Christensen, Rune Haubo Bojesen2; Brockhoff, Per B.1
1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Statistics and Data Analysis, Department of Applied Mathematics and Computer Science, Technical University of Denmark
Examples of categorical rating scales include discrete preference, liking and hedonic rating scales. Data obtained on these scales are often analyzed with normal linear regression methods or with omnibus Pearson chi2 tests. In this paper we propose to use cumulative link models that allow for regression methods similar to linear models while respecting the categorical nature of the observations. We describe how cumulative link models are related to the omnibus chi2 tests and how they can lead to more powerful tests in the non-replicated setting. For replicated categorical ratings data we present a quasi-likelihood approach and a mixed effects approach both being extensions of cumulative link models. We contrast population-average and subject-specific interpretations based on these models and discuss how different approaches lead to different tests. In replicated settings, naive tests that ignore replications are often expected to be too liberal because of over-dispersion.We describe how this depends on whether the experimental design is fully randomized or blocked. For the latter situation we describe how naive tests can be stronger than over-dispersion adjusting approaches, and that mixed effects models can provide even stronger tests than naive tests. Examples will be given throughout the paper and the methodology is implemented in the authors’ free R-package ordinal.
Journal De La Societe Francaise De Statistique and Revue De Statistique Appliquee, 2013, Vol 154, Issue 3, p. 58-79