Laplace approximations and ordinal models for continuous spatial and spatio-temporal health mapping applications
With the increasing ability to collect myriad types of spatial data, we find ourselves regularly presented with new modeling problems that require novel solutions, but many of the available options for fitting spatial statistical models have limited applicability. Here we describe, evaluate and critique Template Model Builder (TMB), an existing but relatively unknown and unvetted (within the statistics community) modeling tool that leverages Laplace approximations to fit a large class of mixed effects models, including many spatial and spatial-temporal models. A large continuous spatial simulation study will be presented which contrasts the methods and results of TMB against the popular Integrated Nested Laplace Approximation (INLA) method, as implemented in the R-INLA package. An example application on a discrete spatial model of joint breast cancer incidence and mortality, which could not be fit with R-INLA will motivate the need for general spatial modeling tools. A second application, that requires novel modeling, is on the spatial mapping of anemia prevalence, using both categorically binned anemia severity data (mild, moderate, severe) and continuous hemoglobin measurements. We conclude with a discussion, and propose directions for future work, including validation and assessment challenges for these models.