Model-based Bayesian methods for estimating cell proportions in cross- classification tables having ordered categories. (English) Zbl 0726.62080
Summary: Bayesian methods are suggested for estimating proportions in the cells of cross-classification tables having at least one classification with ordered categories. These methods utilize models for cell proportions that incorporate the category orderings. The resulting estimators are smoother and can be much more efficient than the sample proportions, yet they are consistent even if the model chosen for the smoothing does not hold. Two approaches are considered:
(1) Bayes estimators using a Dirichlet prior distribution for the proportions; (2) Bayes estimators based on normal prior distributions for association parameters in the saturated loglinear model. In each case, the means of the prior distributions are chosen to satisfy a model for ordered categorical data, such as the uniform association model. Empirical Bayes versions of the two analyses are also given.
(1) Bayes estimators using a Dirichlet prior distribution for the proportions; (2) Bayes estimators based on normal prior distributions for association parameters in the saturated loglinear model. In each case, the means of the prior distributions are chosen to satisfy a model for ordered categorical data, such as the uniform association model. Empirical Bayes versions of the two analyses are also given.
Keywords:
EM algorithm; ordinal variables; smoothing methods; cross-classification tables; ordered categories; cell proportions; Dirichlet prior; normal prior; loglinear model; uniform association model; Empirical BayesReferences:
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