EXPLORING SPATIOTEMPORALLY VARYING REGRESSED RELATIONSHIPS: THE GEOGRAPHICALLY WEIGHTED PANEL REGRESSION ANALYSIS Danlin Yu Department of Earth and Environmental Studies, Montclair State University, Montclair, NJ, 07043 yud@mail.montclair.edu KEY WORDS: Geographic information; spatiotemporal variation of relationships; geographically weighted panel regression; Greater Beijing Area, China ABSTRACT: Regression analysis with geographic information needs to take into consideration the inherent spatial autocorrelation and heterogeneity of the data. Due to such spatial effects, it is found that local regression such as the geographically weighted regression (GWR) tends to capture the relationships better. In addition, in panel data analysis, the variable coefficient panel regression can borrow such ideas of spatial autocorrelation and heterogeneity to develop models that would fit the data better and produce more accurate results than the pooled models. Despite the fact that both methods are well developed and utilized, models that take advantage of both methods simultaneously have eluded the research community. Combination of GWR and panel data analysis techniques has an obvious benefit: the added temporal dimension enlarges the sample size hence contains more degrees of freedom, adds more variability, renders less collinearity among the variables, and gives more efficiency for estimation. This research for the first time attempts such combination using a short regional development panel data from 1995 – 2001 of the Greater Beijing Area (GBA), China. A geographically weighted panel regression (GWPR) model is developed and compared with both cross-sectional GWR and panel regression. The study reveals very promising results that the GWPR indeed produced better and clearer results than both cross-sectional GWR and the panel data model. This indicates the new method would potentially produce substantial new patterns and new findings that cannot be revealed via pure cross-sectional or time-series analysis. 1. INTRODUCTION Geographically weighted regression (GWR) and panel data analysis are well developed data analytical methodologies in geography and econometrics. Recognizing the fundamental question in social science that social processes are not likely governed by any universal “laws”, but might vary depending on where the processes are investigated, Fotheringham and colleagues (2002) proposed the geographically weighted regression to address this “spatial non- stationarity” issue (Fotheringham et al. 2002, p 9). Panel data analysis, on the other hand, has received increasing interests in econometrics due to its obvious advantages over conventional cross- sectional or time-series data analysis techniques and increasingly available panel datasets (Hsiao 2003; Baltagi 2005). The enlarged sample size gives the researcher more degrees of freedom, reduces the collinearity among explanatory variables hence improves the efficiency of econometric estimates. Studies on both fields have yielded fantastic progresses, yet analysis that takes advantages of both methodologies eludes the research community. Two particular reasons would attribute to the lack of such combination. First, geographically weighted regression, as its name suggests, focuses almost entirely on the spatial non-stationarity. The method recognizes that a set of universal coefficients in regression analysis might not be adequate to address the underlying data generating process of the observed geographic dataset. Instead, due either to intrinsic varying mechanisms or potential model misspecification, the regressed relationships are different from location to location. Relationships in regression analysis using geographic information, as evidenced in many a study (Fotheringham et al. 1998; Huang and Leung 2002; Yu and Wu 2004; Yu 2006; Yu et al. 2007), do vary in geographic space. It is only very recently, however, that scholars start to explore the possibility that relationships are potentially varying in not only geographic space, but also temporal space (Crespo et al. 2007; Demsar et al. 2008; Yu 2009). Second, panel data analysis has long been regarded as an important analytical technique for econometric analysis. Although panel data analysis that utilizes geographic information is receiving increased attention in the mainstream econometric analysis (Anselin 1988, 2001; Elhorst 2001, 2003; Baltagi 2005; Anselin et al. 2008; Yu 2009; among others), such development focuses primarily on treating geography as an agent for dependence among cross-section observations. It is well known that the effects of geography are twofold – spatial autocorrelation and heterogeneity (Anselin 2001). Anselin et al. (2008) point out that the case of spatial heterogeneity can be handled by means of standard panel analysis methods. As detailed in Hsiao (2003), there is a full set of methods dealing with the so-called “variable-coefficient models” (Hsiao 2003, Ch. 6). While reviewing these well-developed methods, I found they indeed acknowledge the heterogeneous properties of the cross-sectional units. Such treatment, however, doesn’t necessarily reflect the important characteristics of spatial heterogeneity. As argued in Fotheringham et al. (2002), spatial heterogeneity is not like statistical heterogeneity that might follow certain distribution (Fotheringham et al. 2002). Instead, spatial heterogeneity is very much determined by distances. In GWR analysis, the spatial structure that follows the “First Law of Geography” (Tobler 1970) and generates spatial heterogeneity can be well simulated via the distance decaying Gaussian or Gauss-like kernel functions in which distance is the parameter. While in the “variable-coefficient” panel data analysis, such important characteristics of geographic information are barely utilized. It is with this recognition that this proposed research attempts for the first time to combine research merits of both GWR and panel data analysis to produce new geo-panel data analysis methodology. In this particular study, I will utilize a set of regional development panel data from 1995 – 2001 of the Greater Beijing Area (GBA), China to develop such methodology. The results from this geo-panel analysis will be compared to the ones acquired from conventional methods. It is hoped with the new methods, we’ll be able to discover new insights that was previously hidden in the dataset. Such new findings would potentially bring significant new understandings of regional studies in China. The following section will give detailed reviews of the methodological development in spatiotemporal analysis from both geographic and econometric perspectives. This is followed by an introduction to the study region, GBA, China and the data. The fourth section extends the discussion of GWR and panel analysis and elaborates the development of the geographically weighted panel regression (GWPR) and its implementation. Results from applying the methods to the dataset will be reported in the fifth section. The study concludes with summary and future research foci. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. 38, Part II 134