probs.icar {ref.ICAR}

OLM and ICAR model probabilities for areal data

Description

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

Usage

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

Arguments

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.

Value

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.

Author(s)

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

References

Porter EM, Franck CT, Ferreira MAR (2023). “Objective Bayesian model selection for spatial hierarchical models with intrinsic conditional autoregressive priors.” Bayesian Analysis, 1(1), 1–27. doi:10.1214/23-BA1375.