For example, biodiversity such as the density of species of plants and animals is high near the surface, so if the identically divided height or depth is used as a spatial unit, it is more likely to find fewer number of the plant and animal species as the height or depth increases.
By drawing a boundary around a study area, two types of problems in measurement and analysis takes place.
A typical example is a cross-boundary influence such as cross-border jobs, services and other resources located in a neighbouring municipality.
[17][18][19] For example, the shape can affect the measurement of origin-destination flows since these are often recorded when they cross an artificial boundary.
[21] From the same perspective, Theobald (2001; retrieved from[5]) argued that measures of urban sprawl should consider interdependences and interactions with nearby rural areas.
The problem is noted when the average degree of a variable and its unequal distribution over space are measured.
Its main shortcoming is that empirical phenomena occur within a finite area, so an infinite and homogeneous surface is unrealistic.
[15] The remaining five approaches are similar in that they attempted to produce unbiased parameter estimation, that is, to provide a medium by which the edge effects are removed.
[28] 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.
[14] Martin also argued that some of the underlying assumptions of the statistical techniques are unrealistic or unreasonably strict.
[30] As particularly applicable using GIS technologies,[31][32] 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.
Accordingly, such a sensitivity analysis allows the evaluation of the reliability and robustness of place-based measures that defined within artificial boundaries.