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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?

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  • $\begingroup$ You could try asking Prof. Buis yourself, but first search for some of his posts. $\endgroup$
    – Sycorax
    Commented Mar 28, 2014 at 15:42
  • $\begingroup$ Hi, thanks. Apolgies, new to cross validated as a platform so getting through posts slowly but have yet to come across something which answers the significance question. Although it might be my own misreading of posts. Ive read his Stata tip on the subject and looked on the statlist website but will keep searching thanks. $\endgroup$
    – user42705
    Commented Mar 28, 2014 at 16:03
  • $\begingroup$ No need to apologize, this strikes me as a perfectly reasonable & on-topic question. Be aware, though, that unless he posts an answer himself, CVers will simply try to elucidate the ideas about how to interpret interaction effects in logistic regression, which may or may not be exactly what he means. $\endgroup$ Commented Mar 28, 2014 at 16:15
  • $\begingroup$ I am no prof. just dr. if you really want to use a title, otherwise Maarten is just fine. I have to go now for a couple of days so I won't be answering it in the comming days. $\endgroup$ Commented Mar 28, 2014 at 16:22
  • $\begingroup$ Ai and Norton's paper has also been criticized by other work like Puhani (2012). The article and other potentially useful references are linked here: stats.stackexchange.com/questions/89513/… $\endgroup$
    – Andy
    Commented Mar 28, 2014 at 16:23

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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.

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    $\begingroup$ Maarten, Thanks very much for your answer. It's perfectly clear and much appreciated. $\endgroup$
    – user42705
    Commented Apr 3, 2014 at 9:26

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