[R] Interaction Terms versus Interaction Effects in logistic regression

From: Paul Johnson <pauljohn32_at_gmail.com>
Date: Wed, 19 Mar 2008 11:52:21 -0500

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):123−129.

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):154−167.

These articles are available here:


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




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

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