Boundary problem (spatial analysis)

A boundary problem in analysis is a phenomenon in which geographical patterns are differentiated by the shape and arrangement of boundaries that are drawn for administrative or measurement purposes. The boundary problem occurs because of the loss of neighbors in analyses that depend on the values of the neighbors. While geographic phenomena are measured and analyzed within a specific unit, identical spatial data can appear either dispersed or clustered depending on the boundary placed around the data. In analysis with point data, dispersion is evaluated as dependent of the boundary. In analysis with areal data, statistics should be interpreted based upon the boundary. In spatial analysis, four major problems interfere with an accurate estimation of the statistical parameter: the boundary problem, scale problem, pattern problem (or spatial autocorrelation), and modifiable areal unit problem. The boundary problem occurs because of the loss of neighbours in analyses that depend on the values of the neighbours. While geographic phenomena are measured and analyzed within a specific unit, identical spatial data can appear either dispersed or clustered depending on the boundary placed around the data. In analysis with point data, dispersion is evaluated as dependent of the boundary. In analysis with area data, statistics should be interpreted based upon the boundary. In geographical research, two types of areas are taken into consideration in relation to the boundary: an area surrounded by fixed natural boundaries (e.g., coastlines or streams), outside of which neighbours do not exist, or an area included in a larger region defined by arbitrary artificial boundaries (e.g., an air pollution boundary in modeling studies or an urban boundary in population migration). In an area isolated by the natural boundaries, the spatial process discontinues at the boundaries. In contrast, if a study area is delineated by the artificial boundaries, the process continues beyond the area.