University of Washington - Statistics
Advisors: Thomas Richardson & Tamas Rudas
Contingency tables, as frequency distributions on the Cartesian product of the domains of marginals in the table, are a traditional way of representing categorical data. However, when a sample space is a proper subset of the Cartesian product, not all modeling techniques and inference results apply. The relational models we propose is a general class of multiplicative models that are entirely coordinate-free and apply equally well to both situations. A relational model is generated by a class of subsets of cells, some of which may not be induced by marginals of the table, and, under the model, every cell probability is the product of effects associated with subsets the cell belongs to.
We show that the relational models generalize, among others, log-linear models, quasi models (Goodman 1968, 1972), topological models (Hauser 1978). We proceed with discussing the properties of the maximum likelihood estimators in different subclasses of the relational models. Finally, we use our framework to address the question of whether British social mobility is declining and compare the patterns of occupational mobility in Great Britain in 1991 and 2005.