Computing the Jacobian in Gaussian Spatial Autoregressive Models: An Illustrated Comparison of Available Methods
Journal article, Peer reviewed
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OriginalversjonGeographical Analysis 2013, 45(2):150-179 10.1111/gean.12008
When estimating spatial regression models by maximum likelihood using spatial weights matrices to represent spatial processes, computing the Jacobian, ln(|I - lW|), 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 Cholesky and sparse LU factorizations, and approximations such as Monte Carlo, Chebyshev, and using lower-order moments with interpolation. The results are presented in terms of componentwise differences between sets of Jacobians for selected data sets. In conclusion, recommendations are made for a number of analytical settings.
This is the accepted version of the following article:Computing the Jacobian in Gaussian Spatial Autoregressive Models: An Illustrated Comparison of Available Methods,Geographical Analysis 2013, 45(2):150-179, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/gean.12008/abstract. © 2013 The Ohio State University