Modelling monotonic effects of ordinal predictors in Bayesian regression models

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2020-11
Major/Subject
Mcode
Degree programme
Language
en
Pages
Series
BRITISH JOURNAL OF MATHEMATICAL AND STATISTICAL PSYCHOLOGY
Abstract
Ordinal predictors are commonly used in regression models. They are often incorrectly treated as either nominal or metric, thus under- or overestimating the information contained. Such practices may lead to worse inference and predictions compared to methods which are specifically designed for this purpose. We propose a new method for modelling ordinal predictors that applies in situations in which it is reasonable to assume their effects to be monotonic. The parameterization of such monotonic effects is realized in terms of a scale parameter b representing the direction and size of the effect and a simplex parameter sigma modelling the normalized differences between categories. This ensures that predictions increase or decrease monotonically, while changes between adjacent categories may vary across categories. This formulation generalizes to interaction terms as well as multilevel structures. Monotonic effects may be applied not only to ordinal predictors, but also to other discrete variables for which a monotonic relationship is plausible. In simulation studies we show that the model is well calibrated and, if there is monotonicity present, exhibits predictive performance similar to or even better than other approaches designed to handle ordinal predictors. Using Stan, we developed a Bayesian estimation method for monotonic effects which allows us to incorporate prior information and to check the assumption of monotonicity. We have implemented this method in the R package brms, so that fitting monotonic effects in a fully Bayesian framework is now straightforward.
Description
Keywords
Bayesian statistics, brms, isotonic regression, ordinal variables, R, Stan
Other note
Citation
Bürkner , P C & Charpentier , E 2020 , ' Modelling monotonic effects of ordinal predictors in Bayesian regression models ' , British Journal of Mathematical and Statistical Psychology , vol. 73 , no. 3 , pp. 420-451 . https://doi.org/10.1111/bmsp.12195