Why am I getting “algorithm did not converge” and “fitted prob numerically 0 or 1” warnings with glm?

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If you look at ?glm (or even do a Google search for your second warning message) you may stumble across this from the documentation:

For the background to warning messages about ‘fitted probabilities numerically 0 or 1 occurred’ for binomial GLMs, see Venables & Ripley (2002, pp. 197–8).

Now, not everyone has that book. But assuming it’s kosher for me to do this, here’s the relevant passage:

There is one fairly common circumstance in which both convergence
problems and the Hauck-Donner phenomenon can occur. This is when the
fitted probabilities are extremely close to zero or one. Consider a
medical diagnosis problem with thousands of cases and around 50 binary
explanatory variable (which may arise from coding fewer categorical
variables); one of these indicators is rarely true but always
indicates that the disease is present. Then the fitted probabilities
of cases with that indicator should be one, which can only be achieved
by taking βi = ∞. The result from glm will be
warnings and an estimated coefficient of around +/- 10. There has been
fairly extensive discussion of this in the statistical literature,
usually claiming non-existence of maximum likelihood estimates; see
Sautner and Duffy (1989, p. 234).

One of the authors of this book commented in somewhat more detail here. So the lesson here is to look carefully at one of the levels of your predictor. (And Google the warning message!)

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