SIMPLIFYING THE NORMALIZING FACTOR IN SPATIAL AUTOREGRESSIONS FOR IRREGULAR LATTICES

Abstract

ABSTRACT The Jacobian term appears in certain likelihood functions as a normalizing factor; it ensures that the use of variable transformations still leads to probability density functions whose complete integration yields unity. This term is particularly troublesome when dealing with spatial autoregressive models in that it requires numerically intensive solutions to accompanying parameter estimation problems. For these types of autoregressive models, the Jacobian term is a function of the eigenvalues of the n-by n connectivity matrix that depicts the geographic configuration of the areal units under study. This paper reports on Jacobian approximation results, based upon supercomputer and other experiments, for irregular lattices.