
> the absolute value of -2 log L has no statistical meaning.)
>

That was prescience! I have just discovered that the log-likelihood
given by survreg is that viewing link(T) (by default, log T) as the
data, whereas the natural formulation is to view T (time to event) as the
data. This alters -2 log L by an additive constant that depends only
on the non-censored observations and the `link'. So there is a
problem in comparing -2 log L if the `link' is changed, as then the
base measure is changed.

Brian Ripley
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