Extending Applications of Generalizability Theory-Based Bifactor Model Designs

Abstract

In recent years, researchers have described how to analyze generalizability theory (GT) based univariate, multivariate, and bifactor designs using structural equation models. However, within GT studies of bifactor models, variance components have been limited to those reflecting relative differences in scores for norm-referencing purposes, with only limited guidance provided for estimating key indices when making changes to measurement procedures. In this article, we demonstrate how to derive variance components for multi-facet GT-based bifactor model designs that represent both relative and absolute differences in scores for norm- or criterion-referencing purposes using scores from selected scales within the recently expanded form of the Big Five Inventory (BFI-2). We further develop and apply prophecy formulas for determining how changes in numbers of items, numbers of occasions, and universes of generalization affect a wide variety of indices instrumental in determining the best ways to change measurement procedures for specific purposes. These indices include coefficients representing score generalizability and dependability; scale viability and added value; and proportions of observed score variance attributable to general factor effects, group factor effects, and individual sources of measurement error. To enable readers to apply these techniques, we provide detailed formulas, code in R, and sample data for conducting all demonstrated analyses within this article.