On the Properties of PLS for Analyzing Two-Level Factorial Experimental Designs

We present here a novel methodology to analyze data from two-level factorial experimental designs, with or without missing runs, with just one method: partial least squares regression with one response variable (PLS1, hereinafter PLS). This property is very attractive for practitioners because, to the best of our knowledge, no other statistical tool has comparable versatility. In the case of a full and fractional factorial design, the one-PLS component model yields the same analytical solution as multiple linear regression (MLR), not only in the estimation of the effects but also in their statistical significance. When having missing runs in the factorial design, PLS is of particular interest as it is a powerful tool when dealing with complex correlation structures, as opposed to MLR. Thus, we challenge the widely held view that PLS is useful only when dealing with nonexperimental design (i.e., correlated observational data). The methodology is illustrated by two illustrative examples and synthesized by an easy-to-follow route map useful for practitioners.