[R] Interaction Terms versus Interaction Effects in logistic regression

[Paul Johnson]

I would like to know more about the output from the terms option in
predict(), especially for a glm.  And especially when there is an
interaction effect being considered.

Here's why I ask. These articles were recently brought to my
attention.  They claim that just about everybody who has reported an
interaction coefficient in a logit or probit glm has interpreted it
incorrectly.

Ai, C. and E.C. Norton. 2003. "Interaction Terms in Logit and Probit
Models." Economics
Letters 80(1):123$B!](B129.

Norton, E.C., H. Wang, and C. Ai. 2004. "Computing interaction effects
and standard errors
in logit and probit models." The Stata Journal 4(2):154$B!](B167.

These articles are available here:

http://www.unc.edu/~enorton/

Along with the Stata ado file that makes the calculations.

It seems to me the basic point here is that an interaction changes the
slope of a line, as in

z
   z
     z
        z
          z
xxxxxxxxxxxxxxxxxxxxxxx
              z
                z
                  z
                    z


The predicted value changes, of course, It may go up or down,
depending on whether the case considered is on the left or right. I
don't see that as a unique problem for logit models.  It seems to be
an artifact of Euclidean geometry :)

The logistic regression model does complicate the application of this
model to making predictions because the positioning of a case depends
on the values of all input variables, not just the one considered in
the interaction.

This is why I'm wishing I had a better understanding of the "terms"
option in predict.

-- 
Paul E. Johnson
Professor, Political Science
1541 Lilac Lane, Room 504
University of Kansas