A Statistical Review of Template Model Builder: A Flexible Tool for Spatial Modelling

The integrated nested Laplace approximation (INLA) is a well-known and popular technique for spatial modelling with a user-friendly interface in the R-INLA package. Unfortunately, only a certain class of latent Gaussian models are amenable to fitting with INLA. In this paper, we review template model builder (TMB), an existing technique and software package which is well-suited to fitting complex spatio-temporal models. TMB is relatively unknown to the spatial statistics community, but it is a flexible random effects modelling tool which allows users to define customizable and complex mixed effects models through C++ templates. After contrasting the methodology behind TMB with INLA, we provide a large-scale simulation study assessing and comparing R-INLA and TMB for continuous spatial models, fitted via the stochastic partial differential equations (SPDE) approximation. The results show that the predictive fields from both methods are comparable in most situations even though TMB estimates for fixed or random effects may have slightly larger bias than R-INLA. We also present a smaller discrete spatial simulation study, in which both approaches perform well. We conclude with a joint analysis of breast cancer incidence and mortality data implemented in TMB which requires a model which cannot be fit with R-INLA.