Mmodel_icar {bigDM}  R Documentation 
Intrinsic multivariate CAR latent effect
Description
Mmodel implementation of the intrinsic multivariate CAR latent effect using the rgeneric
model of INLA.
Usage
Mmodel_icar(
cmd = c("graph", "Q", "mu", "initial", "log.norm.const", "log.prior", "quit"),
theta = NULL
)
Arguments
cmd 
Internal functions used by the 
theta 
Vector of hyperparameters. 
Details
This function considers an intrinsic CAR prior for the spatial latent effects of the different diseases and introduces correlation between them using the Mmodel proposal of BotellaRocamora et al. (2015).
Putting the spatial latent effects for each disease in a matrix, the between disease dependence is introduced through the M matrix as \Theta=\Phi M
, where the columns of \Phi
follow an intrinsic CAR prior distribution (withindisease correlation).
A Wishart prior for the between covariance matrix M'M
is considered using the Bartlett decomposition.
The following arguments are required to be defined before calling the functions:

W
: binary adjacency matrix of the spatial areal units 
J
: number of diseases 
initial.values
: initial values defined for the cells of the Mmatrix
Value
This is used internally by the INLA::inla.rgeneric.define()
function.
References
BotellaRocamora P, MartinezBeneito MA, Banerjee S (2015). “A unifying modeling framework for highly multivariate disease mapping.” Statistics in Medicine, 34(9), 1548–1559. doi:10.1002/sim.6423.