Interaction effect in Logit model

[Shreya Jain]

I read the paper "Interaction terms in logit and probit models by Ai & Norton ( 2003). It mentioned that "The magnitude of the interaction effect in nonlinear models does not equal the marginal effect of the interaction term, can be of opposite sign, and its statistical significance is not calculated by standard software". So then how should one go about it? How do I find the interaction effect when using logit model?

[Erik Ruzek]

My approach is to use adjusted predictions (Stata's margins command) to help me understand interactions in general, and for logit/probit models especially. When used correctly (see Rich Williams' excellent margins paper in Stata Journal), the output gives you predictions from your model that are expressed in terms of the probability of the outcome being 1. The adjusted predictions for an "interaction" represent the probability of a 1 on the outcome for each combination of the variables involved in the interaction. They do not give you a "marginal effect of the interaction term" (see pages 329-330 of Williams' paper). He explains this all very nicely and shows you how to get the desired predictions in Stata. I highly recommend it.

[Shreya Jain]

Thank you Erik Ruzek. I will go and read William's paper. Though I am a bit concerned about my interaction of a factor variable(3 categories: Poor, average, well off) and a continuous variable it ranges from 0-17 (as it is years of schooling).

[Erik Ruzek]

You should not be worried about that unless you have really uneven numbers in the groups. The principles are the same, and margins handles it without a problem. For example:

logit outcome i.factor##c.edu
margins factor, dydx(edu) 
*or
margins factor, at(edu=(0(3)17))
*after each of these use marginsplot to get a graph of the association.

[Shreya Jain]

Thank you so much Erik Ruzek once again. I also wanted to ask you if one can interpret the results obtained after logistic regression, eg. my odds ratio for edu is 1.03 as odds of outcome increased by 3% for each additional year of schooling?

[Erik Ruzek]

Yes, that is how odds ratios are typically interpreted. Unless you work in a field in which people are used to thinking about outcomes in odds ratios, you might want to instead express that in terms of a marginal effect or as an increase in the probability of the outcome. Both of those can be had by using margins as suggested in #4.

[Shreya Jain]

Thank you Erik.
I used the command estat classification, all to see the information on degree to which the observed outcome are predicted by the model. I found that sensitivity i.e. percentage of cases observed to fall in the target group (Y=1, observed as having passed the test)) who were correctly predicted by the model to fall into that group (eg. Predicted pass), is quite low at 6%. Where as specificity i.e. percentage of cases observed to fall into the non-target (Y=0) category (e.g., observed did not pass test) who were correctly predicted by the model tofall into that group (e.g., predicted did not pass test). is quite high at 99%. Thus the overall correctly specified is around 80%.
Since sensitivity is fairly low so, what shall i do about it? or if the overall correctly specified is fairly good, just let it be?

[daniel klein]

You want to read Buis (2010) for an excellent discussion of interaction effects in non-linear models.


Buis, M. L. 2010. Stata tip 87: Interpretation of interactions in nonlinear models. The Stata Journal 10(2), 305--308.

[Shreya Jain]

Thank you daniel klein. I will read it.