Ranking in discrete choice experiments

A common problem in ethology is ranking of animal preferences for several discrete stimuli or options. We considered experiments where animals chose one of all possible simultaneously presented options. The animals might be observed at repeated occasions. In the ethological literature the analysis is often focused on testing the global hypotheses of no difference in preferences by non-parametric methods. This fails to address the estimation of a ranking. Often this approach cannot adequately reflect the the experimental setting and the repeated measurement structure. Therefore, we propose to model to the choice probabilities for the options with a multinomial logistic model. The correlation induced by repeated measurements is incorporated by animal specific random intercepts. The ranking of the options is taken as the order of the choice probabilities. Adopting a Bayesian approach samples from the posterior distribution of the choice probabilities provide directly samples from the posterior of the rankings. Based on this an estimate of the ranking and description of its variability can be derived. The computation was performed via Markov chain Monte Carlo sampling and was implemented using WinBUGS. We illustrate our approach with an experiment to determine the preference of pigs for three different rooting materials. The proposed method allowed to derive an overall ranking for different combinations of the materials and the spatial orientation