Test-inversion confidence intervals for estimands in contingency tables subject to equality constraints

The construction of test-inversion approximate confidence intervals is explored for estimands in contingency tables subject to equality constraints. Recommended test statistics include the difference in G2 statistic and nested versions of a family of power-divergence statistics. Efficient and robust computational algorithms are proposed. The computational approach herein is applicable for a broadened class of estimands and constraints: (1) Compared with existing standard methods, which are applicable only for likelihood-explicit estimands, our algorithms can also handle likelihood-implicit estimands, where the log-likelihood cannot be reparameterized in terms of the estimand of interest and a collection of nuisance parameters; (2) Only mild conditions on equality constraints are required, and it is unnecessary to re-express the constraints as a generalized linear model. A simulation study highlights the advantages of using likelihood-ratio intervals rather than bootstrap and Wald intervals, especially when cell counts are small and/or the true estimand is close to the boundary. In addition, appropriate loss functions are proposed to investigate efficiency gain upon imposing constraints. Examples are presented to illustrate the appropriateness of imposing constraints and the utility of test-inversion intervals.