Spatial Statistics Software, Spatial Data, and Articles
Historically, it has been difficult to apply spatial statistics to large datasets (e.g., more than 5,000 observations). This site contains free spatial software written in Matlab (Matlab Spatial Statistics Toolbox 1.1) capable of estimating very large spatial autoregressions (e.g., one example involves 500,000 observations). The spatial software uses sparse matrix methods to compute the matrix determinants employed in the maximum likelihood estimation of the spatial autoregressions. Specifically, the software can estimate simultaneous spatial autoregressions (SAR), conditional spatial autoregressions (CAR), mixed regressive spatially autoregressive (MRSA) estimates as well as other lattice models which are the mainstay of spatial econometrics.
Version 1.1 adds maximum likelihood estimation of spatial autoregressions which uses only nearest neighbor spatial dependence. This special case results in a closed-form for the matrix determinant and also for the log-likelihood. Naturally, this special case lends itself to computational speed. For example, for 500,000 observations one can find the nearest neighbors and compute the maximum likelihood estimates in under 3.5 minutes on a Pentium III 500! Details appear in a forthcoming Geographical Analysis article (also found on the site).
The site also contains a variant of the Spatial Statistics Toolbox written in Fortran 90 (SpaceStatPack 1.0), spatial data, spatial articles, an anonymous FTP directory, and links to various sites having spatial statistics content.
The massive amounts of real estate data generated each year provide a major impetus to developing computationally efficient spatial statistical estimators. Both hedonic pricing models (HPM) and automated valuation models (AVM) rely upon such real estate data. Application of OLS to such data often produces residuals displaying large amounts of spatial autocorrelation. Estimation of the spatial autoregressions, however, usually produces much more accurate predictions and nicer residuals.
New (1/6/00) — the software page also contains a trial zip file containing the documentation, function, and example programs pertaining to the Monte Carlo log-determinant estimator described in:
Barry, Ronald, and R. Kelley Pace, "A Monte Carlo Estimator of the Log Determinant of Large Sparse Matrices," Linear Algebra and its Applications, Volume 289, Number 1-3, 1999, p. 41-54.
I will add this to the toolbox along with some other functions sometime soon.
New (2/11/00) — I have added a mirror site at ftp.spatiotemporal.com as well as the one on this server, ftp.spatial-statistics.com . If one seems slow, try the other.
Spatial Statistics Software and Spatial Data
Kelley Pace Contact Information and Vita
Real Estate Applications of Spatial Statistics at LSU site
