On the meaning of the latent variables in the CT-C(M-1) model: a comment on Maydeu-Olivares and Coffman (2006)

[Correction Notice: An erratum for this article was reported in Vol 13(2) of Psychological Methods (see record 2008-06808-007). In Figures 3B and 3D, the question marks (?) should read as multiplication signs (×). That is, it should read as β×λ₈, β×λ₉, and β×λ₁₂ instead of β?λ₈, β?λ₉, and β?λ₁₂ in Figure 3B and as γ×λ₄ and γ×λ₅ instead of γ?λ₄ and γ?λ₅ in Figure 3D.] In a recent article, A. Maydeu-Olivares and D. L. Coffman (2006; see record 2006-22258-002) presented a random intercept factor approach for modeling idiosyncratic response styles in questionnaire data and compared this approach with competing confirmatory factor analysis models. Among the competing models was the CT-C(M-1) model (M. Eid, 2000). In an application to the Life Orientation Test (M. F. Scheier & C. S. Carver, 1985), Maydeu-Olivares and Coffman found that results obtained from the CT-C(M-1) model were difficult to interpret. In particular, Maydeu-Olivares and Coffman challenged the asymmetry of the CT-C(M-1) model. In the present article, the authors show that the difficulties faced by Maydeu-Olivares and Coffman rest upon an improper interpretation of the meaning of the latent factors. The authors' aim is to clarify the meaning of the latent variables in the CT-C(M-1) model. The authors explain how to properly interpret the results from this model and introduce an alternative restricted model that is conceptually similar to the CT-C(M-1) model and nested within it. The fit of this model is invariant across different reference methods. Finally, the authors provide guidelines as to which model should be used in which research context

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