The PLS model space revisited

Abstract Pell, Ramos and Manne (PRM) in a recent article in this journal claim that the ‘conventional’ PLS algorithm with orthogonal scores has an inherent inconsistency in that it uses different model spaces for calculating the prediction model coefficients and for calculating the X ‐space model and it's residuals [1]. We disagree with PRM. All PLS model scores, residuals, coefficients, etc., obtained by the conventional PLS algorithm do come from the same underlying latent variable (LV) model, and not from different models or model spaces as PRM suggest. PRM have simply posed a different model with different assumptions and obtained slightly different results, as should have been expected. Copyright © 2008 John Wiley & Sons, Ltd. Pell, Ramos and Manne (PRM) in a recent article in this journal claim that the ‘conventional’ PLS algorithm with orthogonal scores has an inherent inconsistency in that it uses different model spaces for calculating the prediction model coefficients and for calculating the X‐space model and it's residuals. We disagree with PRM. All PLS model scores, residuals, coefficients, etc., obtained by the conventional PLS algorithm do come from the same underlying latent variable (LV) model, and not from different models or model spaces as PRM suggest. PRM have simply posed a different model with different assumptions and obtained slightly different results, as should have been expected.