[R] deviance in GLM vs. summary.glm

[Berwin A Turlach]

Dear Yi,

On Wed, 31 May 2017 04:53:25 +0000 (UTC)
array chip via R-help <r-help at r-project.org> wrote:

> Hi, I am running a logistic regression on a simple dataset (attached)
> using glm: [...] As you can see, the interaction term is very
> insignificant (p = 0.996)! 

Well, all terms are not significant (actually, AFAIK, the phrase "very
insignificant" does not exist; and if it does, than it ought not).  

But look at the estimates and the standard errors too (might be easier
if you had formatted your e-mail in a way that was readable)!  What
does an estimate for the intercept of 19.57 on the linear predictor
scale mean?  What it the estimated probability if you transform back?

Perhaps the following command

R> xtabs(~x1+x2+y,dat)

will shed some more light on what is going on in your data set, and why
the interaction term is highly significant.

> But if I use a anova() to compare a full
> vs reduced model to evaluate the interaction term:
> > anova(glm(y~x1+x2,dat,family='binomial'),
> > glm(y~x1*x2,dat,family='binomial'))

To you know about the (optional) argument 'test="ChiSq"' for the
anova() command if you use it to compare models fitted by glm()? (see
help(anova.glm))

> So I get very different p value on the interaction term, can someone
> share what's going wrong here?

Data separation, aka Hauck-Donner phenomenon, discussed in any good
book on logistic regression.

Best wishes,

	Berwin

========================== Full address ============================
A/Prof Berwin A Turlach, Director     Tel.: +61 (8) 6488 3338 (secr)
Centre for Applied Statistics               +61 (8) 6488 3383 (self)
School of Maths and Stats (M019)      FAX : +61 (8) 6488 1028
The University of Western Australia                 
35 Stirling Highway                 e-mail: Berwin.Turlach at gmail.com
Crawley WA 6009          http://staffhome.ecm.uwa.edu.au/~00043886/
Australia                http://www.researcherid.com/rid/A-4995-2008