Spatial context effects at different scales: A formal model for egocentric contexts in two- and three-dimensional space

Spatial context effects are a topic in many scientific disciplines. This paper examines which conceptual steps are necessary for determining the extension, or the appropriate scale, of relevant spatial environments when contexts can be analytically disaggregated into context elements. Adequate models of scale need to specify not only the distance-dependent relevance of context elements but also their distribution and an adequate combination. In this way, it becomes possible to understand why non-monotonic patterns in scale-related context effects have been repeatedly found in spite of common assumptions of distance decay in relevance. In many cases, a distance-related maximum of (aggregate) context relevance can be expected, so that there is an “optimal” range for the measurement of context effects. It is also important to distinguish between applications in two- and three-dimensional space. This general model helps to specify the steps necessary for the determination of spatial context patterns and to identify unrealistic assumptions.