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

• Published in: Applied Statistics 1996-01, Vol.45 (3), p.353-369
• Main Author: Have, Thomas R.Ten
• Format: Article
• Language: English
• Subjects: Alternating logistic regression; Applications; Biology, psychology, social sciences; Bones; Constraint equations maximum likelihood; Data analysis; Degrees of freedom; Dental models; Exact sciences and technology; Generalized estimating equations; Insurance, economics, finance; Linear models; Logit models; Log‐linear models; Mathematics; Matrices; Maximum likelihood estimation; Medical sciences; Modeling; Multivariate analysis; Parametric models; Periodontal diseases; Probability and statistics; Reliability, life testing, quality control; Sciences and techniques of general use; Statistics; Symmetry of associations; Teeth
• ISSN: 0035-9254; 1467-9876
• DOI: 10.2307/2986093

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.