Performing large spatial regressions and autoregressions

Abstract For most spatial data, estimated errors under OLS do not appear identically and independently distributed across locations. While the existence of such non-i.i.d. errors seems widely known, this knowledge has not often been reflected in empirical practice, even though incorporating information about the spatial structure can greatly reduce prediction errors and lead to more efficient parameter estimation. The great expense of computing spatial estimates in both time and storage space accounts for at least some of their lack of use. However, employing sparse matrix technique:; can greatly ameliorate both of these problems. As an example of these techniques, the paper contains an example of a maximum likelihood spatial regression with 56 variables and 3109 observations which required fewer than 30 seconds to compute, despite the need to repeatedly evaluate the determinant of a 3109 by 3109 matrix.