Bayesian non-homogeneous cumulative probability models for ordinal data from designed experiments

Cumulative probability models are standard tools for analyzing ordinal response data. The cumulative probability models can however be very restrictive in practice because of the inherent homogeneous assumption. In this work we propose a new Bayesian model to analyze ordinal data collected in statistically designed experiments. In the proposed model, we assume that the intercepts on the latent variable representation of cumulative probability models are realizations of different Gaussian processes that satisfy an order condition. By doing this, the homogeneous assumption is relaxed. Moreover, the order condition guaranties a positive probability when predicting the result under an arbitrary experimental setting. We use the Bayesian non-homogeneous cumulative probability model to analyze a foam experiment by which this work is motivated. From the analysis, we obtain a better fit than fitting conventional cumulative probability models to the data.