Skip to content

Smoothed Anova

Jim Hodges, Yue Cui, Daniel Sargent, and Brad Carlin completed their paper on “smoothed Anova”. The abstract begins: “We present an approach to smoothing balanced, single-term analysis of variance (ANOVA) that emphasizes smoothing interactions, the premise being that for a dependent variable on the right scale, interactions are often absent or small. . . .”

The topic is hugely important, I believe (see also here): especially in observational studies, regression models work because they can handle multiple inputs (for example, see Michael Stastny’s quick discussion here). Once we have multiple inputs, you gotta look at interactions, which quickly leads to a combinatorical explosion, the usual “solution” to which is to ignore high-level interactions. But in some problems–including many decision analyses and many research studies in psychology–interactions are what we really care about. (Here‘s an example from our own work where we would have liked to include more interactions than we actually did.)

Anyway, I think this is one of the major unsolved problems in statistics. It can be attacked in several ways, including regression/Anova (that’s where Hodges et al. and I are working), neural nets, nonparametric models, etc etc. My best published method so far of handling high-level interactions isn’t so great, and I think that Hodges et al. are doing interesting stuff.

I hope lots of people read the article, try out the methods presented there, and take the ideas even further.