| Mmodel_pcar {bigDM} | R Documentation |
Proper multivariate CAR latent effect
Description
M-model implementation of the proper multivariate CAR latent effect with different spatial autocorrelation parameters using the rgeneric model of INLA.
Usage
Mmodel_pcar(
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 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 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 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
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.
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.