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When estimating a non-linear model such as [R] logit or [R] poisson, we often have two options when it comes to interpreting the regression coefficients: compute some form of marginal effect; or exponentiate the coefficients, which will give us an odds ratio or incidence-rate ratio. The marginal effect is an approximation of how much the dependent variable is expected to increase or decrease for a unit change in an explanatory variable: that is, the effect is presented on an additive scale. The exponentiated coefficients give the ratio by which the dependent variable changes for a unit change in an explanatory variable: that is, the effect is presented on a multiplicative scale. An extensive overview is given by Long and Freese (2006). Sometimes we are also interested in how the effect of one variable changes when another variable changes, namely, the interaction effect. As there is more than one way in which we can define an effect in a non-linear model, there must also be more than one way in which we can define an interaction effect. This tip deals with how to interpret these interaction effects when we want to present effects as odds ratios or incidence-rate ratios. This can be an attractive alternative to interpreting interactions effects in terms of marginal effects.

Stata Tip 87: Interpretation of Interactions in Nonlinear Models