[R] Model averaging with (and without) interaction terms

[Ben Bolker]

Leslie Young <leslie.young101 <at> gmail.com> writes:

> 
> I’ve used logistic regression to create models to assess the effect of
> 3 variables on the presence or absence of a species, including the
> interaction terms between variables and model averaging using MuMI:
> model.avg
> 
> The top models (delta<4) include several models with interaction terms
> and some models without; model weights are quite low for all models
> (<0.25). My problem is that the models with interactions have negative
> coefficients on the variables with a positive interaction term whereas
> the same model without an interaction has positive coefficients.
> MuMIn: model.avg averages all these models together, so the
> relationship is washed out (CI overlaps 0).
> 
> Eg.
> 
> mod1<-glm(presence ~ x1*x2, family=”binomial”)
> coefficients: -0.661 x1, -0.043 x2, 0.02 x1:x2
> 
> mod2 <- glm(presence ~ x1 + x2, family=”binomial”)
> coefficients: 0.245 x1, 0.021 x2
> 
> I’ve read that it is difficult to compare models with and without
> interaction terms, but nothing regarding how one might go about doing
> so. Should interaction models be averaged differently or separately
> than models without interaction terms?  Is there another way to
> approach this?

  The tricky aspect of comparing models with and without interaction
terms is that the main effect parameters have different meanings
when the interactions are included.  It looks like your parameters
are both continuous, so I'll discuss things in this context.
In the interaction model, the x1 parameter gives the expected change
in log-odds (logit probability) for a 1-unit increase in the
corresponding predictor variable **when x2 is equal to 0**. In the
non-interaction model, the x1 parameter gives the *average* expected
change in log-odds across the distribution of x2 values observed in
the data sets.
   It will help a bit if you follow Schielzeth [Schielzeth, Holger. 2010. Simple
means to improve the interpretability of regression coefficients. Methods in
Ecology and Evolution 9999, no. 9999. doi:10.1111/j.2041-210X.2010.00012.x.] and
mean-correct your predictors
before fitting the model.
   I have a bigger problem (which perhaps luckily for you is not shared
with much of the ecological community), which is that usually people
who are model-averaging *parameters* (rather than *predictions*) are
essentially trying to use information-theoretic approaches to test
hypotheses ...