This function is used to specify a (non-default) GMRF structure
to pass to argument strucA of function gen.
GMRF_structure(
type = c("default", "bym2", "leroux"),
scale.precision = (type == "bym2"),
prior = NULL,
control = NULL
)An environment defining the desired GMRF structure, for use by other package functions.
one of "default", "bym2" or "leroux". The default choice
corresponds to the precision matrix \(Q_A\) as specified by argument factor
of gen. Type "bym2" modifies the default structure to one with
covariance matrix \(\phi \tilde{Q}_{A}^- + (1 - \phi) I\) where
\(\tilde{Q}_{A*}^-\) is the generalized inverse of \(Q_A\), by default
scaled such that the geometric mean of the marginal variances equals 1.
Type "leroux" modifies the default structure to one with precision matrix
\(\phi Q_A + (1 - \phi) I\).
whether to scale the structured precision matrix. By default
set to TRUE only for type "bym2".
prior for the parameter \(phi\) in the "bym2" or "leroux" extension.
Supported priors can be set using functions pr_fixed or pr_unif.
options for the Metropolis-Hastings sampler used to sample
from the full conditional distribution of parameter \(phi\) in case of
"bym2" or "leroux" extensions. If NULL a reasonable default configuration
is used. A user can change these settings using function set_MH.
Supported proposal distribution types are "RWTN", "RWN", "unif" and "beta".
B. Leroux, X. Lei and N. Breslow (1999). Estimation of Disease Rates in Small Areas: A New Mixed Model for Spatial Dependence. In M. Halloran and D. Berry (Eds.), Statistical Models in Epidemiology, the Environment and Clinical Trials, 135-178.
A. Riebler, S.H. Sorbye, D. Simpson and H. Rue (2016). An intuitive Bayesian spatial model for disease mapping that accounts for scaling. Statistical methods in medical research, 25(4), 1145-1165.