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Peter Kennedy’s regression tips

From Michael Stastny comes a link to two articles with advice and more advice from Peter Kennedy on the practicalities of econometrics (what we in statistics would call “regression analysis,” I think). As a writer of textbooks and also a consumer of such methods in my applied work, I’m interested in this sort of general advice.

Oh no! I got the wrong sign! What should I do?

Kennedy’s article on what should be done when a regression coefficient has the “wrong sign,” has a lot of good examples and goes beyond the usual advice I give students about interpreting the sign and statistical significance of coefficients. I’m a little disturbed at how Kennedy mixes data-modeling issues in with causal-inference issues without clearly separating them, but that’s probably just a mater of taste. From his perspective, just about everything he wants to do is causal inference so it wouldn’t make sense to rope that off as a separate topic.

The main thing I would add to the paper is a discussion of the magnitudes of coefficients as well as their sign. Sometimes a coefficient looks very small (or large) because of the scale on which the predictor is measured. An obvious point but often missed. Many researchers seem to think that it’s “cheating” to transform predictors in any way, even linearly, not recognizing the importance of interpretation of results. The other minor point I’d make in Kennedy’s article is in his point 11: as is noted in many textbooks, models with interaction terms become easier to interpret if the input variables are centered before including them in the regression.

The ten commandments of applied econometrics

This other paper by Kennedy is interesting too. I’d quibble with some of his advice in “Rule #5: Keep it sensibly simple,” in that multilevel models allow the applied researcher to include lots of ocefficients without being overwhelmed by the problems that arise in stepwise model selection. But overall, I don’t have much to add. Both papers give us a lot to think about.

Where next?

The challenge to me, as a methodological researcher, is to try to incorporate some of these practical insights into our statistical theory and methods. To some extent I think we, as Bayesians, have done so, by incorporating model checking in our formal inference procedure using posterior predictive checks. But more needs to be done, especially in linking regression models to causal interpretations.

One Comment

  1. Jack says:

    Econometrics consists of much more than regression analysis, although it is correct to say that much econometrics uses regression.