PLSe: Efficient Estimators and Tests for Partial Least Squares

This dissertation extends Dijkstra's (2011) consistent partial least squares estimator for structural equation models by deriving new estimators that are efficient. The new methods allow formal testing of models via chi-square statistics and evaluation of parameter estimates by deriving standard error estimates, which are previously not directly available. Two approaches are developed: (1) PLSe1: a one-step improvement methodology based on PLSc-estimated factor loadings and TSLS-estimated structural parameters; (2) PLSe2: an optimal generalized least squares methodology using PLSc-implied covariance matrix. The performances of the proposed methods are evaluated by Monte Carlo simulations. We generated data under a non-recursive structural equation model. We investigated the performances of the proposed estimators relative to the classical Maximum Likelihood estimator under a variety of sample sizes for both normal data (with PLSe1 and PLSe2) and non-normal data (with PLSe1 only). The results indicate that the proposed estimators provide estimates that are almost as good as the theoretically optimal ML estimator under normality. We also demonstrate that the standard error estimates closely correspond to the empirical Monte Carlo variation. Under non-normality, PLSe1 performs favorably with non-normal (i.e. robust) adjustments to model fit statistics and standard errors. The standard error estimates are consistent with corresponding sampling variance and the robust model fit chi-squares statistics are well calibrated. In particular, Satorra-Bentler's (1994) scaled chi-square statistic stands out clearly.