Combinatorial procedures for the analysis of alternate models: An example from interregional migration

In this paper we present a methodology for comparing the adequacy of two or more models in terms of how well they represent a given data set. A set of interregional migration models is tested, including several variations of push-pull models, Wilson's entropy maximizing model, a quadratic programming solution, and and ANOVA model. Testing is undertaken using a heuristic procedure based on a pair by pair comparison of models to see which one best represents migration flows as estimated by the Census Bureau. The results of the pairwise testing are presented visually in a “matrix map” which allows us to illustrate the degree to which a perfect ordering of the comparison indices exists, and the degree to which individual models cluster together.