Hierarchical Bayesian models for continuous and positively skewed data from small areas

Abstract

There are numerous types of continuous and positively skewed data. We develop a hierarchical Bayesian generalized gamma regression model for continuous and positively skewed data. For skewed data, the log-transformation is one of the widely used transformation to meet the normality assumption. However, log-transformation could be problematic, so we use a generalized gamma distribution instead. Because the posterior distribution corresponding to this model is complex, we have used a second order Taylor’s series to obtain approximate multivariate normal distributions, which provide proposal densities for Metropolis samplers. We have applied our models to consumption data from a national household survey and chose the best-fitted model among the generalized gamma distribution and two special cases, the gamma and the exponential distributions. It is then linked to census data to provide small area estimates for poverty indicators. A simulation study shows that our methodology is reasonable.