Summary: Bayesian Testing and Estimation of Association in a TwoWay
James H. Albert
Duke University and Bowling Green State University
March 8, 1996
In a twoway contingency table, one is interested in checking the goodness of fit of simple mod
els such as independence, quasiindependence, symmetry, or constant association, and estimating
parameters which describe the association structure of the table. In a large table, one may be
interested in detecting a few outlying cells which deviate from the main association pattern in the
table. Bayesian tests of the above hypotheses are described using a prior defined on the set of inter
action terms of the loglinear model. These tests and associated estimation procedures have several
advantages over classical fitting/estimation procedures First, the tests above can give measures of
evidence in support of simple hypotheses. Second, the Bayes factors can be used to give estimates
of association parameters of the table which allow for uncertainty that the hypothesized model is
true. These methods are illustrated for a number of tables.
Key words and phrases: Bayes factors, Laplace method, Gibbs sampling, Model selection, Odds
AMS subject classifications: Primary 62H17, 62F15, 62J12.