Consistent Partial Least Squares estimators for linear and polynomial factor models. A report of a belated, serious and not even unsuccessful attempt. Comments are invited

Partial Least Squares algorithms for structural equation models are well-known for their fast convergence, but the ensuing estimators are as a rule inconsistent. The probability limits of the (absolute) loadings on latent variables are generally too large, whereas the limits of (absolute) bivariate and multiple correlations between latent variables are generally too small. Structural coe¢ cients can be highly distorted as a result. In this report we suggest a computationally very simple approach to correct for the inconsistency. We deal with a general class of linear factor models (essentially the ‘basic design’in PLS parlance) and invade the …eld of polynomial factor models. A small simulation study was done using variants of a simple model with interaction that in one form or another has been used for testing many times in the literature. For the models analyzed the approach yielded encouraging results.