Mmodel_icar {bigDM}

Intrinsic multivariate CAR latent effect

Description

M-model 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 rgeneric model to define the latent effect.

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 M-model proposal of Botella-Rocamora 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 (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

Value

This is used internally by the INLA::inla.rgeneric.define() function.

References

Botella-Rocamora P, Martinez-Beneito 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.