Enhancing generalizability theory with mixed-effects models for heteroscedasticity in psychological measurement: A...

Generalizability theory (G-theory) defines a statistical framework for assessing measurement reliability by decomposing observed variance into meaningful components attributable to persons, facets, and error. Classic G-theory assumes homoscedastic residual variances across measurement conditions, an assumption that is often violated in psychological and behavioural data. The main focus of this work is to extend G-theory using a mixed-effects location-scale model (MELSM) that allows residual error variance to vary systematically across conditions and persons. By modeling heteroscedasticity, we can extend the computation of condition-specific generalizability ( $G_t$ ) and dependability ( $D_t$ ) coefficients to reflect local reliability under varying degrees of measurement precision. As an illustration, we apply the model to empirical data from an EEG experiment and show that failing to account for variance heterogeneity can mask meaningful differences in measurement quality. A simulation-based decision study further demonstrates how targeted increases in measurement density can improve reliability for low-precision conditions or participants. The proposed framework retains the interpretative character of classical G-theory while enhancing its flexibility. We argue that it supports finer-grained insights on conditions that influence reliability and better-informed design decisions in psychological measurements. We discuss implications for individualized reliability assessment, adaptive measurement strategies, and future extensions to multi-facet designs.