An unbalanced multidimensional latent effects-based logistic mixed model and GQL estimation for spatial binary data

Spatial correlation structure is the most essential tool in a spatial data analysis. However, the difficulty of modelling spatial correlations between two responses collected from two neighbouring locations is a challenge, when it is known that each of the responses may also be influenced by certain visible and/or invisible effects of other neighbouring locations. Further difficulties arise when one deals with spatial binary data as opposed to linear spatial data. In this paper, we resolve this correlation model issue for spatial binary data by using a mixed logits model approach where pair-wise correlations are computed by accommodating both within and between correlations for paired-responses. For inferences, we use the true correlation based generalized quasi-likelihood (GQL) approach. The asymptotic normality of the estimators of the main regression and random effects variance parameters are studied. The model and estimation methodology used are illustrated by a finite sample-based simulation study.