A Data Colada post describes a problem and one proposed solution: how to assess a moderator’s interaction in a model like y ~ x + z + x:z. One paper suggests binning the covariate into thirds and fitting separate regressions on the bins. Uri Simonsohn observes that this approach is biased when the y ~ x or y ~ z relationship is nonlinear.

The third problem is that if x and z in that x·z interaction are correlated, and either x or z impacts y non-linearly, the estimate of interaction term, d, in y=a+bx+cz+dxz is biased, and the binning estimator from the Political Analysis paper is also biased, possibly by the same amount.

Most notably, one is likely to find false-positive interactions, and marginal effects of the wrong sign.

The author instead advocates for using a “GAM simple slope” and point to their article (DOI: 10.1177/2515245923120778).

The thing that I like most about the article from skimming it is that it describes curves that are linear and ceiling out as “canopy” shaped.

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