W_sampler {estimateW}

An R6 class for sampling the elements of W

Description

An R6 class for sampling the elements of W

An R6 class for sampling the elements of W

Format

An R6Class generator object

Details

This class samples the spatial weight matrix. Use the function W_priors class for setup.

The sampling procedure relies on conditional Bernoulli posteriors outlined in Krisztin and Piribauer (2022).

Public fields

W_prior

The current W_priors

curr_w

numeric, non-negative n by n spatial weight matrix with zeros on the main diagonal. Depending on the W_priors settings can be symmetric and/or row-standardized.

curr_W

binary n by n spatial connectivity matrix \Omega

curr_A

The current spatial projection matrix I - \rho W.

curr_AI

The inverse of curr_A

curr_logdet

The current log-determinant of curr_A

curr_rho

single number between -1 and 1 or NULL, depending on whether the sampler updates the spatial autoregressive parameter \rho. Set while invoking initialize or using the function set_rho.

Methods

Public methods

• W_sampler$new()

• W_sampler$set_rho()

• W_sampler$sample()

Method new()

Usage

W_sampler$new(W_prior, curr_rho = NULL)

Arguments

W_prior

The list returned by W_priors

curr_rho

optional single number between -1 and 1. Value of the spatial autoregressive parameter \rho. Defaults to NULL, in which case no updates of the log-determinant, the spatial projection matrix, and its inverse are carried out.

Method set_rho()

If the spatial autoregressive parameter \rho is updated during the sampling procedure the log determinant, the spatial projection matrix I - \rho W and it's inverse must be updated. This function should be used for a consistent update. At least the new scalar value for \rho must be supplied.

Usage

W_sampler$set_rho(new_rho, newLogdet = NULL, newA = NULL, newAI = NULL)

Arguments

new_rho

single, number; must be between -1 and 1.

newLogdet

An optional value for the log determinant corresponding to newW and curr_rho

newA

An optional value for the spatial projection matrix using newW and curr_rho

newAI

An optional value for the matrix inverse of newA

Method sample()

Usage

W_sampler$sample(Y, curr_sigma, mu, lag_mu = matrix(0, nrow(tY), ncol(tY)))

Arguments

Y

The n by tt matrix of responses

curr_sigma

The variance parameter \sigma^2

mu

The n by tt matrix of means.

lag_mu

n by tt matrix of means that will be spatially lagged with the estimated W. Defaults to a matrix with zero elements.

References

Krisztin, T., and Piribauer, P. (2022) A Bayesian approach for the estimation of weight matrices in spatial autoregressive models. Spatial Economic Analysis, 1-20.