An Integrated PLS Regression-Based Approach for Multidimensional Blocks in PLS Path Modeling

Abstract

PLS Path Modeling (PLS-PM) is classically regarded as a component-based ap- proach to Structural Equation Models and has been more recently revisited as a general frame- work for multiple table analysis. Here we propose two new modes for estimating outer weights in PLS-PM: the PLScore Mode and the PLScow Mode. Both modes involve integrating a PLS Regression as an estimation technique within the outer estimation phase of PLS-PM. However, in PLScore Mode a PLS Regression is run under the classical PLS-PM constraints of unitary variance for the latent variable scores, while in PLScow Mode the outer weights are constrained to have a unitary norm thus importing the classical normalization constraints of PLS Regres- sion. Moreover, we show how the newly proposed modes are linked to the standard Mode A and Mode B outer estimates in PLS-PM as well as to the New Mode A recently proposed in a criterion-based approach by Tenenhaus & Tenenhaus (2009).