Partial least squares analysis in developmental psychopathology

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Abstract
Despite extensive theoretical and empirical advances in the last two decades, little attention has been paid to the development of statistical techniques suited for the analysis of data gathered in studies of developmental psychopathology. As in most other studies of developmental processes, research in this area often involves complex constructs, such as intelligence and antisocial behavior, measured indirectly using multiple observed indicators. Relations between pairs of such constructs are sometimes reported in terms of latent variables (LVs): linear combinations of the indicators of each construct. We introduce the assumptions and procedures associated with one method for exploring these relations: partial least squares (PLS) analysis, which maximizes covariances between predictor and outcome LVs; its coefficients are correlations between observed variables and LVs, and its LVs are sums of observable variables weighted by these correlations. In the least squares logic of PLS, familiar notions about simple regressions and principal component analyses may be reinterpreted as rules for including or excluding particular blocks in a model and for “splitting” blocks into multiple dimensions. Guidelines for conducting PLS analyses and interpreting their results are provided using data from the Goteborg Daycare Study and the Seattle Longitudinal Prospective Study on Alcohol and Pregnancy. The major advantages of PLS analysis are that it (1) concisely summarizes the intercorrelations among a large number of variables regardless of sample size, (2) yields coefficients that are readily interpretable, and (3) provides straightforward decision rules about modeling. The advantages make PLS a highly desirable technique for use in longitudinal research on developmental psychopathology. The primer is written primarily for the nonstatistician, although formal mathematical details are provided in Appendix 1.