Bayesian Spatial Homogeneity Pursuit of Functional Data: an Application to the U.S. Income Distribution

An income distribution describes how an entity's total wealth is distributed amongst its population. A problem of interest to regional economics researchers is to understand the spatial homogeneity of income distributions among different regions. In economics, the Lorenz curve is a well-known functional representation of income distribution. In this article, we propose a mixture of finite mixtures (MFM) model as well as a Markov random field constrained mixture of finite mixtures (MRFC-MFM) model in the context of spatial functional data analysis to capture spatial homogeneity of Lorenz curves. We design efficient Markov chain Monte Carlo (MCMC) algorithms to simultaneously infer the posterior distributions of the number of clusters and the clustering configuration of spatial functional data. Extensive simulation studies are carried out to show the effectiveness of the proposed methods compared with existing methods. We apply the proposed spatial functional clustering method to state level income Lorenz curves from the American Community Survey Public Use Microdata Sample (PUMS) data. The results reveal a number of important clustering patterns of state-level income distributions across US.