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Abstract:
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We developed a robust Bayesian method, based on the generalized beta distribution of the second kind (GB2) to analyze consumption data from Nepal. Our objective is to predict the poverty rates of small areas. The consumption data are positively-skewed and this suggests transforming the data using a logarithmic transformation, which however could be problematic. We use a standard small area model with two covariates and we assume that the consumption data have a flexible distribution that can be conveniently expressed as the scale mixture of generalized gamma distributions with another generalized gamma distribution being the mixing distribution. We have constructed a hierarchical Bayesian model and we have incorporated the covariates in an innovative manner. We have applied this model to the second Nepal Living Standards Survey (NLSS-II). We have compared our model with the hierarchical Bayesian nested error regression (NER) model which uses normality assumption. Under the GB2 density the joint posterior density is complex, so we have used Markov chain Monte Carlo (MCMC) methods to fit it. The NER model does not need MCMC methods but, as indicated, it could be problematic under the logarithmic transformation.
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