2 Citations (Scopus)


In spatial data analysis, the prior conditional autoregressive (CAR) model is used to ex-press 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 flex-ible, 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.

Original languageEnglish
Article number545
Issue number4
Publication statusPublished - Apr 2021


  • Bayesian estimation
  • Conditional autoregressive (CAR)
  • Fernan-dez–Steel skew normal (FSSN) CAR
  • Intrinsic conditional autoregressive (ICAR)
  • Stan


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