Bartlett factor scores: General formulas and applications to structural equation models

Abstract

This paper extends Bartlett’s formula for computing factor scores to general structural equation modeling. The derived formulas can handle modeling situations where existing formulas cannot apply, namely, when there are exogenous observed variables in the model. The derivation of general formulas for computing Bartlett factor scores leads to extended formulas for defining residual and leverage M-distances, which were originally proposed by Yuan and Hayashi (Psychological Methods 15:335–351, 2010). These formulas are shown to have useful applications in residual diagnostics, outlier and leverage point detection, and robust estimation. Application of the derived formulas to a simulated data set is illustrated. This paper is based on a presentation by the first author at the International Meeting of Psychometric Society held in Lincoln, Nebraska, July 2012.