Hierarchical multivariate mixture generalized linear models for the analysis of spatial data: An application to disease mapping

Disease mapping of a single disease has been widely studied in the public health setup. Simultaneous modeling of related diseases can also be a valuable tool both from the epidemiological and from the statistical point of view. In particular, when we have several measurements recorded at each spatial location, we need to consider multivariate models in order to handle the dependence among the multivariate components as well as the spatial dependence between locations. It is then customary to use multivariate spatial models assuming the same distribution through the entire population density. However, in many circumstances, it is a very strong assumption to have the same distribution for all the areas of population density. To overcome this issue, we propose a hierarchical multivariate mixture generalized linear model to simultaneously analyze spatial Normal and non-Normal outcomes. As an application of our proposed approach, esophageal and lung cancer deaths in Minnesota are used to show the outperformance of assuming different distributions for different counties of Minnesota rather than assuming a single distribution for the population density. Performance of the proposed approach is also evaluated through a simulation study.