Bayesian spatial quantile modeling applied to the incidence of extreme poverty in Lima-Peru

Peru is an emerging nation with a nonuniform development where the growth is focused on some specific cities and districts, as a result there is serious economic inequalities across the country. Despite the poverty in Peru has declined in the last decades, there is still poor districts in risk to become extremely poor, even in its capital, Lima. In this context, it is relevant to study the incidence of extreme poverty at district levels. In this paper, we propose to estimate the quantiles of the incidence of extreme poverty of districts in Lima by using spatial quantile models based on the Kumaraswamy distribution and spatial random effects for areal data. Furthermore, in order to deal with spatial confounding random effects we used the Spatial Orthogonal Centroid "K"orrection approach. Bayesian inference for these hierarchical models is conveniently performed based on the Hamiltonian Monte Carlo method. Our modeling is flexible and able to describe the quantiles of incidence of extreme poverty in Lima.