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

Abstract

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.

Keywords:

• Binary responses from correlated locations
• correlated random effects
• family-based spatial correlations
• joint generalized quasi-likelihood estimation
• normality-based higher order moments
• spatial binary responses

2010 Mathematics Subject Classification:

• 62H11

Acknowledgments

The authors are grateful to the editors and referees whose comments have led to improvements in the quality of this paper. This research was partially supported by grants from the Natural Sciences and the Engineering Research Council of Canada.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was partially supported by grants from the Natural Sciences and Engineering Research Council of Canada.