[R] What kind of test in summary(glm)?
Prof Brian Ripley
ripley at stats.ox.ac.uk
Wed Oct 10 14:14:43 CEST 2001
On Wed, 10 Oct 2001, Anne Morgenstern wrote:
> Hello R Users,
> when I use summary(glm) for a logistic regression model with logit as link
> function I get one column "z value". What kind of test does R use? (I would
> have expected a t-test).
It's not doing a test at all. It is reporting a z value, the coefficient
divided by the estimated standard error. Now although that is often
called a `t value', it is not for a GLM (except in special cases)
t-distributed under the null hypothesis. If you mean that you used
glm(family=binomial), the scale is not estimated and the relevant
asymptotic theory suggests a normal distribution. However, that can be
rather misleading. Under glm(family=pseudobinomial) the scale is
estimated, but there is no really relevant theory (as you have a
quasi-likelihood model) suggesting a t distribution.
If you want to test, use anova.glm not the Wald statistic given by the
`z value', because of the Hauck-Donner effect.
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 272860 (secr)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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