Variation Sharing: A Novel Numeric Solution to the Path Bias Underestimation Problem of PLS-Based SEM

The most fundamental problem currently associated with structural equation modeling employing the partial least squares method is that it does not properly account for measurement error, which often leads to path coefficient estimates that asymptotically converge to values of lower magnitude than the true values. This attenuation phenomenon affects applications in the field of business data analytics; and is in fact a characteristic of composite-based models in general, where latent variables are modeled as exact linear combinations of their indicators. The underestimation is often of around 10% per path in models that meet generally accepted measurement quality assessment criteria. We propose a numeric solution to this problem, which we call the factor-based partial least squares regression (FPLSR) algorithm, whereby variation lost in composites is restored in proportion to measurement error and amount of attenuation. Six variations of the solution are developed based on different reliability measures, and contrasted in Monte Carlo simulations. Our solution is nonparametric and seems to perform generally well with small samples and severely non-normal data.