# A Joint Partial Least Squares Component-based Approach to Structural Equation Modeling and Multi-block Data Analysis

Partial Least Squares Path Modelling (PLS-PM) is generally meant as a component-based approach to structural equation models and multi-block data analysis that privileges a prediction oriented discovery process to the statistical testing of causal hypotheses. In case of formative relationships in the measurement model between the manifest variables and their corresponding latent ones, PLS-PM estimates the outer weights by means of multiple OLS regressions. These regressions might often yield unstable results in case of strong correlations between manifest variables while being not feasible when the number of observations is smaller than the number of variables or in presence of missing data. An external estimation mode based on PLS regression (PLS-R) may overcome these problems while preserving the formative nature of the measurement model. At the same time, this innovative estimation mode provides new tools for interpreting the components, validating the results and improving the predictions in PLS-PM. PLS-R is also profitably extended to: the internal estimation step of PLS-PM as a generalization of path weighting scheme, the estimation of path coefficients in structural models affected by strongly correlated latent variables or missing scores. Finally, the implementation of PLS regression in the estimation steps of PLS Path Modeling defines a regularized comprehensive PLS approach that yields more stable and robust results while enriching interpretation.

ESPOSITO VINZI, V. (2009). A Joint Partial Least Squares Component-based Approach to Structural Equation Modeling and Multi-block Data Analysis. In: PLS'09 - 6th International Conference on Partial Least Squares and Related Methods.

Mots clés : #Multicollinerity, #Multidimensional-Blocks