[R] "logistic" + "neg binomial" + ...

[Prof Brian Ripley]

On Fri, 22 Sep 2006, Ted.Harding at nessie.mcc.ac.uk wrote:

> Hi Folks,
>
> I've just come across a kind of problem which leads
> me to wonder how to approach it in R.
>
> Basically, each a set of items is subjected to a series
> of "impacts" until it eventually "fails". The "force"
> of each impact would depend on  covariates X,Y say;
> but as a result of preceding impacts an item would be
> expected to have a "cumulative frailty" such that the
> probability of failure due to a particular impact would
> possibly increase according to the series of impacts
> already survived.

So this is a discrete-time survival model.

> Without the "cumulative frailty" one could envisage
> something like a logistic model for the probabiliy
> of failure at each impact, leading to a kind of
> generalised "exponential distribution" -- that is,
> the likelihood for each item would be of the form
>
>  (1-P[1])*(1-P[2])*...*(1-P[n-1])*P[n]
>
> where P[i] could have a logistic model in terms of
> the values of X[i] and Y[i], and n is the index of
> the impact at which failure occurred. That is then
> a solvable problem.
>
> Even so, I'm not (so far) finding in the R resources
> the appropriate analogue of glm for this kind of
> model. I dare say a prolonged trawl through the various
> "survival" resources might lead to something applicable,
> but ...

What is inadequate about glm itself?  The log-likelihood is a sum of terms 
over impacts, so fitting logisitic models for each impact can be done 
separately for each model. However, nnet() can fit them simultaneously 
(and couple them if you want).

> And then there's the cumulative frailty ... !

Add the history to that point into the model.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595