Michael Tiefelsdorf

Multicollinearity and correlation among local regression coefficients in geographically weighted regression

Present methodological research on geographically weighted regression (GWR) focuses primarily on extensions of the basic GWR model, while ignoring well-established diagnostics tests commonly used in standard global regression analysis. This paper investigates multicollinearity issues surrounding the local GWR coefficients at a single location and the overall correlation between GWR coefficients associated with two different exogenous variables. Results indicate that the local regression coefficients are potentially collinear even if the underlying exogenous variables in the data generating process are uncorrelated. Based on these findings, applied GWR research should practice caution in substantively interpreting the spatial patterns of local GWR coefficients. An empirical disease-mapping example is used to motivate the GWR multicollinearity problem. Controlled experiments are performed to systematically explore coefficient dependency issues in GWR. These experiments specify global models that use eigenvectors from a spatial link matrix as exogenous variables.

Semiparametric Filtering of Spatial Autocorrelation: The Eigenvector Approach

In the context of spatial regression analysis, several methods can be used to control for the statistical effects of spatial dependencies among observations. Maximum likelihood or Bayesian approaches account for spatial dependencies in a parametric framework, whereas recent spatial filtering approaches focus on nonparametrically removing spatial autocorrelation. In this paper we propose a semiparametric spatial filtering approach that allows researchers to deal explicitly with (a) spatially lagged autoregressive models and (b) simultaneous autoregressive spatial models. As in one non-parametric spatial filtering approach, a specific subset of eigenvectors from a transformed spatial link matrix is used to capture dependencies among the disturbances of a spatial regression model. However, the optimal subset in the proposed filtering model is identified more intuitively by an objective function that minimizes spatial autocorrelation rather than maximizes a model fit. The proposed objective function has the advantage that it leads to a robust and smaller subset of selected eigenvectors. An application of the proposed eigenvector spatial filtering approach, which uses a cancer mortality dataset for the 508 US State Economic Areas, demonstrates its feasibility, flexibility, and simplicity.

The Use of Spatial Filtering Techniques: The Spatial and Space-Time Structure of German Unemployment Data

Socio-economic interrelationships among regions can be measured in terms of economic flows, migration, or physical geographically-based measures, such as distance or length of shared areal unit boundaries. In general, proximity and openness tend to favour a similar economic performance among adjacent regions. Therefore, proper forecasting of socio-economic variables, such as employment, requires an understanding of spatial (or spatio-temporal) autocorrelation effects associated with a particular geographic configuration of a system of regions. Several spatial econometric techniques have been developed in recent years to identify spatial interaction effects within a parametric framework. Alternatively, newly devised spatial filtering techniques aim to achieve this end as well through the use of a semi-parametric approach. Experiments presented in this paper deal with the analysis of and accounting for spatial autocorrelation by means of spatial filtering t! echniques for data pertaining to regional unemployment in Germany. The available data set comprises information about the share of unemployed workers in 439 German districts (the NUTS-III regional aggregation level). Results based upon an eigenvector spatial filter model formulation (that is, the use of orthogonal map pattern components), constructed for the 439 German districts, are presented, with an emphasis on their consistency over several years. Insights obtained by applying spatial filtering to the database are also discussed.

A Variance-Stabilizing Transformation to Mitigate Biased Variogram Estimation in Heterogeneous Surfaces with Clustered Samples

Due to the inherent variance heterogeneity in clustered preferential sampling, the underlying variogram cannot be estimated directly. A variance-stabilizing declustering method is proposed here using a modified Box–Cox transformation. In contrast to the traditional Box–Cox transformation that aims at achieving normally distributed data, its modified version has the objective to match the variance in clustered sample observations to the variance of the remaining more dispersed background sample observations. The proposed approach leads to predictions with lower standard errors than alternative proposed methods.