Title:      Testing for Interaction in Binary Logit and Probit Models:
Is a Product Term Essential?

Authors:    William Berry, Justin Esarey, Jacqueline Rubin

Entrydate:  2007-05-06 20:51:39

Keywords:   interaction, logit, probit

Abstract:   Political scientists presenting binary dependent variable
(BDV) models often offer hypotheses that independent variables
interact in their influence on the probability that an event Y
occurs, Pr(Y).  A consensus appears to have evolved on how to test
such hypotheses: (i) estimate a logit or probit model including
product terms to specify the interaction, (ii) test the hypothesis by
determining whether the coefficients for these terms are statistically
significant, and (iii) if they are, describe the nature of the
interaction by estimating how the marginal effect of one independent
variable on Pr(Y) varies with the value of the other independent
variables.  We contend that in the BDV context, statistically
significant product term coefficients are neither necessary nor
sufficient for concluding that there is substantively meaningful
interaction among variables in their influence on Pr(Y).  Even when
no product terms are included in a logit or probit model, if the
marginal effect of one variable on Pr(Y) is related to another
independent variable then substantively meaningful interaction is
present, and describing such interaction is essential to an accurate
portrayal of the data generating process at work.  We propose a
strategy for studying interaction in the BDV context that is
consistent with the recent emphasis in the discipline on casting
hypotheses in terms of effects on the probability of an
event�s occurrence and reporting estimated marginal effects on
this probability.

http://polmeth.wustl.edu/retrieve.php?id=692