ref.analysis: MCMC Analysis and Summaries for Reference Prior on an...

In ref.ICAR: Objective Bayes Intrinsic Conditional Autoregressive Model for Areal Data

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 \insertCitekeefe2018ref.ICAR. 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.

ref.ICAR documentation built on Aug. 22, 2023, 9:12 a.m.