Computing the J acobian in G aussian Spatial Autoregressive Models: An Illustrated Comparison of Available Methods

作者：Roger Bivand, Jan Hauke, Tomasz M. Kossowski · 发表于：Geographical Analysis · 年份：2013 · DOI：10.1111/gean.12008 · 被引用次数：370 · 研究领域：Spatial and Panel Data Analysis、Economic and Environmental Valuation、Regional Economic and Spatial Analysis

When estimating spatial regression models by maximum likelihood using spatial weights matrices to represent spatial processes, computing the J acobian, ln(| I − λ W |), remains a central problem. In principle, and for smaller data sets, the use of the eigenvalues of the spatial weights matrix provides a very rapid resolution. Analytical eigenvalues are available for large regular grids. For larger problems not on regular grids, including those induced in spatial panel and dyadic (network) problems, solving the eigenproblem may not be feasible, and a number of alternatives have been proposed. This article surveys selected alternatives, and comments on their relative usefulness, covering sparse C holesky and sparse LU factorizations, and approximations such as M onte C arlo, C hebyshev, and using lower‐order moments with interpolation. The results are presented in terms of component‐wise differences between sets of J acobians for selected data sets. In conclusion, recommendations are made for a number of analytical settings. Al estimar modelos de regresión espacial con el método del máxima verosimilitud (máximum likelihood) y usando matrices de pesos espaciales para representar procesos espaciales, cálculo del término jacobiano ( jabobian) —ln(| I −λ W |)‐ sigue siendo un problema central. En principio, y para bases de datos más pequeñas, el uso de los valores propios ( eigenvalues) de la matriz de pesos espaciales proporciona una solución muy rápida. Los eigenvalues analíticos...