M-model implementation of the proper multivariate CAR latent effect with different spatial autocorrelation parameters using the rgeneric model of INLA.
Mmodel_pcar(
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 a proper CAR prior (denoted as pCAR) 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 a pCAR 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 autocorrelation 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
botella2015unifyingbigDM