Computation of the Information Matrix for Models With Spatial Interaction on a Lattice
Oleg A. Smirnov · Journal of Computational and Graphical Statistics · 2005
This article demonstrates a fast and practical procedure for the maximum likelihood estimation of models with spatial interaction on a lattice, such as Gaussian Markov random fields (conditional autoregressive models, or CAR) and spatial autoregressive models (SAR). Focusing on the computation of the information matrix, I designed an algorithm for computing the information matrix without storing an inverse of the spatial differencing operator, a large sparse matrix. To accomplish this efficiently, I developed a sparse version of the conjugate gradient method for the case of sparse matrices and sparse vectors. Numerical stability and modest computational requirements of the proposed method make it a viable method for large spatial datasets. Large datasets are becoming fairly popular in spatial statistics, so this method's advantages in accelerating ML estimation and effectively relaxing limitations on the size of data underscore its practicality. I apply the method to the analysis of employment in a spatial economy.