Mmodel_lcar {bigDM} | R Documentation |
M-model implementation of the Leroux et al. (1999) multivariate CAR latent effect with different spatial smoothing parameters using the rgeneric
model of INLA.
Mmodel_lcar(
cmd = c("graph", "Q", "mu", "initial", "log.norm.const", "log.prior", "quit"),
theta = NULL
)
cmd |
Internal functions used by the |
theta |
Vector of hyperparameters. |
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 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 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
This is used internally by the INLA::inla.rgeneric.define()
function.
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.
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.
Leroux BG, Lei X, Breslow N (1999). “Estimation of disease rates in small areas: A new mixed model for spatial dependence.” In Halloran ME, Berry D (eds.), Statistical Models in Epidemiology, the Environment, and Clinical Trials, 179–191. Springer-Verlag: New York.