Mmodel_lcar: Leroux et al. (1999) multivariate CAR latent effect
In bigDM: Scalable Bayesian Disease Mapping Models for High-Dimensional Data

Mmodel_lcar

R Documentation

Leroux et al. (1999) multivariate CAR latent effect

Description

M-model implementation of the Leroux et al. (1999) multivariate CAR latent effect with different spatial smoothing parameters using the rgeneric model of INLA.

Usage

Mmodel_lcar(
  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 a Leroux et al. (1999) CAR prior (denoted as LCAR) for the spatial latent effects of the different diseases and introduces correlation between them using the M-model proposal of \insertCitebotella2015unifying;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 a LCAR prior distribution (within-disease correlation). A Wishart prior for the between covariance matrix M'M is considered using the Bartlett decomposition. Uniform prior distributions on the interval [alpha.min, alpha.max] are considered for all the spatial smoothing parameters.

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
alpha.min: lower limit defined for the uniform prior distribution of the spatial smoothing parameters
alpha.max: upper limit defined for the uniform prior distribution of the spatial smoothing parameters

Value

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

Note

The M-model implementation of this model using R-INLA requires the use of J \times (J+3)/2 hyperparameters. So, the results must be carefully checked.