Effects of beta, alpha and lambda on Spatial Interactions

Effects of beta alpha and lambda on Spatial Interactions

Variations of the beta, alpha, and lambda exponents have different impacts on the level of spatial interactions. For instance, the relationship between distance and spatial interactions will change according to the beta exponent. If the value of beta is high (higher than 0.5), the friction of distance will be much more important (steep decline of spatial interactions) than with a low value of beta (e.g. 0.25). A beta of 0 means that distance has no effects and that interactions remain the same, whatever the concerned distance.

Alpha and lambda exponents have the same effect on the interaction level. For a value of 1, there is a linear relationship between population (or any attribute of weight) and the level of interactions. Any value higher than 1 implies exponential growth of the interaction level as the population increases.