Averaging the output of many simple regressions for prediction in mass univariate analysis

Question

Mass univariate analysis typically means running many univariate tests (e.g. simple regression, t-test), predicting the response from one of many predictors (e.g. ROIs in fMRI analysis, genes in GWAS) each time, and then correcting for multiple testing (typically FDR or Bonferroni).

I want to compare mass univariate to other, multivariate methods, on both inference and prediction. Mass univariate was clearly developed with inference in mind, but I'm wondering whether it's ever been used for prediction. Specifically, I was wondering whether it's been used for prediction by averaging the outputs of the simple regressions in some way. I've been searching but I haven't been able to find anything yet.

Answer 1

It turns out that averaging the predictions of many simple regressions is closely related to Partial Least Squares -- specifically, with suitable scaling of variable it gives exactly the first component of a univariate-response PLS model, and the successive components come from doing the same thing to residuals from the earlier components.

The comparison is described in "An Interpretation of Partial Least Squares" by Paul Garthwaite