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Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression

Green, Martin J.; Medley, Graham F.; Browne, William J.

Authors

MARTIN GREEN martin.green@nottingham.ac.uk
Professor of Cattle Health & Epidemiology

Graham F. Medley

William J. Browne



Abstract

Assessing the fit of a model is an important final step in any statistical analysis, but this is not straightforward when complex discrete response models are used. Cross validation and posterior predictions have been suggested as methods to aid model criticism. In this paper a comparison is made between four methods of model predictive assessment in the context of a three level logistic regression model for clinical mastitis in dairy cattle; cross validation, a prediction using the full posterior predictive distribution and two “mixed” predictive methods that incorporate higher level random effects simulated from the underlying model distribution. Cross validation is considered a gold standard method but is computationally intensive and thus a comparison is made between posterior predictive assessments and cross validation. The analyses revealed that mixed prediction methods produced results close to cross validation whilst the full posterior predictive assessment gave predictions that were over-optimistic (closer to the observed disease rates) compared with cross validation. A mixed prediction method that simulated random effects from both higher levels was best at identifying the outlying level two (farm-year) units of interest. It is concluded that this mixed prediction method, simulating random effects from both higher levels, is straightforward and may be of value in model criticism of multilevel logistic regression, a technique commonly used for animal health data with a hierarchical structure.

Citation

Green, M. J., Medley, G. F., & Browne, W. J. (2009). Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression. Veterinary Research, 40(4), doi:10.1051/vetres/2009013

Journal Article Type Article
Publication Date Jan 1, 2009
Deposit Date Apr 19, 2010
Publicly Available Date Apr 19, 2010
Journal Veterinary Research
Print ISSN 0928-4249
Electronic ISSN 0928-4249
Publisher Humana Press
Peer Reviewed Peer Reviewed
Volume 40
Issue 4
Article Number Article 30
DOI https://doi.org/10.1051/vetres/2009013
Keywords model fit, posterior predictive assessment, mixed predictive assessment, cross validation, Bayesian multilevel model
Public URL http://eprints.nottingham.ac.uk/id/eprint/1273
Publisher URL http://dx.doi.org/10.1051/vetres/2009013

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