What kind of test in summary(glm)?
To go a bit farther, simulations have shown that a t distribution is inappropriate because it is overly conservative (due to not having to estimate sigma). P-values using the normal distribution are more accurate than those from t. As Brian noted, the Hauck-Donner effect can ruin Wald statistics. When a variable does not have a dominating effect (i.e., when there is no cell containing less than perhaps two observations but this depends on N) Wald stats work reasonably well. Frank Harrell
Prof Brian Ripley wrote:
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 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
Frank E Harrell Jr Prof. of Biostatistics & Statistics Div. of Biostatistics & Epidem. Dept. of Health Evaluation Sciences U. Virginia School of Medicine http://hesweb1.med.virginia.edu/biostat -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._