[R] Interaction term not significant when using glm???

[Thomas Lumley]

On Fri, 6 Mar 2009, joris meys wrote:

> Dear all,
>
> I have a dataset where the interaction is more than obvious, but I was asked
> to give a p-value, so I ran a logistic regression using glm. Very funny, in
> the outcome the interaction term is NOT significant, although that's
> completely counterintuitive. There are 3 variables : spot (binary response),
> constr (gene construct) and vernalized (growth conditions). Only for the FLC
> construct after vernalization, the chance on spots should be lower. So in
> the model one would suspect the interaction term to be significant.
>
> Yet, only the two main terms are significant here. Can it be my data is too
> sparse to use these models? Am I using the wrong method?

The point estimate for the interaction term is large: 1.79, or an odds ratio of nearly 6.

The data are very strongly overdispersed (variance is 45 times larger than it should be), so they don't fit a binomial model well. If you used a quasibinomial model you would get no statistical significance for any of the terms.

I would say the problem is partly combination of the overdispersion and the sample size.  It doesn't help that the situation appears to be a difference between the FLC:yes cell and the other three cells, a difference that is spread out over the three parameters.

      -thomas


> # data generation
> testdata <-
> matrix(c(rep(0:1,times=4),rep(c("FLC","FLC","free","free"),times=2),
>  rep(c("no","yes"),each =4),3,42,1,44,27,20,3,42),ncol=4)
> colnames(testdata) <-c("spot","constr","vernalized","Freq")
> testdata <- as.data.frame(testdata)
>
> # model
> T0fit <- glm(spot~constr*vernalized, weights=Freq, data=testdata,
> family="binomial")
> anova(T0fit)
>
> Kind regards
> Joris
>
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>
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Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle