MONTE-CARLO EXACT CONDITIONAL TESTS FOR LOG-LINEAR AND LOGISTIC-MODELS

The form of the exact conditional distribution of a sufficient statist ic for the interest parameters, given a sufficient statistic for the n uisance parameters, is derived for a generalized linear model with can onical link. General results for log-linear and logistic models are gi ven. A Gibbs sampling approach for generating from the conditional dis tribution is proposed, which enables Monte Carlo exact conditional tes ts to be performed. Examples include tests for goodness of fit of the all-two-way interaction model for a 2(8)-table and of a simple logisti c model. Tests against non-saturated alternatives are also considered.