PLSSEM

Partial Least Squares Structural Equation Modeling (PLS-SEM) is a variance-based multivariate technique used to estimate complex cause-effect relationships among latent variables. It combines elements of factor analysis and multiple regression to model relationships between observed indicators and latent constructs, as well as the relationships among those constructs themselves.

PLS-SEM differentiates itself from covariance-based SEM by prioritizing prediction and variance explanation rather than fitting a theoretical covariance matrix. It is particularly suited for theory development and exploratory research, small sample sizes, and data that depart from multivariate normality. The method can accommodate models with formative and reflective measurement specifications and handles complex models with many constructs and indicators.

Modeling in PLS-SEM involves two submodels. The outer (measurement) model specifies how latent variables are measured by their indicators, which can be reflective (indicators reflect the latent construct) or formative (indicators form the latent construct). The inner (structural) model specifies the causal relationships among latent variables. The estimation procedure iteratively assigns weights to indicators and latent variables to maximize the explained variance of endogenous constructs, producing path coefficients, loadings, and indicator weights.

Validation focuses on reliability and validity rather than global fit indices. Key criteria include composite reliability and average variance extracted (AVE) for convergent validity, and discriminant validity assessments such as the Fornell-Larcker criterion or the HTMT ratio. Significance and relevance are evaluated via bootstrapping, generating t-values for path coefficients and indirect effects. Predictive relevance can be assessed with cross-validated redundancy or PLS-Predict.

PLS-SEM software tools include SmartPLS, ADANCO, WarpPLS, and R packages such as plspm.