Bayesian non-homogeneous cumulative probability models for ordinal data from designed experiments. Issue 17 (2nd September 2022)

• Record Type: Journal Article
• Authors: Yu, I-Tang
• Is Part Of: Communications in statistics. Volume 51:Issue 17(2022)
• Page Start: 6008
• Page End: 6020
• Publication Date: 2022-09-02
• Subjects: Bayesian estimation -- Gaussian process -- ordinal response; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2020.1851719
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: 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.