Categorical data squashing by combining factor levels
نویسندگان
چکیده
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× 3× 4 contingency table.
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