# [R-sig-ME] extracting p values for main effects of binomial glmm

Jonathan Baron baron at psych.upenn.edu
Thu Mar 5 20:13:29 CET 2015

```I can't resist butting in here on the general problem of interpreting
main effects when interactions are included in the model, even though
this was not the original topic. The standard advice is that you
should be "very careful" when you do this, but what should you be

I think the most common answer is this: Think of a graph in which Y is
the dependent variable, X1 is 2-level factor, and X2 is another
variable. The graph has one line for each level of X1. If there is no
X1*X2 interaction, they are parallel lines, and the distance between
them is the main effect of X1. If there is an X1*X2 interaction, then
the distance between them depends on X2. If the lines are straight and
lone enough, they will cross somewhere. So what does the main effect
mean?

What it means in the output of the function is the intercept when X2
is zero. This will change if you simply add/subtract a constant from
your measure of X2, although the measure of the interaction will not
change. Thus, the scaling of X2 is crucial for looking at main effects
when interactions are present, although it doesn't matter for looking
at the interaction. If you don't have a natural way to define the zero
point of X2, then it could be meaningless to talk about THE main
effect of X1.

In some cases you can define the level of X2 so that this intercept is
exactly what you want to know. For example, X2 could be some
contaminating variable whose effect you want to remove, and it could
be positive or negative, with effects in opposite directions, but when
it is zero it cannot have an effect. In this case, the intercept when
X2 is 0 is exactly what you want. You do NOT want to remove the
interaction term from the model, because then the main effect will
depend on the distribution of X2. But you want to know what happens
when X2 is zero and thus has no effect. In this case, then, you want
to examine the main effect in the presence of the interaction.

On 03/05/15 18:14, Steve Denham via R-sig-mixed-models wrote:
>Hmm. � I have never had a problem interpreting interactions that I got from SAS
>procedures (MIXED, GLIMMIX, HPMIXED). � What do you mean as 'not sensible'?
>Thanks,� Steve Denham
>Director, Biostatistics
>MPI Research, Inc.

--
Jonathan Baron, Professor of Psychology, University of Pennsylvania