A probability analysis of some spatial interaction models

This paper derives several well-known spatial models in a framework based upon the laws of conditional probability analysis. In particular, it relates the structure of some existing models of trip distribution, elementary residential location and residential location with capacity constraints, to either the multinomial or hypergeometric probability distributions. The major changes from traditional methods for developing these models deal with the derivation and form of the objective function for each interaction model. This alternative analysis reaches a wider audience than that only familiar with entropy methods and leads to several improvements in generality. Further, when population constraints were imposed on residential location models, it was found that the model which developed naturally from the approach taken in the paper contained as a special case the model proposed by Dacey and Norcliffe and not the Wilson model.