[R] what does the it when there is a zero events in the Logistic Regression with glm?

[Prof Brian Ripley]

On Tue, 22 Nov 2005, S. Sun wrote:

> I have a question about the glm.

Not really: your question is about understanding logistic regressions.

> When the events of an observation is 0,
> the logit function on it is Inf. I wonder how the glm solve it.

Note that logit(0)  = -Inf whereas logit(1) = Inf.

It is the fitted probabilities which are passed to logit, not the 
empirical proportions.  Logistic regression is often applied to Bernouilli 
trials with 0/1 proportions, with nothing to `solve'.

So the issue only arises if the MLE would give 0 (or 1) fitted values, and 
it cannot in a logistic regression.  You have here an example in which the 
MLE does not exist and the log-likelihood does not attain its maximum. 
Such situations are known as `separation' and it is well-known that there 
are better algorithms for such problems.

> An example:
> Treat Events Trials
> A     0      50
> B     7      50
> C     10     50
> D     15     50
> E     17     50
>
> Program:
>
> treat <- factor(c("A", "B", "C", "D", "E"))
> events <- c(0, 7, 10, 15, 17)
> trials <- rep(50, 5)
> glm(cbind(events, trials-events)~treat, family=binomial)
>
> What's wrong with it? And are there better ideas?

Nothing is `wrong with it'.  It finds fitted values which are very close 
to the observed values.  You have chosen an inappropriate model and an 
inappropriate parametrization (see ?relevel).

I presume you did think something is wrong, but you did not tell us what.
Please do read the posting guide and try to provide us with enough 
information to help you.  Also, please do sign your messages indicating 
who you are and what your background is.  In cases like this the best 
advice is to suggest asking your supervisor (if you have one) or to read 
the literature (but what specifically depends on your background).

-- 
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)
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