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

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 condit...

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Bibliographic Details
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
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Description
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.
ISSN:0035-9254
1467-9876
DOI:10.2307/2986093