A study of covariance-based and partial least squares structural equation modeling

Abstract

Structural equation modeling (SEM) is a diverse collection of statistical methods used to model two types of causal relationships: (i) relationships linking pairs of latent (unobserved) concepts and (ii) relationships linking each latent concept to a set of manifest (observed) variables that indirectly measure it. The powerful tool of SEM can be implemented through two central approaches, namely Covariance-Based Structural Equation Modeling ( CBSEM) and Partial Least Squares Path Modeling (PLS-PM). This dissertation aims to provide insight into the appropriate use of the two abovementioned approaches for analysing structural equation models. This is primarily achieved through covering the theoretical background of both CBSEM, based on Robust Maximum Likelihood (RML) estimation, and PLS-PM. The two approaches are then used to fit a structural equation model to a set of responses gathered by administering a questionnaire to undergraduate students at the University of Malta. The questionnaire is based on a short form of the Gratitude, Resentment, and Appreciation Test (GRAT) (Thomas & Watkins, 2003), a test which reveals the level of gratitude exuded by individuals. Comparisons between CBSEM and PLS-PM are addressed by highlighting the strengths and weaknesses of both approaches. A simulation study is also carried out to investigate the relative performance of CBSEM, based on Maximum Likelihood Estimation (MLE), and PLS-PM in the context of formative manifest variables. Results of this study indicate that, under the presumed framework, estimates produced by PLS-PM are globally better than those produced by CBSEM in terms of bias and precision.