Bayesian Inference of Spatially Correlated Binary Data Using Skew-Normal Latent Variables with Application in Tooth Caries Analysis

Abstract

The analysis of spatially correlated binary data observed on lattices is an interesting topic that catches the attention of many scholars of different scientific fields like epidemiology, medicine, agriculture, biology, geology and geography. To overcome the encountered difficulties upon fitting the autologistic regression model to analyze such data via Bayesian and/or Markov chain Monte Carlo (MCMC) techniques, the Gaussian latent variable model has been enrolled in the methodology. Assuming a normal distribution for the latent random variable may not be realistic and wrong, normal assumptions might cause bias in parameter estimates and affect the accuracy of results and inferences. Thus, it entails more flexible prior distributions for the latent variable in the spatial models. A review of the recent literature in spatial statistics shows that there is an increasing tendency in presenting models that are involving skew distributions, especially skew-normal ones. In this study, a skew-normal latent variable modeling was developed in Bayesian analysis of the spatially correlated binary data that were acquired on uncorrelated lattices. The proposed methodology was applied in inspecting spatial dependency and related factors of tooth caries occurrences in a sample of students of Yasuj University of Medical Sciences, Yasuj, Iran. The results indicated that the skew-normal latent variable model had validity and it made a decent criterion that fitted caries data.

Flexible Bayesian hierarchical spatial modelling in disease mapping.

“…According to the values of these indicators the spatial model (MICAR-skew-normal) that assumes the structured spatial components are drawn from multivariate skew-normal distribution appears to perform better than the MICAR-normal model; suggesting that the MICAR-skew-normal model has a better predictive capacity and fits the skew-normal multivariate intrinsic conditional autoregressive spatial model and its application for disease mapping district ART coverage and knowledge of HIV status data better as compared to the MICAR-normal model. A similar study conducted by Afroughi et al (2015) indicated that a skew-normal distribution assumption to the spatially structured components fits the data well as compared to its normal counterpart. The skewness parameters are not significantly different from zero for both outcome variables suggesting little evidence of heavy tails; however as indicated above the MICAR-skew-normal model performs better than the MICAR-normal which supports our argument that our proposed approach should also be considered as alternative method in spatial modelling.…”