# Review: Modeling and Interpreting Interactive Hypotheses in Regression Analysis

Many hypothesis in the social sciences involve interaction: The effect of some variable x (say xenophobia) on some variable y (say support for the extreme right) is conditional on a third variable z (say ethnicity). Modelling interactive hypotheses looks straightforward on the surface: simply generate a third variable by multiplying x and z and plug all three in your regression. In Stata, this process can be automated by means of the built-in command xi or by desmat, which is available from SSC.

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Unfortunately, the interpretation of the resulting coefficients is less straightforward. A recent review by Brambor, Clark and Golder (2006), however, suggests that even in top political science journals many interpretations of interaction effects are dubious if not plain wrong. The new book by Kam and Franzese has the potential to rectify this situation. Kam and Franzese start out from the proposition that in interactive models (like in a number of other models they discuss in passing), the effect of an interacted variable x does not equal its coefficient. Rather, one has to differentiate the model equation with respect to x (which requires a working knowledge in introductory calculus or a licence for Mathematica) or must calculate first differences (which is easy). The slim volume will appeal both to advanced students and applied researchers that want to get it right. It is organised around a number of running examples of recent real world political research and compares well with the older monographs in the QASS series (“the green Sage papers”) because “modern” issues such as multi-level models and standard errors for effects are addressed. The latter point is of particular importance because the very concise discussion in Kam and Franzese will save the reader the effort to skim through pages and pages of highly technical econometric treatises. While the mathematical apparatus may look a little daunting at first, it is actually very helpful. Moreover, it is accompanied by clear instructions on how to perform the necessary calculations in Stata.

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