P.Dellaportas C.Tarantola
Quaderni di Dipartimento #153 (03-03)
Dipartimento di economia politica e metodi quantitativi
Università degli studi di Pavia
Abstract
We deal with contingency table data that are
used to examine the relationships between a set of categorical variables or
factors. We assume that such relationships can be adequately described by the
conditional independent structure imposed by an undirected graphical
model. If the contingency table is
large, a desirable simplified interpretation can be achieved by combining some
categories, or levels, of the factors. We introduce conditions under which such
an operation does not alter the Markov properties of the graph. Implementation
of these conditions leads to likelihood ratio tests and Bayesian model
uncertainty procedures based on reversible jump MCMC. The methodology is
illustrated with reference to a 2
x 3 x 4 contingency table.