A Note on Equality and Inequality of Some Factor Score Predictors

Anderson and Rubin (1956), as well as Takeuchi et al. (1982) finally Schneeweiss and Mathes (1995) proposed factor score predictors that were regarded as orthogonal. Anderson and Rubin's and Takeuchi et al.'s factor score predictors are shown to be identical for non zero unique variances, although they have never been claimed being identical. It is shown that the Schneeweiss and Mathe's factor score predictor is not equal to McDonald's factor score predictor, although it has been claimed that these predictors are identical. It is, moreover, shown that the Schneeweiss and Mathe's factor score predictor is orthogonal only for the canonical orthogonal factor model.