  The integrated nested Laplace approximation (INLA) is a well-known and
popular technique for spatial modeling 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 describe Template Model
Builder (TMB), an existing technique which is well-suited to fitting complex
spatio-temporal models. TMB is relatively unknown to the spatial statistics
community, but is a highly flexible random effects modeling tool which allows
users to define complex random effects models through simple 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 an analysis of breast cancer incidence and
mortality data using a joint model which cannot be fit with INLA.
