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Vanbrabant K, Boddez Y, Verduyn P, et al. A new approach for modeling generalization gradients: a case for hierarchical models. Front Psychol. 2015;6:652doi: 10.3389/fpsyg.2015.00652.
Vanbrabant, K., Boddez, Y., Verduyn, P., Mestdagh, M., Hermans, D., & Raes, F. (2015). A new approach for modeling generalization gradients: a case for hierarchical models. Frontiers in psychology, 6652. https://doi.org/10.3389/fpsyg.2015.00652
Vanbrabant, Koen, et al. "A new approach for modeling generalization gradients: a case for hierarchical models." Frontiers in psychology vol. 6 (2015): 652. doi: https://doi.org/10.3389/fpsyg.2015.00652
Vanbrabant K, Boddez Y, Verduyn P, Mestdagh M, Hermans D, Raes F. A new approach for modeling generalization gradients: a case for hierarchical models. Front Psychol. 2015 May 28;6:652. doi: 10.3389/fpsyg.2015.00652. eCollection 2015. PMID: 26074834; PMCID: PMC4446539.
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Front Psychol. 2015 May 28;6:652. doi: 10.3389/fpsyg.2015.00652. eCollection 2015.

A new approach for modeling generalization gradients: a case for hierarchical models.

Frontiers in psychology

Koen Vanbrabant, Yannick Boddez, Philippe Verduyn, Merijn Mestdagh, Dirk Hermans, Filip Raes

Affiliations

  1. Faculty of Psychology and Educational Sciences, University of Leuven Leuven, Belgium.

PMID: 26074834 PMCID: PMC4446539 DOI: 10.3389/fpsyg.2015.00652

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.

Keywords: R; hierarchical (linear) models; individual differences; lme4; repeated measures ANOVA; stimulus generalization

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