Abstract

For binary regression models, adopting a symmetric link function would not be a reasonable approach when there is an uneven number of 0’s and 1’s in the response variable. In fact, as is documented in the literature, the choice of link functions can be a critical issue as inference can be sensitive to the choice of this map, in particular if a symmetric link is used instead of an asymmetric one.

In this work we develop Bayesian Hamiltonian Monte Carlo inference under sparsity for spatial binary regression models employing a number competing link functions. In this multivariate scenario, flexible skewed link functions are probably preferred and investigating the implications of these functions is one of the contributions of the work. Another contribution is that we rely on a G-Wishart distribution which is more flexible in estimating spatial associations than the standard conditionally autoregressive (CAR) model which does not allow for non-stationarity, spatially varying autocorrelation and smoothing parameters.

We developed HMC samplers for parameter estimation and model comparison of binary regression models with a spatial ingredient. We then apply our methodology to a motivating dataset on periodontal disease and also include a simulation study to investigate robustness of our methods. All the computations in this paper were implemented using the C++ programming language through the Rcpp and RcppArmadillo which are available in the open-source statistical software language and environment R.