probs.icar: OLM and ICAR model probabilities for areal data

Description

Performs simultaneous selection of covariates and spatial model structure for areal data.

probs.icar(
  Y,
  X,
  H,
  H.spectral = NULL,
  Sig_phi = NULL,
  b = 0.05,
  verbose = FALSE
)

A list containing a data frame with all posterior model probabilities and other selection information.

probs.mat: Data frame containing posterior model probabilities for all candidate OLMs and ICAR models from the data.
mod.prior: Vector of model priors used to obtain the posterior model probabilities.
logmargin.all: Vector of all (log) fractional integrated likelihoods.
base.model: Maximum (log) fractional integrated likelihood among all candidate models. All fractional Bayes factors are obtained with respect to this model.
BF.vec: Vector of fractional Bayes factors for all candidate models.

Y: A vector of responses.
X: A matrix of covariates, which should include a column of 1's for models with a non-zero intercept
H: Neighborhood matrix for spatial subregions.
H.spectral: Spectral decomposition of neighborhood matrix, if user wants to pre-compute it to save time.
Sig_phi: Pseudo inverse of the neighborhood matrix, if user wants to pre-compute it to save time.
b: Training fraction for the fractional Bayes factor (FBF) approach.
verbose: If FALSE, marginal likelihood progress is not printed.

Erica M. Porter, Christopher T. Franck, and Marco A.R. Ferreira

Porter_2024ref.ICAR