I am trying to find information regarding the assumptions of PLS regression (single $y$). I am especially interested in a comparison of the assumptions of PLS with regards to those of OLS regression.
I have read/skimmed through a great deal of literature on the topic of PLS; papers by Wold (Svante and Herman), Abdi, and many others but haven't found a satisfactory source.
Wold et al. (2001) PLS-regression: a basic tool of chemometrics does mention assumptions of PLS, but it only mentions that
- Xs need not be independent,
- the system is a function of a few underlying latent variables,
- the system should exhibit homogeneity throughout the analytical process, and
- measurement error in $X$ is acceptable.
There is no mention of any requirements of the observed data, or model residuals. Does anyone know of a source that addresses any of this? Considering underlying math is analogous to PCA (with goal of maximizing covariance between $y$ and $X$) is multivariate normality of $(y, X)$ an assumption? Do model residuals need to exhibit homogeneity of variance?
I also believe I read somewhere that the observations need not be independent; what does this mean in terms of repeated measure studies?