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

Michael Eid,Tobias Koch,Julian Schulze,Stefan Krumm

doi:10.3390/jintelligence6030042

Michael Eid, Tobias Koch + Show 2 more

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https://doi.org/10.3390/jintelligence6030042

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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.

Highlights

In 1904, Charles Spearman [1] published his groundbreaking article “General intelligence objectively determined and measured” that has been affecting intelligence research since
The bifactor model with criterion variables as covariates is not identified if (a) the indicators do not differ in their loadings on the general and specific factors, and (b) both the general and specific factors are correlated with the criterion variables
As we have shown in the empirical application, one can specify the model in such a way that either the g factor or the specific factors are the relevant source of individual differences in the criterion variables, thereby making this model arbitrary for determining the relative importance of g versus specific abilities

Summary

Introduction

In 1904, Charles Spearman [1] published his groundbreaking article “General intelligence objectively determined and measured” that has been affecting intelligence research since . Given Spearman’s distinction into general and specific cognitive abilities, one fundamental topic of intelligence research has been the question to which degree these general and specific facets are important for predicting real-world criteria (e.g., [2,3]; for an overview see [4]). This consensus has shifted from “not much more than g” (see [7]) to the notion that there may be something more than g predicting real-world criteria. Reflecting this shift, Kell and Lang [4]

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