ref.analysis {ref.ICAR}

MCMC Analysis and Summaries for Reference Prior on an Intrinsic Autoregressive Model for Areal Data

Description

Performs analysis on a geographical areal data set using the objective prior for intrinsic conditional autoregressive (ICAR) random effects (Keefe et al. 2019). It takes a shapefile, data, and region names to construct a neighborhood matrix and perform Markov chain Monte Carlo sampling on the unstructured and spatial random effects. Finally, the function obtains regional estimates and performs posterior inference on the model parameters.

Usage

ref.analysis(
  shape.file,
  X,
  y,
  x.reg.names,
  y.reg.names,
  shp.reg.names = NULL,
  iters = 10000,
  burnin = 5000,
  verbose = TRUE,
  tauc.start = 1,
  beta.start = 1,
  sigma2.start = 1,
  step.tauc = 0.5,
  step.sigma2 = 0.5
)

Arguments

shape.file

A shapefile corresponding to the regions for analysis.

X

A matrix of covariates, which should include a column of 1's for models with a non-zero intercept

y

A vector of responses.

x.reg.names

A vector specifying the order of region names contained in X.

y.reg.names

A vector specifying the order of region names contained in y.

shp.reg.names

A vector specifying the order of region names contained in the shapefile, if there is not a NAME column in the file.

iters

Number of MCMC iterations to perform. Defaults to 10,000.

burnin

Number of MCMC iterations to discard as burn-in. Defaults to 5,000.

verbose

If FALSE, MCMC progress is not printed.

tauc.start

Starting MCMC value for the spatial dependence parameter.

beta.start

Starting MCMC value for the fixed effect regression coefficients.

sigma2.start

Starting MCMC value for the variance of the unstructured random effects.

step.tauc

Step size for the spatial dependence parameter.

step.sigma2

Step size for the variance of the unstructured random effects.

Value

A list containing H, MCMC chains, parameter summaries, fitted regional values, and regional summaries.

H

The neighborhood matrix.

MCMC

Matrix of MCMC chains for all model parameters.

beta.median

Posterior medians of the fixed effect regression coefficients.

beta.hpd

Highest Posterior Density intervals for the fixed effect regression coefficients.

tauc.median

Posterior median of the spatial dependence parameter.

tauc.hpd

Highest Posterior Density interval for the spatial dependence parameter.

sigma2.median

Posterior median of the unstructured random effects variance.

sigma2.hpd

Highest Posterior Density interval for the unstructured random effects variance.

tauc.accept

Final acceptance rate for the spatial dependence parameter.

sigma2.accept

Final acceptance rate for the unstructured random effects variance.

fit.dist

Matrix of fitted posterior values for each region in the data.

reg.medians

Vector of posterior medians for fitted response by region.

reg.hpd

Data frame of Highest Posterior Density intervals by region.

Author(s)

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

Examples

## Refer to the vignette attached to the package.