Friday, March 17, 2006

st: GLMs that fail - an effect (Hauck-Donner)

I've been fitting a logistic glm to some count data: six treatments, each duplicated, response is r/n: treat r n 1 8 13 1 9 15 2 14 15 2 14 15 3 12 15 3 9 15 5 14 15 5 13 15 4 15 15 4 15 15 6 15 15 6 15 15

The glm blows up for treatments (4) and (6), giving a p-value that indicates they do not differ from (1) and huge variance for the parameter estimates. Hence the Wald tests fail. This is the Hauck-Donner effect, described in previous messages on Statalist and S-Plus list. On both lists it was described as "uncommon", but may be caused by "separation", which is similar to colinearity in that one or more group results are predicted exactly. There are also messages that I deplore, blaming the user for using an "inappropriate model". The model is appropriate for the data, but the internal algorithm breaks down and the user has to interpret the output.

Given that so many datasets will share the characteristic that the control (group 6 here) shows zero effect (leading to either 0/n or n/n as the response to analyse), I wonder if this is so rare. A solution was offered on Statalist http://www.stata.com/statalist/archive/2003-03/msg00188.html which is simply to ask for "robust" estimation.

Since the effect is due, in this and similar examples, to groups having zero variance, is it not possible to modify glm (and other estimating commands?) to detect this and either issue a warning or switch automatically to robust estimators?

Allan

PS: I join statalist quite regularly, but each time get dropped from membership after a few days or weeks. This has not happened with other lists.

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