Paper in Psychometrika
- Grayson, D. (2006). Might "unique" factors be "common"? On the possibility of indeterminate common-unique covariances. Psychometrika, 71: 521-528.
The present paper shows that the usual factor analytic structured data dispersion matrix ΛΨΛ′ + Δ can readily arise from a set of scores y = Λη + ε, where the “common” (η) and “unique” (ε) factors have nonzero covariance: Γ = Cov(ε, η) ≠ 0. Implications of this finding are discussed for the indeterminacy of factor scores, and for the issue of invariance of factor analytic covariance models. The size of the problem is explored with numerical examples.