|
|
|
Spatial Statistics Software Historically, it has been difficult to apply spatial statistics to large datasets (e.g., more than 10,000 observations). This site contains public domain spatial software written in Matlab (Matlab Spatial Statistics Toolbox 2.0) capable of estimating very large spatial autoregressions (e.g., one example involves 1,000,000 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 contained routines for specifying dependence via nearest neighbors or contiguity, exact log-determinant computations, and closed form maximum likelihood estimation of closest neighbor dependence. Relative to version 1.1, version 2.0 adds spatiotemporal routines, multivariate dependence, matrix exponential spatial specifications, doubly stochastic weight matrices, spatial autoregessive local estimation, and a couple of log-determinant approximations. To give an idea of the performance, finding the contiguous observations and forming a weight matrix takes 130 seconds for 1,000,000 observations, simulating a spatially dependent random variable takes 60 seconds, and estimating a spatial autoregression using this variate takes 20 seconds (times on a 1700 Athlon). The spatial autoregressive local estimation example estimates a sequence of 150 spatial autoregressions around each of 3,107 observations in under two minutes. This routine provides a way of estimating spatially varying parameters with spatial dependence as well. The Spatial Statistics Manuscripts section contains several manuscripts. One discusses the use of doubly stochastic weight matrices to yield both semiparametric and autoregressive interpretations from the same estimator. One provides a closed-form solution to the spatial maximum likelihood estimates. A spatial autoregression using 57,647 observations takes under one second to run on an PC (after loading neighbors and data). Fortran 90 source and executable code as well as data are available. One employs MCMC and matrix exponentials to provide fast inference. The Spatial Statistics Articles section contains a number of articles using some of the techniques in the toolbox. The site also contains a variant of the Spatial Statistics Toolbox written in Fortran 90 (SpaceStatPack 1.0), links to a Fortran 90 program I wrote to find the spatially nearest neighbors to prior observations for spatial-temporal estimation, spatial data, spatial statistical articles, 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 and automated valuation models 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 more accurate predictions.
Conference on Spatial and Spatiotemporal Econometrics (held at LSU on November 7-9, 2003) Spatial Statistics Software and Spatial Data Spatial Statistics Manuscripts Search Spatial-Statistics.com for terms of interest Real Estate Applications of Spatial Statistics at LSU site Comments? — Click here to send me an email
Contact Information: LREC Endowed Chair of Real Estate
Some of the material in this site is based upon work supported by the National Science Foundation under Grant No. BSC-0136229. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).
|