Conditional autoregressive model approach to generalized linear spatial models

Spatial analysis is a method used to describe spatial patterns on a geographical region. During this analysis, the attributes and location information of the objects forming the spatial data are used. Response variable exhibits spatial autocorrelation because objects that are close to each other have similar characteristics rather than the objects further apart. Thus, even if explanatory variables are used in the model, the spatial relation remains in the residuals. Because of this, the assumption of independence by linear model approaches is violated. In such cases, random effects involving spatial relations are included in the model and conditional autoregressive priors are used for these effects. In the analysis of non-overlapping spatial data, the CARBayes package in R programming is used in order to set up a Bayesian spatial model with conditional autoregressive (CAR) priors. This package is based on the Markov Chain Monte Carlo (MCMC) simulation using the Gibbs sampling and Metropolis Hastings algorithms. In this study, provinces of Turkey are used as spatial areal units. The response variable, determined as the number of earthquakes in 2016, reveals spatial autocorrelation as a result of Moran's I permutation test. Hence, when generalized linear model under the assumption of Poisson distribution is used to model the number of earthquakes, spatial autocorrelation remains in the residual. On the basis of this, the relation between the number of earthquakes and magnitude is investigated with the Leroux conditional autoregressive model in which the random effects are included in the model. The risk values of each province are calculated and risk mapping is implemented based on the fitted values obtained from the model result.