An importance sampling algorithm for exact conditional tests in log-linearmodels

A simple but quite general simulation method for conducting exact condition al lack-of-fit tests in log-linear models is proposed. Our Monte Carlo appr oximation utilises an importance sampling method motivated by the crude nor mal approximation to the Poisson distribution. Examples considered include tests of quasi-symmetry and related models for square tables and tests conc erning higher-order interactions in multi-way tables. The method is competi tive with direct simulation from the exact conditional distribution when th is is feasible and outperforms alternative Monte Carlo procedures when dire ct simulation is infeasible provided the number of degrees of freedom of th e test is not too large. Extension of the method to tests against non-satur ated alternatives is straightforward and is briefly discussed and illustrat ed.