Revisiting the Boston Data Set (Harrison and Rubinfeld, 1978): A Case Study in the Challenges of System Articulation

Bivand, Roger

doi:10.2139/ssrn.2719454

Cited by 1 publication

(2 citation statements)

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“…33 In this enlarged map it can also be seen that a number of census tracts are missing (including downtown Boston itself). As noted by Bivand (2015), this is in part due to missing data or to small number of housing units in these tracts. regression estimates and significance levels for each variable obtained by both Pace-Gilley and Deng in panel (a).…”

Section: Global Predictions and Variable Relevancementioning

confidence: 99%

“…Recall that for VLS, such identification is in terms of variable inclusion probabilities (VIP). In Table 5.1 below, we compare these VIPs in panel (b) [using both SPB and MAP] with the spatial 29 As discussed in Bivand (2015), this NOX data is based on measurements in 122 meteorological (TASSIM) zones that were in turn "copied out" to more aggregate collections of census tracts. 30 In ArcMap, for example, the condition-number restrictions mentioned in Section 4.1 above only allow GWR to be run with small subsets of the Boston variables.…”

Section: Global Predictions and Variable Relevancementioning

confidence: 99%

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Local Marginal Analysis of Spatial Data: A Gaussian Process Regression Approach with Bayesian Model and Kernel Averaging

Dearmon¹,

Smith²

2016

Spatial Econometrics: Qualitative and Limited Dependent Variables

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Statistical methods of spatial analysis are often successful at either prediction or explanation, but not necessarily both. In a recent paper, Dearmon and Smith (2015) showed that by combining Gaussian Process Regression (GPR) with Bayesian Model Averaging (BMA), a modeling framework could be developed in which both needs are addressed. In particular, the smoothness properties of GPR together with the robustness of BMA allow local spatial analyses of individual variable effects that yield remarkably stable results. However, this GPR-BMA approach is not without its limitations. In particular, the standard (isotropic) covariance kernel of GPR treats all explanatory variables in a symmetric way that limits the analysis of their individual effects. Here we extend this approach by introducing a mixture of kernels (both isotropic and anisotropic) which allow different length scales for each variable. To do so in a computationally efficient manner, we also explore a number of Bayes-factor approximations that avoid the need for costly reversible-jump Monte Carlo methods. To demonstrate the effectiveness of this Variable Length Scale (VLS) model in terms of both predictions and local marginal analyses, we employ selected simulations to compare VLS with Geographically Weighted Regression (GWR), which is currently the most popular method for such spatial modeling. In addition, we employ the classical Boston Housing data to compare VLS not only with GWR, but also with other well-known spatial regression models that have been applied to this same data. Our main results are to show that VLS not only compares favorably with spatial regression at the aggregate level, but is also far more accurate than GWR at the local level. * The authors are grateful to Kelley Pace, James LeSage, Chandra Bhat and an anonymous referee for their constructive comments on an earlier version of this paper.

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Section: Global Predictions and Variable Relevancementioning

confidence: 99%

Section: Global Predictions and Variable Relevancementioning

confidence: 99%