Abstract
In spatial data analysis, the prior conditional autoregressive (CAR) model is used to express the spatial dependence on random effects from adjacent regions. This paper provides a new proposed approach regarding the development of the existing normal CAR model into a more flexible, Fernandez–Steel skew normal (FSSN) CAR model. This approach is able to capture spatial random effects that have both symmetrical and asymmetrical patterns. The FSSN CAR model is built on the basis of the normal CAR with an additional skew parameter. The FSSN distribution is able to provide good estimates for symmetry with heavy- or light-tailed and skewed-right and skewed-left data. The effects of this approach are demonstrated by establishing the FSSN distribution and FSSN CAR model in spatial data using Stan language. On the basis of the plot of the estimation results and histogram of the model error, the FSSN CAR model was shown to behave better than both models without a spatial effect and with the normal CAR model. Moreover, the smallest widely applicable information criterion (WAIC) and leave-one-out (LOO) statistical values also validate the model, as FSSN CAR is shown to be the best model used.
Highlights
Spatial analysis is one of the analytic approaches that considers the important aspects of spatial data; that is, data indicated by spatial effects
On the basis of the research conducted by Rantini et al [3], the survival model coupled with the normal conditional autoregressive (CAR) spatial effect is considered more representative in modeling correlated spatial data than the survival model without spatial random effects
Handling the small data in this study, we proposed to use a simulation with Hamiltonian Monte Carlo (HMC), which is applied to the distribution of non-normal data, namely the Fernandez–Steel skew normal (FSSN) distribution
Summary
Spatial analysis is one of the analytic approaches that considers the important aspects of spatial data; that is, data indicated by spatial effects. Considering that there have been many studies using the normal CAR model, Stan provides researchers with a new opportunity to conduct data-driven analysis by incorporating the concept of spatial effect modeling with a non-normal CAR model. The aim of this study is to show the new creation of the user-defined FSSN distribution and the FSSN CAR model in Stan and to demonstrate their flexibility to explain the distribution of spatial effects adaptively. The latter exhibits the ability and adaptability to model symmetrical and asymmetrical spatial data patterns. Where, for si ∼ s j , it means that si neighbors s j and i 6= j
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