M-model implementation of the intrinsic multivariate CAR latent effect using the rgeneric model of INLA.
Mmodel_icar(
cmd = c("graph", "Q", "mu", "initial", "log.norm.const", "log.prior", "quit"),
theta = NULL
)This is used internally by the INLA::inla.rgeneric.define() function.
Internal functions used by the rgeneric model to define the latent effect.
Vector of hyperparameters.
This function considers an intrinsic CAR prior for the spatial latent effects of the different diseases and introduces correlation between them using the M-model proposal of botella2015unifying;textualbigDM.
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 (within-disease 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 M-matrix
botella2015unifyingbigDM