A Structural Model of the Mobility Table

We propose a multiplicative (log-linear) model for mobility tables (or other cross-classifications) which is helpful in locating cells where counts are especially dense or sparse. This specification eliminates the confounding of main effects and interaction effects, which has plagued many other methods of measuring and interpreting association in mobility tables, especially those methods based on the model of simple statistical independence. The model yields a parsimonious set of parameters which describe the table, and goodness of fit can be assessed with standard inferential procedures. For each cell of the table the model yields a useful measure of association, which we call the new mobility ratio. We illustrate the model by reanalyzing the classic British mobility table of 1949, and we use that example to compare our measure of association with other mobility measures.