TY - JOUR

T1 - Bifactor Models for Predicting Criteria by General and Specific Factors

T2 - Problems of Nonidentifiability and Alternative Solutions

AU - Eid, Michael

AU - Krumm, Stefan

AU - Koch, Tobias

AU - Schulze, Julian

N1 - Publisher Copyright: © 2018 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2018/9/7

Y1 - 2018/9/7

N2 - 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.

AB - 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.

KW - Social Work and Social Pedagogics

KW - bifactor model

KW - identification

KW - bifactor (s-1) model

KW - general factor

KW - specific factors

KW - Sociology

UR - http://www.scopus.com/inward/record.url?scp=85074341125&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/f315784d-ea5b-3f1f-8fc8-b84595352b2b/

U2 - 10.3390/jintelligence6030042

DO - 10.3390/jintelligence6030042

M3 - Journal articles

C2 - 31162469

VL - 6

JO - Intelligence

JF - Intelligence

SN - 0160-2896

IS - 3

M1 - 42

ER -