A Bayesian beta linear model to analyze fuzzy rating responses

In this short paper, we describe a Bayesian beta linear model to analyse imprecise rating responses. The non-random imprecision is extracted from crisp responses via the Item Response Theory tree (IRtree) method and it is represented by means of beta fuzzy numbers. The parameters of the beta linear model are estimated using the adaptive Metropolis-Hastings algorithm, with the fuzzy likelihood function being used as empirical evidence for the imprecise observations. A real case study is used to show the characteristics of the fuzzy beta regression model.