# Partial Least Squares: a Critical Review and a Potential Alternative

Structural equation modelling (SEM) is now a popular technique in the social, behavioural and business sciences for exploring and assessing complex linear relationships among many variables, in particular between endogenous and exogenous latent variables that cannot be directly observed but that must be inferred by means of manifest indicator variables, that is variables measured without error. The main category of SEM techniques, which is based on fitting the model-implied covariance matrix of the manifest variables (or items) to the empirically determined covariance matrix, is implemented in a number of software package including Mplus (Muthen and Muthen, 2001) and LISREL (Joreskog and Sorbom, 1996). The covariance-based approach to SEM is of particular interest because it explicitly models the measurement error associated with each latent variable and therefore ensures that estimates of the SEM parameters are consistent. Consistency of estimation is an important (some would say essential) statistical property which states that with high probability, an estimate will become closer and closer to its true value for increasingly large sample sizes. An alternative approach to SEM modeling called partial least squares (PLS) was developed by Wold (1982, 1985), based on earlier work of his dating from the mid-1960’s (for references see Tenenhaus, Vinzi, Chatelin and Lauro, 2005). PLS uses an iterative application of ordinary least squares (OLS) to first estimate values of the latent variables for each individual, followed by OLS estimation of model parameters based on the latent variable values, or scores. Joreskog and Wold (1982) and Wold (1982, 1985) referred to the PLS technique as “soft modelling”, because it did not require the “hard “ distributional assumptions of ML-SEM, and because it used a sub-optimal estimation technique that is faster to run than ML-SEM and which therefore allowed for more user interaction. They claimed that PLS and ML-SEM provided similar results, i.e., estimates for which numerical differences “cannot or should not be substantial” (Joreskog and Wold, 1982, page 266), a claim is difficult to justify for reasons that will be discussed’

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