Model Boosting for Spatial Weighting Matrix Selection in Spatial Lag Models

Abstract

Kostov, Phillip (2010) Model boosting for spatial weighting matrix selection in spatial lag models. Environment and Planning B: Planning and Design, 37 (3). pp. 533 549. ISSN 0265 8135 It is advisable to refer to the publisher's version if you intend to cite from the work. [Kostov, 2010]. This is a postprint of a research article. The definitive, peer-reviewed and edited version of this article is published in Environment and Planning B: Planning and Design, volume 37, issue 3, pages 533-549, 2010, http://dx.doi.org/10.1068/b35137 1 Model boosting for spatial weighting matrix selection in spatial lag models Philip Kostov Lancashire Business School University of Central Lancashire AbstractThe spatial lag specification is often used in spatial econometrics. The choice of an appropriate spatial weighting matrix is an important outstanding methodological problem in the quantitative spatial dependence literature. This paper proposes applying a componentwise model boosting algorithm to deal with the issue of the choice of a spatial weighting matrix amongst a predetermined set of alternatives. The resulting procedure is computationally simple and easy to implement. We present an empirical application of the proposed methodology. Some possible extensions to a more general setting are discussed.

The Biggest Myth in Spatial Econometrics

“…For three of the estimated coefficients, one spatial weight matrix produces results qualitatively different from the others, and, for three more of the estimated coefficients, two spatial weight matrices produce results 6 It is not surprising there are few reports of cases where estimates were found to be sensitive to the choice used by the practitioner.…”

“…Using the relations in Equations (3)-(5), simple expressions exist for covariance in Equation (6) and correlation between W a u, W b u for the case of row-stochastic nearest neighbor matrices W as shown in Equation (7). The simplicity stems from the known common elements in W a and W b which equal m b .…”

“…6 However, this is not the appropriate basis for inference about sensitivity of estimates and inferences from these models, since these should rely on the partial derivatives (or effects estimates). In Section 3.2 we examine an article that is widely cited as a justification for sensitivity of spatial regression estimates to small changes in the weight matrix specification.…”

The impact of weight matrices on parameter estimation and inference: A case study of binary response using land-use data

“…In the application of spatial statistics and spatial econometrics, weight matrices (W=[w i j ]) are crucial components; these represent the underlying spatial interdependence among proximate units, such as the simple inverse of network distances between traffic detectors, contiguity indicators of census tracts across a region, and who qualifies as a Knearest neighbor within a social network. The functional specification of appropriate weight matrices has long proven a controversial topic in spatial econometrics (as discussed in Anselin 1988 andKostov 2010). Nearly all weight matrices are specified a priori, simply as a function of distance or contiguity-raising the question of whether weight-matrix specification carries any important implications for interpretation of model results.…”

“…These sorts of weight matrices were rarely used in practice because of estimation challenges and identification issues. In most applications, the weight matrix is more likely to be based on distance between units, or simply contiguity (Anselin 1988;Anselin 2002;LeSage and Pace 2009;and Kostov 2010).…”