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Nonparametric Bayes Testing of Changes in a Response Distribution with an Ordinal Predictor
Author(s) -
Pennell Michael L.,
Dunson David B.
Publication year - 2008
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2007.00885.x
Subject(s) - prior probability , nonparametric statistics , skewness , statistics , quantile , dirichlet distribution , dirichlet process , hyperparameter , econometrics , bayesian probability , bayes' theorem , ordinal data , mathematics , categorical distribution , computer science , bayesian hierarchical modeling , machine learning , mathematical analysis , boundary value problem
Summary In certain biomedical studies, one may anticipate changes in the shape of a response distribution across the levels of an ordinal predictor. For instance, in toxicology studies, skewness and modality might change as dose increases. To address this issue, we propose a Bayesian nonparametric method for testing for distribution changes across an ordinal predictor. Using a dynamic mixture of Dirichlet processes, we allow the response distribution to change flexibly at each level of the predictor. In addition, by assigning mixture priors to the hyperparameters, we can obtain posterior probabilities of no effect of the predictor and identify the lowest dose level for which there is an appreciable change in distribution. The method also provides a natural framework for performing tests across multiple outcomes. We apply our method to data from a genotoxicity experiment.