[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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