PARTIAL LEAST SQUARES: A DOSE-RESPONSE MODEL FOR
MEASUREMENT IN THE BEHAVIORAL AND BRAIN SCIENCES
Target Article by Bookstein on Least Squares

Abstract

Partial Least Squares (PLS) is a relatively new multivariate statistical method for the analysis of indirectly measured cause and effect in complex behavioral systems. The core of the technique is a rearrangement of the singular-value decomposition (SVD) of the correlation matrix between two blocks of variables. In this setting, the SVD can be reinterpreted as dealing with two latent variable (LV) scores, one for each block, such that the coefficients of either are proportional to the predictive salience of the corresponding variable for the other LV. In the presence of a true causal nexus, subsequent statistical manipulation of these coefficients and scores can be very enlightening. The strengths of PLS are demonstrated using the Seattle study of the effects of prenatal alcohol exposure on offspring development. This longitudinal study is based on 13 diverse measures of prenatal exposure and hundreds of outcome scores that assay attentional behavior, neuromotor maturation, cognitive functioning, and socialization to school in a population-based sample of 500 children born in 1975. There is an enduring effect of prenatal exposure on outcomes in all of these channels. I argue that PLS is the best method for discovering and reporting the nature of the dose-response relationship and the characteristics of affected children in studies such as these.

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