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# Interpreting Interaction Terms in Non-Linear Regression Models

A colleague of mine found the following article which says that most statistical packages for non-linear models produce the marginal effect of an interaction term which does not equal the magnitude of the interaction effect.

http://www.sciencedirect.com/science/article/pii/S0165176503000326

Can anyone point me to resources as to how SAS handles this problem?   This is part of a broader discussion of how often we want our analytics team to use non-linear models.

Thanks,

Aran Canes

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## Re: Interpreting Interaction Terms in Non-Linear Regression Models

Actually, SAS procedures such as LOGISTIC, GENMOD, and NLMIXED (with the right code) give beta12, the interaction parameter estimate, and its SE, for the linear predictor (which is a nonlinear function of the mean).  It is not attempting to give what you call the marginal effect or magnitude effect (which is on the scale of y, not g(y)). .It is not that one is wrong and the other is correct, so I would definitely not call it a "problem". It is a matter of what the researcher wants, and how one interprets the results. beta12 is truly the interaction effect of x1 and x1 on g(E(y)), but not on E(y). Since the model is often defined in terms of g(E(y)), one does want beta12, at least to start with. The differences between beta12 and the interactions on the E(y) scale are due to the nonlinear relationship between y and x1, x2. I don't think there is anything built into SAS procedures to give you what you want. You would need to do post-model-fitting processing using stored output (or ods) files.

I did some google searching, and I see that the subject has come up a few times regarding SAS procedures. The link below may be helpful. It is also clear that the use of so-called marginal or magnitude interactions is controversial (even mentioned in this link). I personally like dealing directly with beta12 and the associated odds ratio(s). But I know many economists want something else. Interactions on the scale of y will be functions of E(y), so there will not be a single number, but a continuous function.

http://stats.stackexchange.com/questions/13334/marginal-effects-of-a-logistic-model-and-their-standa...

I did not thoroughly search for code to do what is not covered in this link, but I bet it is out there.....

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Posts: 684

## Re: Interpreting Interaction Terms in Non-Linear Regression Models

This useage note

http://support.sas.com/kb/22/604.html

may be very helpful to you. Deals with some of the different types of interactions with generalized linear models. Good luck.

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