A Robust Indicator Mean-Based Method for Estimating Generalizability Theory Absolute Error and Related Dependability Indices within Structural Equation Modeling Frameworks

Abstract

In this study, we introduce a novel and robust approach for computing Generalizability Theory (GT) absolute error and related dependability indices using indicator intercepts that represent observed means within structural equation models (SEMs). We demonstrate the applicability of our method using one-, two-, and three-facet designs with self-report measures having varying numbers of scale points. Results for the indicator mean-based method align well with those obtained from the GENOVA and R gtheory packages for doing conventional GT analyses and improve upon previously suggested methods for deriving absolute error and corresponding dependability indices from SEMs when analyzing three-facet designs. We further extend our approach to derive Monte Carlo confidence intervals for all key indices and to incorporate estimation procedures that correct for scale coarseness effects commonly observed when analyzing binary or ordinal data.

Keywords

• generalizability theory
• structural equation modeling
• R programming
• Music Self-Perception Inventory
• reliability
• psychometrics