The analysis of some contingency tables is based on hierarchical log linear models. Inferences about sets of parameters can then be made from conditional distributions. We discuss three ways of improving the asymptotic methods generally used in practice. They comprise (i) better approximations to moments of cell frequencies than those derived from the iterative scaling procedure, (ii) exact distributions obtained by enumerating all tables consistent with given marginal totals, and (iii) simulated random sampling for tables where exact enumeration is impossible.
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Cox et al. (1980) studied this question.
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