16

PLS models

Giuseppe Boari and Gabriele Cantaluppi

This chapter deals with the partial least squares (PLS) estimation algorithm and its use in the context of structural equation models with latent variables (SEM-LV). After a short description of the general structure of SEM-LV models, the PLS algorithm is introduced; then, statistical and geometrical interpretations of PLS are given. A detailed application example based on the ABC annual customer satisfaction survey data concludes the chapter.

16.1 Introduction

The partial least squares (PLS) algorithm, developed by Wold (1982, 1985), was first introduced in the context of multiple linear regression models, in order to overcome the problems arising in the estimation procedures when overparameterization and multicollinearity occur. The former, often encountered in chemiometric analyses, is due to the presence of more explanatory variables than there are observations available, so that ordinary least squares (OLS) procedures cannot operate correctly. The latter derives from subsets of explanatory variables being highly correlated, which dramatically reduces estimator efficiency.

In these cases, the so-called PLS regression algorithm may be adopted: in order to summarize the original explanatory variables, a new set of latent (non-observable) auxiliary variables is generated, which, in a fashion similar to latent factors, reduces the complexity of the model. These factors are then used as the regressors of the dependent variables ...

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