Figure 1.
Confirmatory factor models for multi-facet data. Yif: ith observed variable or symptom pertaining to facet (or syndrome) f. Ff: true score variable (latent factor) pertaining to facet f. Sf: specific (residual) factor pertaining to facet f. λif, γif, δif: factor loadings. βf: latent regression slope coefficient. A: correlated first-order factors model. B: Standard bifactor S – 1 model. C: Reformulation of the correlated first-order factors model into a latent regression model. D: Reformulation of the latent regression model into a restricted bifactor S – 1 model. Models A, C, and D are equivalent. In Models B, C, and D, Facet 1 serves as reference. Note that in Model D, the reference factor loadings of the non-reference indicators are constrained to equal the product λif ∙ βf.