Bayesian Method for Hurdle Regression
Keywords:excess zero, Gibbs sampling, MCMC, over-dispersion, two-part model
Hurdle model is an alternative model to overcome overdispersion caused by excess zero. The model consists of two stages: a binary process that determines whether the response variable has zero values or positive values, and the second stage to model only the positive counts. The first stage is modelled using binary logistic regression, and the next stage is modeled with the zero-truncated model using Poisson regression. Bayesian method was employed to estimate the models’ parameters. Non-informative priors were specified for the parameters, and combined with the likelihood from the data, the non-closed form of posterior distributions were obtained, thus leading to the use of Markov Chain Monte Carlo (MCMC) with Gibbs Sampling to obtain samples from the posterior distributions. This method was applied to model the frequency of motoric complication in people with Parkinson’s disease. The result showed that subtotal scores from the three parts of Movement Disorder Society-Unified Parkinson’s Disease Rating Scale (MDS-UPDRS) could explain the frequency of motoric complication well, implied by the significance of the regression coefficients.