Marginal and Conditional Association Models for Analysing Departures from Exchangeability of Tooth Bone Loss

SUMMARY Departures from exchangeability are investigated for binary periodontal disease data collected from a sample of members of the Pima native American community. The analysis of exchangeability conducted by Ten Have and Becker under the conditional association log‐linear model is extended to the conditional and marginal association models under a new set of constraints. Maximum likelihood estimation of log‐linear models is presented for conditional associations, whereas constrained equations maximum likelihood estimation and alternating generalized estimating equations are described for fitting marginal models. In the absence of exchangeability, a set of constraints representing a compromise between unconstrained associations and those satisfying exchangeability is introduced and assessed in terms of both marginal and conditional association models. A comparison of these two classes of model under this set of compromise constraints provides preliminary evidence of a potential pathway of bacteria associated with periodontal disease.