Exact Hypothesis Tests for Log-linear Models with exactLoglinTest

This manuscript overviews exact testing of goodness of fit for log-linear models using the R package exactLoglinTest. This package evaluates model fit for Poisson log-linear models by conditioning on minimal sufficient statistics to remove nuisance parameters. A Monte Carlo algorithm is proposed to estimate P values from the resulting conditional distribution. In particular, this package implements a sequentially rounded normal approximation and importance sampling to approximate probabilities from the conditional distribution. Usually, this results in a high percentage of valid samples. However, in instances where this is not the case, a Metropolis Hastings algorithm can be implemented that makes more localized jumps within the reference set. The manuscript details how some conditional tests for binomial logit models can also be viewed as conditional Poisson log-linear models and hence can be performed via exactLoglinTest. A diverse battery of examples is considered to highlight use, features and extensions of the software. Notably, potential extensions to evaluating disclosure risk are also considered.