The Multiple Facets of Partial Least Squares and Related Methods by Hervé Abdi Vincenzo Esposito Vinzi Giorgio Russolillo Gilbert Saporta & Laura Trinchera

The Multiple Facets of Partial Least Squares and Related Methods by Hervé Abdi Vincenzo Esposito Vinzi Giorgio Russolillo Gilbert Saporta & Laura Trinchera

Author:Hervé Abdi, Vincenzo Esposito Vinzi, Giorgio Russolillo, Gilbert Saporta & Laura Trinchera
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham


(12.8)

Since in covariance-based approaches there is a unique minimization function related to the ability of the model to reproduce the sample covariance matrix, it is possible to have a global measure of fit that is defined as

(12.9)

CBSEMs consider the three residual terms ε, δ, and ζ in a unique minimization problem such that all the parameters are estimated simultaneously.

In VBSEMs the three residual terms ε, δ, and ζ play a crucial role in the modeling process. In practice, PLSPM aims to minimize the sum of residual variances of all the dependent variables in the model, both latent and observed ones, rather than explain the covariance structure of all the indicators. Hence, PLSPM is more strongly oriented to prediction than to parameter estimation. The logic behind the PLSPM is to partially estimate parameters by minimizing in each step of the procedure a residual variance with respect to a subset of the parameters being estimated given proxies or fixed estimates for other parameters (Chin 1998). For this reason PLSPM uses a three-stage estimation algorithm: first it performs an iterative scheme of simple/multiple regressions until the solution converges to a set of weights that are used for estimating the latent variables scores, and then uses these scores for obtaining loadings and path coefficients, using OLS regressions. PLSPM lacks a global optimization criterion but separately minimizes the following residual variances



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