Composite likelihood inference for ordinal periodontal data with replicated spatial patterns

Spatial ordinal data observed separately for multiple subjects are common in biomedical research, yet statistical methodology for such ordinal data analysis is limited. The existing methodology often assumes a single realization of spatial ordinal data without replications, a commonplace in disease mapping studies, and thus are not directly applicable. Motivated by a dataset evaluating periodontal disease (PD) status, we propose a multisubject spatial ordinal model that assumes a geostatistical spatial structure within a regression framework through an elegant latent variable representation. For achieving computational scalability within a classical inferential framework, we develop a maximum composite likelihood method for parameter estimation, and establish the asymptotic properties of the parameter estimates. Another major contribution is the development of model diagnostic measures for our dependent data scenario using generalized surrogate residuals. A simulation study suggests sound finite sample properties of the proposed methods. We also illustrate our proposed methodology via application to the motivating PD dataset. A companion R package clordr is available for easy implementation.