B1403
Title: Block-diagonal matrix-logarithmic covariance model for large spatial binary data
Authors: Cheng Peng - The University of Manchester (United Kingdom) [presenting]
Abstract: Spatially distributed data possess a fundamental characteristic whereby the sample size equals the dimension of its covariance matrix. As a result, modelling the covariance matrix becomes impractical when the sample size expands due to the computational complexity. The aim is to propose an approach based on the matrix-logarithmic covariance model and its invariant property of a block-diagonal structure. The block-diagonal structure of the covariance matrix is pre-specified by partitioning observations into clusters and adopting an independence assumption between clusters. Additionally, a challenge in characterizing pairwise correlations between binary responses arises, as correlation coefficients must conform to Frechet-Hoeffding bounds. By virtue of a latent Gaussian copula model, which assumes that binary variables are generated via thresholding correlated latent Gaussian variables with constant cutoff points, the modelling of correlation between binary responses can be transformed into the unconstrained correlation between latent Gaussian variables. Two separate generalized estimating equations are used to estimate parameters in the proposed regression models for the marginal mean and latent correlation matrix. The consistency and asymptotic normality of parameter estimators are established. Moreover, simulation studies and the analyses of two data examples evaluate the numerical performance of the proposed modelling method and estimation procedure.
