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 rgeneric model to define the latent effect.
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.

---