Expected predictive least squares for model selection in covariance structures

Predictive least squares (PLS) using future data to be predicted by current data are defined in covariance structure analysis. The expected predictive least squares (EPLS) obtained by two-fold expectation of PLS are unknown fit indexes. Using the asymptotic biases of weighted least squares given by current data for estimation of EPLS in covariance structures, corrected least square criteria derived similarly to the Takeuchi information criterion are shown to be asymptotically unbiased under arbitrary distributions. Simulations for model selection in exploratory factor analysis show improvements over typical current fit indexes as RMSEA and AIC.