R. Kelley Pace

Spatial Econometric Modeling of Origin-Destination Flows

ABSTRACT Standard spatial autoregressive models rely on spatial weight structures constructed to model dependence among n regions. Ways of parsimoniously modeling the connectivity among the sample of N=n2 origin‐destination (OD) pairs that arise in a closed system of interregional flows has remained a stumbling block. We overcome this problem by proposing spatial weight structures that model dependence among the N OD pairs in a fashion consistent with standard spatial autoregressive models. This results in a family of spatial OD models introduced here that represent an extension of the spatial regression models described in Anselin (1988).

Spatiotemporal Autoregressive Models of Neighborhood Effects

Using 70,822 observations on housing prices from 1969 to 1991 from Fairfax County Virginia, this article demonstrates the substantial benefits obtained by modeling the spatial as well as the temporal dependence of the data. Specifically, the spatiotemporal autoregression with twelve variables reduced median absolute error by 37.35% relative to an indicator-based model with twenty-six variables. One-step ahead forecasts also document the improved performance of the proposed spatiotemporal model. In addition, the article illustrates techniques for rapidly computing the estimates and shows how to compute indices for any location.

Sparse spatial autoregressions

Given local spatial error dependence, one can construct sparse spatial weight matrices. As an illustration of the power of such sparse structures, we computed a simultaneous autoregression using 20 640 observations in under 19 min despite needing to compute a 20 640 by 20 640 determinant 10 times.

Using the Spatial Configuration of the Data to Improve Estimation

Using the well-known Harrison and Rubinfeld (1978) hedonic pricing data, this manuscript demonstrates the substantial benefits obtained by modeling the spatial dependence of the errors. Specifically, the estimated errors on the spatial autoregression fell by 44% relative to OLS. The spatial autoregression corrects predicted values by a nonparametric estimate of the error on nearby observations and thus mimics the behavior of appraisers. The spatial autoregression, by formally incorporating the areal configuration of the data to increase predictive accuracy and estimation efficiency, has great potential in real estate empirical work.

Spatial Autoregression Techniques for Real Estate Data

This paper describes how spatial techniques can be used to improve the accuracy of market value estimates obtained using multiple regression analysis. Rather than eliminating the problem of spatial residual dependencies through the inclusion of many independent variables, spatial statistical methods typically keep fewer independent variables and augment these with a simple model of the spatial error dependence. We discuss alternative spatial autoregression model specifications, estimation methods, and prediction procedures. An empirical example is provided in the appendix.

A method for spatial–temporal forecasting with an application to real estate prices

Abstract Using 5243 housing price observations during 1984–92 from Baton Rouge, this manuscript demonstrates the substantial benefits obtained by modeling the spatial as well as the temporal dependence of the errors. Specifically, the spatial–temporal autoregression with 14 variables produced 46.9% less SSE than a 12-variable regression using simple indicator variables for time. More impressively, the spatial–temporal regression with 14 variables displayed 8% lower SSE than a regression using 211 variables attempting to control for the housing characteristics, time, and space via continuous and indicator variables. One-step ahead forecasts document the utility of the proposed spatial–temporal model. In addition, the manuscript illustrates techniques for rapidly computing the estimates based upon an interesting decomposition for modeling spatial and temporal effects. The decomposition maximizes the use of sparsity in some of the matrices and consequently accelerates computations. In fact, the model uses the frequent transactions in the housing market to help simplify computations. The techniques employed also have applications to other dimensions and metrics.

Monte Carlo estimates of the log determinant of large sparse matrices

Maximum likelihood estimates of parameters of some spatial models require the computation of the log-determinant of positive-definite matrices of the formI —αD. whereD is a large, sparse matrix with eigenvalues in [−1, 1] and where 0<α<1, with extremely large matrices the usual direct methods of obtaining the log-determinant require too much time and memory. We propose a Monte Carlo estimate of the log-determinant. This estimate is simple to program, very sparing in its use of memory, easily computed in parallel and can estimate log det(I-αD) for many values ofα simultaneously Using this estimator, we estimate the log-determinant for a 1,000,000 × 1,000,000 matrixD, for 100 values ofα, in 23.1 min on 133 MHz pentium with 64 MB of memory using Matlab.

Chebyshev approximation of log-determinants of spatial weight matrices

Abstract To cope with the increased sample sizes stemming from geocoding and other technological innovations, this paper introduces an O( n ) approximation to the log-determinant term required for likelihood-based estimation of spatial autoregressive models. It takes as a point of departure Martins (1993) Taylor series approximation based on traces of powers of the spatial weight matrix. Using a Chebyshev approximation along with techniques to efficiently compute the initial matrix power traces results in an extremely fast approximation along with bounds on the true value of the log-determinant. Using this approach, it takes less than a second to compute the approximate log-determinant of an 890,091×890,091 matrix. This represents a tremendous increase in speed relative to exact computation that should allow researchers to explore much larger problems and facilitate spatial specification searches.

Nonparametric methods with applications to hedonic models

Current real estate statistical valuation involves the estimation of parameters within a posited specification. Suchparametric estimation requires judgment concerning model (1) variables; and (2) functional form. In contrast,nonparametric regression estimation requires attention to (1) but permits greatly reduced attention to (2). Parametric estimators functionally model the parameters and variables affectingE(y¦x) while nonparametric estimators directly modelpdf(y, x) and henceE(y¦x).This article applies the kernel nonparametric regression estimator to two different data sets and specifications. The article shows the nonparametric estimator outperforms the standard parametric estimator (OLS) across variable transformations and across data subsets differing in quality. In addition, the article reviews properties of nonparametric estimators, presents the history of nonparametric estimators in real estate, and discusses a representation of the kernel estimator as a nonparametric grid method.

Spatial Econometric Models

Spatial regression models allow us to account for dependence among observations, which often arises when observations are collected from points or regions located in space. The spatial sample of observations being analyzed could come from a number of sources. Examples of point-level observations would be individual homes, firms, or schools. Regional observations could reflect average regional household income, total employment or population levels, tax rates, and soon. Regions often have widely varying spatial scales (for example, European Unionregions, countries, or administrative regions such as postal zones or census tracts).