Solved – Interaction effects in non-linear models

interactionlogitnonlinear regressionprobit

I have a general question about interpreting interaction effects in a non-linear model. I understand the reasons Ai and Norton (2004) suggest using the stata inteff command to help interpret interaction effects in a non-linear model.

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

However, Buis (2010) seems to suggest that interpreting a logit model through odds ratios overcomes the problem in a much simpler way.

http://www.stata-journal.com/sjpdf.html?articlenum=st0194

It is not clear to me how Buis's suggestion helps with the issues of Ai and Norton (2004) namely that the sign and significance of interaction effects in non-linear models vary across observations. Any help in understanding this would be much appreciated?

Best Answer

The way I solved the issue that the interaction effects in terms of marginal effect differ across observations is that in my article I did not look at interaction effects in terms of marginal effects but in terms of odds ratios.

With marginal effects you try to fit a linear line on top of a non-linear line, and this does not fit perfectly. It is these deviations that are the cause of the variation in marginal effects across observations.

There is no such "leakage" between a logit model and odds ratios, so I can describe an interaction effect in that model with just one parameter (a ratio of odds ratios) that works for all observations.