TMB: Automatic Differentiation and Laplace Approximation}
TMB is an open source R package that enables quick
implementation of complex nonlinear random effect (latent variable) models
in a manner similar to the established AD Model Builder package
In addition, it offers easy access to parallel computations.
The user defines the joint likelihood for the data and the random effects
as a C++ template function,
while all the other operations are done in R; e.g.,
reading in the data.
The package evaluates and maximizes
the Laplace approximation of the marginal likelihood
where the random effects are automatically integrated out.
This approximation, and its derivatives, are
obtained using automatic differentiation
(up to order three) of the joint likelihood.
The computations are
designed to be fast for problems with many random effects
(~ 10^6) and fixed effects (~ 10^3). Computation times
using ADMB and TMB are compared on a suite of examples ranging from
simple models to large spatial models where the random effects are
a Gaussian random field.
Speedups ranging from 1.5 to about
100 are obtained with increasing gains for large problems.
The package and examples are available at