Component Analysis for Structural Equation Models with Concomitant Indicators

A new approach to structural equation modelling based on so-called Extended Redundancy Analysis has been recently proposed in literature, enhanced with the added characteristic of generalizing Redundancy Analysis and ReducedRank Regression models for more than two blocks. However, in presence of direct effects linking exogenous and endogenous variables, the latent composite scores are estimated by ignoring the presence of the specified direct effects. In this paper, we extend Extended Redundancy Analysis, permitting us to specify and fit a variety of relationships among latent composites and endogenous variables. In particular, covariates are allowed to affect endogenous indicators indirectly through the latent composites and/or directly.