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: 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
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