Geoadditive Bayesian Model For Data With Limited Spatial Information

Abstract

Large area estimation has been mostly accomplished using Geoadditive Models (GM) which combines the ideas of Geostatistics and additive models. The GM relaxes the classical assumptions of traditional parametric model by simultaneously incorporating linear and nonlinear, nonparametric effects of covariates, nonlinear interactions and spatial effects into a Geoadditive predictor. In the past, estimation of GM has been based on large area as a result of insufficient information in small areas. However, Bayesian approach allows out-of-sample information which can be used to augment the limited information in small areas. Hence, this study adopted the Geoadditive Bayesian model to estimate small areas with insufficient spatial information focusing on small district areas. The GM by Kamman and Wand was specified by using Effect Coding (EC) to capture the spatial effect. The posterior was obtained by combining the likelihood (data) with the prior (out-of-sample) information. The likelihood and the prior information were assumed to be Gaussian and inverse gamma distribution respectively. The numerical solutions were obtained for the posterior distribution, which were not having a closed form solution, using Markov Chain Monte Carlo (MCMC) simulation technique. Finite difference and partial derivative methods were used to estimate other components of the Geoadditive Bayesian model. Kane analyser was used to collect vehicular emission (carbondioxide, carbonmonoxide and hydrocarbon). Information were also collected on age of vehicles, vehicle types (car and buses), vehicle uses (private and commercial) from 9211 vehicles for 3 years (2008-2011) covering 4 locations: Abeokuta, Sagamu, Ijebu-Ode and Sango-Ota. Data were also collected on respiratory health records of 9211 individuals (18 years and below) in six different hospitals on number of visits (nv) and diagnosis within the locality of the collection point of pollutants.