Spatial Structure, Spatial Interaction, and Distance-Decay Parameters

Abstract

<p>One result of calibrating a spatial interaction model using interaction data specific to an origin i is to produce an estimate of the distance-decay parameter specific to that origin (βᵢ). A correct interpretation of βᵢ is important since it is frequently used as a descriptive statistic of the spatial system under investigation and as a parameter for predicting unknown interactions.</p> <p>The traditional and still commonly-accepted interpretation of βᵢ is that it is a purely behavioural measure of the relationship between distance and interaction from an origin, ceteris paribus. The distance-decay parameter is assumed to measure the rate of decline of interaction between centres as the distance separating the centres increases. However, when a set of origin-specific, distance-decay parameters, {βᵢ}, is mapped, there is usually a marked spatial pattern to the values; accessible origins have less-negative values while inaccessible origins have more-negative values. As a result, several studies have recently attempted to reinterpret βᵢ in terms of the spatial structure of the system under investigation. These attempts have not gained general acceptance, however, and no sound theory has been posited to explain how spatial structure can determine βᵢ.</p> <p>This thesis demonstrates that a strong relationship between spatial structure and βᵢ exists and that the present interpretation of such parameters is wrong. Spatial structure can determine βᵢ in two ways: one is a calibration-specific effect (to which existing literature has unsuccessfully alluded) and the second is a calibration-independent effect which until now has been unrecoginized. The former results from multicollinearity in unconstrained interaction models and from the presence of balancing factors in constrained interaction models. The latter is a result of model mis-specification: the accessibility of a destination is shown to be an important explanatory variable of the volume of interaction into the destination. Theoretical and empirical evidence is given that the more accessible is a destination to other destinations, the less attractive it is for interaction, ceteris paribus. This relationship is not measured in present spatial interaction models and when it is, the exaggerated spatial variation of distance-decay parameters disappears and the parameters can be interpreted as purely behavioural measures. When the effect of spatial structure is not taken into account, βᵢ is shown to be primarily an index of accessibility and not a behavioural parameter.</p> <p>Thus, current spatial interaction models are mis-specified. A new type of spatial interaction model is presented which is correctly specified and which removes the spatial structure bias from distance-decay parameter estimates.</p>