[R] Logit reality check

[Thomas Lumley]

On Sun, 28 Sep 2003, Andrew Criswell wrote:

> Hello all:
>
> I've been given the following data and have been asked to run a logit
> model using glm().  The variable, Y, is a proportion ranging from 0 to
> 1, X is a covariate.  Without a base number of observations from which Y
> is computed as a proportion, I believe there is not sufficient information.
>
> If I try the model below, R seems to grumble with a complaint.
>
> glm(cbind(Y,1-Y) ~ X, family = binomial)
>
> non-integer counts in a binomial glm! in: eval(expr, envir, enclos)
>
> Am I correct to believe that more information is required?

Yes, probably.

If they are proportions without a well-defined denominator you may be able
to model them using family=quasi() and specifying the link and variance
function for a logistic regression model.  You'd need to look at what the
variance function actually is, though.

McCullagh & Nelder's book has an example using proportions of leaf damage
that's a bit like this, although they end up using (mu(1-mu))^2 as the
variance function.

	-thomas