Continuum redundancy-PLS regression: A simple continuum approach

In this paper, we discuss new formulations of both redundancy analysis (RA) and partial least squares regression (PLS) which clearly show the connection between these two methods. These new formulations also show that RA and PLS regression are the two end points of a continuum approach that we propose to investigate. Moreover, it enjoys very interesting properties which highlight the rational of the continuum approach and how it handles the multicollinearity problem. As the method of analysis establishes a bridge between RA and PLS regression, we shall refer to it as ”continuum redundancy PLS regression” (CR-PLS). The interest of the method is illustrated on the basis of a data set pertaining to epidemiology.