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Abstract:
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It is well-known that standard chi-squared asymptotic approximations for assessing the fit of a log-linear model to a sparse contingency table can be very misleading. An alternative is to assess the fit based on the conditional distribution of the table, given the sufficient statistics. Because this distribution does not involve any unknowns, it is possible---in principle---to construct an exact test for lack-of-fit. In practice, the support of the conditional distribution can be so large or complicated as to make exact computation infeasible. In many of these cases, Monte Carlo approximation algorithms have been developed that render 'essentially' exact inferences. In this paper, we show exact calculation is possible for some models that were previously thought to be intractable. Moreover, the exact calculations are sometimes actually faster than competing Monte Carlo approximations.
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