Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions

Abstract

The bifactor model is a widely applied model to analyze general and specific abilities. Extensions of bifactor models additionally include criterion variables. In such extended bifactor models, the general and specific factors can be correlated with criterion variables. Moreover, the influence of general and specific factors on criterion variables can be scrutinized in latent multiple regression models that are built on bifactor measurement models. This study employs an extended bifactor model to predict mathematics and English grades by three facets of intelligence (number series, verbal analogies, and unfolding). We show that, if the observed variables do not differ in their loadings, extended bifactor models are not identified and not applicable. Moreover, we reveal that standard errors of regression weights in extended bifactor models can be very large and, thus, lead to invalid conclusions. A formal proof of the nonidentification is presented. Subsequently, we suggest alternative approaches for predicting criterion variables by general and specific factors. In particular, we illustrate how (1) composite ability factors can be defined in extended first-order factor models and (2) how bifactor(S-1) models can be applied. The differences between first-order factor models and bifactor(S-1) models for predicting criterion variables are discussed in detail and illustrated with the empirical example.

Well-being is more than happiness and life satisfaction: a multidimensional analysis of 21 countries

“…However, this bi-factor model showed a problematic bi-polar group factor with weak loadings. Whether this group factor was removed (resulting in a S-1 bi-factor model, as in [16]), model fit deteriorated. Thus, neither bi-factor alternative was considered to be acceptable.…”

Exploring the Dimensionality of the Social Skills Improvement System Using Exploratory Graph Analysis and Bifactor-(S− 1) Modeling

“…Bifactor-(S − 1) is a reconfiguration of the classical bifactor model, where one specific factor is omitted. In this model, the general factor is defined by the omitted (reference) factor and the specific factors capture variation in the items that are not accounted for by the general factor (Eid et al, 2018). A bifactor-(S − 1) with empathy and prosocial skills (F1) as the general reference factor resulted in acceptable fit χ 2 (960) = 1583.320, p < .001, RMSEA = .021, (90% CI [.019, .022]), CFI = .955, TLI = .951, SRMR = .043 (see Figure 3).…”

Appropriate Use of Bifactor Analysis in Psychopathology Research: Appreciating Benefits and Limitations

“…However, recent conceptual, methodological, and empirical work has highlighted problems with common approaches to evaluating and interpreting bifactor models. These criticisms include a tendency to overfit, such that the bifactor model is inappropriately favored by fit indices; frequent anomalous results, including small factor loadings and zero or negative group factor variances; instability of the general factor, such that the nature of the general factor changes across samples or indicators; problems with identification; questions regarding interpretation of orthogonal latent factors; and concerns about reification in searches for genetic or biological substrates of the p-factor (29)(30)(31)(32). Here, we suggest that, properly applied and interpreted, bifactor models can be useful for answering some important questions in psychology and psychiatry research.…”