Abstract: According to the features of the proportional data taken values on the closed interval ［0,1］ for the household coverage rate of commercial health insurance, in this paper, the Bayesian quantile regression modeling method is investigated for proportional response data based on the Tobit model. By introducing the “spike-and-slab” prior distributions of coefficients, the threshold rule-based Bayesian variable selection method is proposed by applying the EM algorithm. Extensive numerical simulation studies are used to verify the effectiveness of the proposed Bayesian variable selection method, and it has many merits such as easy implementation and cheap computation. Finally, the newly proposed method is applied to analyze the household coverage rate of commercial health insurance data, the influence factors of the coverage rate of commercial health insurance are uncovered at different quantile levels and some interesting results are gotten.

Key words: proportional data; tobit quantile regression; Bayesian variable selection; “Spike-and-slab” prior; EM algorithm