An Approximate Bayesian Inference for Beta Regression Models

In modeling the variables related to each other, regression models are usually used assuming that the response variable is Normal. But in problems dealing with data such as the rate or ratio of an event distributed in the (0,1) interval, these models may provide out-of-range predictions for the response variable. In addition rate or ratio data are oftem asymmetrically distributed, and the use of symmetric distributions leads to invalid results. In such cases, the Beta regression model is used, in which the distribution of the response variable is in the Beta family. Bayesian analysis of these models generally requires the calculation of multiple integrals. The use of MCMC algorithms sometimes encounters long computation times and divergence. This work presents approximate methods for obtaining posterior distributions for Bayesian analysis of Beta regression models. Then the Integrated Nested Laplace Approximation will be offered for getting the posterior distributions in the Bayesian analysis of these models. Moreover, these models' application is illustrated on a real data set.