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This note shows how some specific models proposed by Duncan (1979), Goodman (1972), Haberman (1974), and Simon (1974), which turn out to be useful for the analysis of occupational mobility tables and other kinds of cross-classification tables, are related to models obtained by applying the general formulations of multiplicative models in Goodman (1972), Darroch and Ratcliff (1972), Darroch and Ratcliff (1972), and Haberman (1974). It also shows how each model can be described in terms of its expected frequencies, or equivalently in terms of its pattern of oddsratios, or equivalently in terms of its pattern of odds. In so doing, it provides (a) further insight into the meaning of some of the specific models, (b) greater flexibility in the possible interpretations of a wide range of potentially useful specific models included within the general class of multiplicative models developed for the analysis of cross-classification tables, and (c) improved methods for estimating the expected frequencies under some of the specific models.
Leo A. Goodman (Mon,) studied this question.