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Distance Association Models for the Analysis of Repeated Transition Frequency Tables

The present paper is concerned with the analysis of repeated transition frequency tables, for example, occupational mobility data measured in different cohorts. The association present in such a table will be modeled by a distance in Euclidean space. A large distance corresponds to a small association; a small distance corresponds to a large association. A more direct interpretation is that more transitions occur between categories that are close together in a social space. It is assumed that the same social structure (space) exists for the different slices (cohorts/time points) of a table, but that the dimensions of this space are weighted for the different slices, i.e., for each slice the dimensions are stretched or squeezed. We will propose a model, discuss an algorithm to obtain maximum likelihood estimates and apply the model to an empirical data set.