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

[Thompson,Paul]

The issue with interactions is that the two factors have differing differences. Sometimes the interactions are CROSSING. Sometimes they are DIVERGENT. However, they simply mean that UNCONDITIONAL statements are incorrect.

Consider Factors A and B which interact. 

1) What is the main problem? If you wish to say "Level A1 is higher than Level A2", an interaction makes this unwise. UNCONDITIONAL statements cannot be made.

2) What is a solution? Do not make UNCONDITIONAL statements. Make CONDITIONAL statements. These are termed "simple main effets" or "designed contrasts". If you say "Level A1 is higher than Level A2 for B1 cases, but Level A1 is lower than Level A2 for B2 cases". This statement is not UNCONDITIONAL. 

It's really not a problem. It just depends on what you wish to do.

________________________________________
From: R-sig-mixed-models [r-sig-mixed-models-bounces at r-project.org] on behalf of Jonathan Baron [baron at psych.upenn.edu]
Sent: Thursday, March 05, 2015 1:13 PM
To: Steve Denham
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] extracting p values for main effects of binomial glmm

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
careful ABOUT?

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
Home page: http://www.sas.upenn.edu/~baron
Editor: Judgment and Decision Making (http://journal.sjdm.org)

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