Disaggregated spatial modeling for areal unit categorical data

We consider joint spatial modelling of areal multivariate categorical data assuming a multiway contingency table for the variables, modelled by using a log-linear model, and connected across units by using spatial random effects. With no distinction regarding whether variables are response or explanatory, we do not limit inference to conditional probabilities, as in customary spatial logistic regression. With joint probabilities we can calculate arbitrary marginal and conditional probabilities without having to refit models to investigate different hypotheses. Flexible aggregation allows us to investigate subgroups of interest; flexible conditioning enables not only the study of outcomes given risk factors but also retrospective study of risk factors given outcomes. A benefit of joint spatial modelling is the opportunity to reveal disparities in health in a richer fashion, e.g. across space for any particular group of cells, across groups of cells at a particular location, and, hence, potential space–group interaction. We illustrate with an analysis of birth records for the state of North Carolina and compare with spatial logistic regression.