Examining the integrity of measurement of cognitive abilities in the prediction of achievement: Comparisons and contrasts across variables from higher-order and bifactor models

Prior research examining cognitive ability and academic achievement relations have been based on different theoretical models, have employed both latent variables as well as observed variables, and have used a variety of analytic methods. Not surprisingly, results have been inconsistent across studies. The aims of this study were to (a) examine how relations between psychometric g, Cattell–Horn–Carroll (CHC) broad abilities, and academic achievement differ across higher-order and bifactor models; (b) examine how well various types of observed scores corresponded with latent variables; and (c) compare two types of observed scores (i.e., refined and non-refined factor scores) as predictors of academic achievement. Results suggest that cognitive–achievement relations vary across theoretical models and that both types of factor scores tend to correspond well with the models on which they are based. However, orthogonal refined factor scores (derived from a bifactor model) have the advantage of controlling for multicollinearity arising from the measurement of psychometric g across all measures of cognitive abilities. Results indicate that the refined factor scores provide more precise representations of their targeted constructs than non-refined factor scores and maintain close correspondence with the cognitive–achievement relations observed for latent variables. Thus, we argue that orthogonal refined factor scores provide more accurate representations of the relations between CHC broad abilities and achievement outcomes than non-refined scores do. Further, the use of refined factor scores addresses calls for the application of scores based on latent variable models.