Dirichlet-Multinomial Estimation of Small Area Proportions of Socio-Economic Classes
The hierarchical Bayesian Dirichlet-multinomial model is explored in this study to estimate small area proportions of socio-economic levels in regional and provincial levels using the Family and Income Expenditure Survey (FIES). The data include 38,484 households which are divided into three socio-economic classes such as low income, middle income and high income based on per capita income (PCI). Dirichlet-multinomial model was used to generate Bayesian small area estimates of households belonging to the low income, middle income, and high income socio-economic levels. Bayesian statistics were generated using Gibb’s sampling and simulation techniques to provide estimates with small Markov Chain Monte Carlo (MCMC) standard errors. Results include direct and Bayesian estimates of households belonging to the three socio-economic groups in regional and provincial levels. Wide disparities in the distributions of low income, middle income, and high income are noted in the results. A notable advantage of Dirichlet-multinomial estimates is the absence of zero proportion in high income level in comparison with direct estimates. Regions and provinces were ranked based on the estimates obtained from the hierarchical Bayesian Dirichlet-multinomial model with comparison on rankings using the direct estimates.
KeywordsDirichlet-multinomial model Hierarchical bayesian Small area statistics Socio-economic classes
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