Boundary problem (spatial analysis): Difference between revisions

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As alternatives to operational solutions, Griffith examined three correction techniques (i.e., ''statistical solutions'') in removing boundary-induced bias from inference.<ref name="Griffith83"/> They are (1) based on [[generalized least squares]] theory, (2) using dummy variables and a regression structure (as a way of creating a buffer zone), and (3) regarding the boundary problem as a missing values problem. However, these techniques require rather strict assumptions about the process of interest.<ref>Yoo, E.-H. and Kyriakidis, P. C. (2008) Area-to-point prediction under boundary conditions. Geographical Analysis 40, 355–379.</ref> For example, the solution according to the generalized least squares theory utilizes time-series modeling that needs an arbitrary transformation matrix to fit the multidirectional dependencies and multiple boundary units found in geographical data.<ref name=Griffith80/> Martin also argued that some of the underlying assumptions of the statistical techniques are unrealistic or unreasonably strict.<ref>Martin, R. J. (1989) The role of spatial statistical processes in geographic modeling. In D. A. Griffith (ed) Spatial Statistics: Past, Present, and Future. Institute of Mathematical Geography: Syracuse, NY, pp.&nbsp;107–129.</ref> Moreover, Griffith (1985) himself also identified the inferiority of the techniques through simulation analysis.<ref>Griffith, D. A. (1985) An evaluation of correction techniques for boundary effects in spatial statistical analysis: contemporary methods. Geographical Analysis 17, 81–88.</ref>

As particularly applicable using GIS technologies,<ref>Haslett, J., Wills, G., and Unwin, A. (1990) SPIDER: an interactive statistical tool for the analysis of spatially distributed data. International Journal of Geographical Information Systems 3, 285–296.</ref><ref>Openshaw, S., Charlton, M., and Wymer, C. (1987) A mark I geographical analysis machine for the automated analysis of point pattern data. International Journal of Geographical Information Systems 1, 335–350.</ref> a possible solution for addressing both edge and shape effects is to an re-estimation of the spatial or process under repeated random realizations of the boundary. This solution provides an experimental distribution that can be subjected to statistical tests.<ref name=Fotheringham93/> As such, thisThis strategy examines the sensitivity in the estimation result according to changes in the boundary assumptions. With GIS tools, boundaries can be systematically manipulated. The tools then conduct the measurement and analysis of the spatial process in such differentiated boundaries. Accordingly, suchSuch a [[sensitivity analysis]] allows the evaluation of the reliability and robustness of place-based measures that are defined within artificial boundaries.<ref>BESR (2002) Community and Quality of Life: Data Needs for Informed Decision Making. Board on Earth Sciences and Resources: Washington, DC.</ref> In the meantime,{{Cclarify}} the changes in the boundary assumptions refer not only to altering or tilting the angles of the boundary, but also differentiating between the boundary and interior areas in examination and considering a possibility that isolated data collection points close to the boundary may show large variances.

== See also ==