From composites to factors: Bridging the gap between PLS and covariance-based structural equation modelling

Partial least squares (PLS) methods possess desirable characteristics that have led to their extensive use in the field of information systems, as well as many other fields, for path analyses with latent variables. Such variables are typically conceptualized as factors in structural equation modelling (SEM). In spite of their desirable characteristics, PLS methods suffer from a fundamental problem: Unlike covariance-based SEM, they do not deal with factors, but with composites, and as such do not fully account for measurement error. This leads to biased parameters, even as sample sizes grow to infinity. Anchored on a new conceptual foundation, we discuss a method that builds on the consistent PLS technique and that estimates factors, fully accounting for measurement error. We provide evidence that this new method shares the property of statistical consistency with covariance-based SEM but, like classic PLS methods, has greater statistical power. Moreover, our method provides correlation-preserving estimates of the factors, which can be used in a variety of other tests. For readers interested in trying it, the new method is implemented in the software WarpPLS. Our detailed discussion should facilitate the implementation of the method in any numeric computing environment, including open source environments such as R and GNU Octave.