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

Prof Brian Ripley ripley at stats.ox.ac.uk
Tue Nov 22 09:07:23 CET 2005

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

> I have a question about the glm.

> 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
who you are and what your background is.  In cases like this the best
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)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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