Bayesian
model comparison for the order restricted RC association model
G. Iliopoulos, M.Kateri and I. Ntzoufras
Association
models constitute an attractive alternative to the usual log-linear models for
modeling the dependence between classification variables. They impose special
structure on the underlying association by assigning scores on the levels of
each classification variable, which can be fixed or parametric. Under the
general row-column (RC) association model, both row and column scores are
unknown parameters without any restriction concerning their ordinality.
However, when the classification variables are ordinal, order restrictions on
the scores arise naturally. Under such restrictions, we adopt an alternative
parameterization and draw inferences about the equality of adjacent scores
using the Bayesian approach. To achieve that, we have constructed a reversible
jump Markov chain Monte Carlo algorithm for moving across models of different
dimension and estimate accurately the posterior model probabilities which can
be used either for model comparison or for model averaging. The proposed
methodology is evaluated through a simulation study and illustrated using
actual datasets.
Key words and phrases: Contingency tables,
ordinal variables, Reversible jump MCMC algorithm, Equality of Odds, Bayesian
model averaging.
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