In systems epidemiology such as in metabolomics, sometimes we are interested in identifying putative biomarkers of intake e.g., intake of a food item. So we analyse the metabolome to investigate signatures/pertubations of intake. Expectedly, most metabolome datasets are n<<p. Partial least squares regression (PLS) and its variants (sPLS, PLSDA etc) are popular methods for selecting such features.
Short question:
In using PLS for feature selection, is directionality between X and Y (X -> Y) necessarily implied?
Long description:
Most PLS algorithms for feature selection require a matrix of metabolites as X and treat food intake as variable Y. Statistically, this seems okay for the purpose of variable selection, but when applied to some biological experiments, it doesnt seem consistent with biological relationship i.e., where metabolite matrix should be the response variable (Y) - because we are studying metabolome pertubations in response to intake of food item,which intuitively would be (X) in a normal regression model e.g., MLR.
So after reading many papers on PLS, and discussion here: Theory behind partial least squares regression these two questions remains a bit unclear:
a) In PLS, is directionality necessarily implied?
b) Technically, is it ok to have Y-variables anterior to X-variables?
After selecting features, inference will be made through other methods.
Many thanks!