PLS think twice about partial least squares

One of the great things about writing a statistics book was finding an excuse to read about dozens of topics that I knew a little about but hadn't got around to studying in depth. Even so, there were a number of topics I ended up missing out on completely (apparently once the book gets to over a 900 pages or so they make you leave stuff out). One of those topics is partial least squares (PLS).

I knew a bit about the technique (but it turns out even less than I thought). I recently came across an excellent paper on partial least squares by Mikko Rönkkö, Cameron McIntosh and John Antonakis. The main thrust of the paper is simple - partial least squares is a widely used technique outside psychology, and it has been suggested should be more widely used within psychology. Rönkkö et al., however argue that this is probably a bad idea. A very bad idea. Their argument rests on two main arguments. First, that partial least squares is equivalent to a regression model using indicator variables to create weighted composite predictors. Second, that the benefits of partial least squares  have been greatly overstated. In particular the claim that PLS can deal with measurement error seems simply to be be false (as just creating composites from indicator variables can't do this). Worryingly, some implementations of PLS seem to have dangerous properties (notably one with a 100% false positive rate) and PLS generally seems to inflate Type I error for small effects. The latter property may give the impression of attenuating measurement error (but merely provides a bias that that may sometimes counteract attenuation arising from measurement error).

Rönkkö et al. paper is, I think, a model of clarity and implies that PLS is going to be of limited value to psychologists. I found the paper particularly interesting because I have mostly seen PLS advocated as a way of dealing with multicollinearity. This makes sense as multicollinearity can reasonably be handled by replacing predictors with composites. The main drawback of PLS, however, is that the composites are derived automatically by the PLS algorithm. This sort of 'black box' solution produces good prediction but can overcapitalise on quirks in the sample and thus may not generalise (especially for small samples). More importantly, the composites may well be uninterpretable. For most psychological applications I'd rather use an interpretable but 'non-optimal' composite (e.g., a simple average of highly correlated predictors) than go down this route.

For the same reason I'd generally rather not use MANOVA (which  finds an optimum linear combination of DVs in your sample). Of common analytic methods MANOVA is one of the least well understood techniques in psychology (and I have rarely seen a published application of MANOVA that wouldn't be enhanced using a different, often simpler, technique).