title: A new approach for modeling generalization gradients: a case for hierarchical models.
abstract: A case is made for the use of hierarchical models in the analysis of generalization gradients. Hierarchical models overcome several restrictions that are imposed by repeated measures analysis-of-variance (rANOVA), the default statistical method in current generalization research. More specifically, hierarchical models allow to include continuous independent variables and overcomes problematic assumptions such as sphericity. We focus on how generalization research can benefit from this added flexibility. In a simulation study we demonstrate the dominance of hierarchical models over rANOVA. In addition, we show the lack of efficiency of the Mauchly's sphericity test in sample sizes typical for generalization research, and confirm how violations of sphericity increase the probability of type I errors. A worked example of a hierarchical model is provided, with a specific emphasis on the interpretation of parameters relevant for generalization research.
authors.affiliation: Faculty of Psychology and Educational Sciences, University of Leuven Leuven, Belgium.
authors.forename: Koen
authors.initials: K
authors.lastname: Vanbrabant
authors.affiliation: Faculty of Psychology and Educational Sciences, University of Leuven Leuven, Belgium.
authors.forename: Yannick
authors.initials: Y
authors.lastname: Boddez
authors.affiliation: Faculty of Psychology and Educational Sciences, University of Leuven Leuven, Belgium.
authors.forename: Philippe
authors.initials: P
authors.lastname: Verduyn
authors.affiliation: Faculty of Psychology and Educational Sciences, University of Leuven Leuven, Belgium.
authors.forename: Merijn
authors.initials: M
authors.lastname: Mestdagh
authors.affiliation: Faculty of Psychology and Educational Sciences, University of Leuven Leuven, Belgium.
authors.forename: Dirk
authors.initials: D
authors.lastname: Hermans
authors.affiliation: Faculty of Psychology and Educational Sciences, University of Leuven Leuven, Belgium.
authors.forename: Filip
authors.initials: F
authors.lastname: Raes
keywords: R; hierarchical (linear) models; individual differences; lme4; repeated measures ANOVA; stimulus generalization