Promises and Pitfalls of Latent Variable Approaches to Understanding Psychopathology: Reply to Burke and Johnston, Eid, Junghänel and Colleagues, and Willoughby

Abstract

The commentaries by Burke and Johnston (this issue), Eid (this issue), Junghänel et al. (this issue), and Willoughby (this issue) on Burns et al. (this issue) provide useful context for comparing three latent variable modeling approaches to understanding psychopathology-the correlated first-order syndrome-specific factors model, the bifactor S - 1 model, and the symmetrical bifactor model. The correlated first-order syndrome-specific factors model has proven useful in constructing explanatory models of psychopathology. The bifactor S - 1 model is also useful for examining the latent structure of psychopathology, especially in contexts with clear theoretical predictions. Joint use of correlated first-order syndrome-specific model and bifactor S - 1 model provides leverage for explaining psychopathology, and both models can also guide individual clinical assessment. In this reply, we further clarify reasons why the symmetrical bifactor model should not be used to study the latent structure of psychopathology and also discuss a restricted bifactor S - 1 model that is equivalent to the first-order syndrome-specific factors model.

Keywords: ADHD; Attention-deficit/hyperactivity disorder; Bifactor model; Factor analysis; Oppositional defiant disorder; Psychopathology; Restricted bifactor S – 1 model; p factor.

Figure 1.

Confirmatory factor models for multi-facet data. Y_if: ith observed variable or symptom pertaining to facet (or syndrome) f. F_f: true score variable (latent factor) pertaining to facet f. S_f: specific (residual) factor pertaining to facet f. λ_if, γ_if, δ_if: factor loadings. β_f: 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 λ_if ∙ β_f.