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For correlated binary data, generalized estimating Equation (GEE) approach is commonly used for inference of the mean parameters. When the associated correlation is of interest, e.g., in spatial data analysis, some traditional correlation structures such as compound symmetry and AR(1) were employed in the literature, which is not appropriate for the inherent correlation for correlated binary data. In this paper, we proposed another set of GEE implemented with alternative hypersphere decomposition (AHPC) to model the correlation parameters. An iterative algorithm is provided to estimate the mean and correlation parameters simultaneously. By utilizing the AHPC, we developed a parametrization for the correlation matrix that automatically ensures the order independence and non-negative definiteness. We also addressed the issue of asymptotic properties. For illustration, the proposed methods were used to fit a spatial bovine tuberculosis infection data in Ireland, aiming to analyse the influential factors which affect the infection of cattle and/or badgers.

Spatially correlated binary data modelling using generalized estimating equations with alternative hypersphere decomposition