Multivariate skew-normal distribution for modelling skewed spatial data

Abstract

Multivariate spatial data are commonly modelled using the shared spatial component and multivariate intrinsic conditional autoregressive (MICAR) models where the spatial random variables are assumed to be normally distributed. However, the normality assumption may not be always right as the spatially structured component may show non-normal distributions. We present, multivariate skew-normal spatial distribution in the modelling of multivariate conditional autoregressive models. Simulations and an application to estimate district HIV rates in South Africa are used for illustrating the capabilities of the proposed multivariate skewed spatial model. The estimation is done in a Bayesian framework. A comparison between our suggested approach and the common MICAR model is made using conditional predictive ordinate (CPO). The CPO values indicate that our suggested approach is better than the MICAR model for predicting the outcome variables of both the simulated and HIV data.

Keywords: MICAR-normal; Multivariate; Skew-normal distribution; Spatial model; Spatial random effects.