logdetPaceBarry {estimateW}

Pace and Barry's log determinant approximation

Description

Bayesian estimates of parameters of SAR and SDM type spatial models require the computation of the log-determinant of positive-definite spatial projection matrices of the form (I_n - \rho W), where W is a n by n spatial weight matrix. However, direct computation of the log-determinant is computationally expensive.

Usage

logdetPaceBarry(W, length.out = 200, rmin = -1, rmax = 1)

Arguments

W

numeric n by n non-negative spatial weights matrix, with zeros on the main diagonal.

length.out

single, integer number, has to be at least 51 (due to order of approximation). Sets how fine the grid approximation is. Default value is 200.

rmin

single number between -1 and 1. Sets the minimum value of the spatial autoregressive parameter \rho. Has to be lower than rmax. Default value is -1.

rmax

single number between -1 and 1. Sets the maximum value of the spatial autoregressive parameter \rho. Has to be higher than rmin. Default value is 1.

Details

This function wraps the log-determinant approximation by Barry and Pace (1999), which can be used to precompute the log-determinants over a grid of \rho values.

Value

numeric length.out by 2 matrix; the first column contains the approximated log-determinants the second column the \rho values ranging between rmin and rmax.

References

Barry, R. P., and Pace, R. K. (1999) Monte Carlo estimates of the log determinant of large sparse matrices. Linear Algebra and its applications, 289(1-3), 41-54.