Skip to main content
Article thumbnail
Location of Repository

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

By M. J. Green, Graham Medley and W. J. Browne


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

Topics: QA, HA
Publisher: EDP Sciences
Year: 2009
OAI identifier:

Suggested articles


  1. (2006). A comparison of Bayesian and likelihood-based methods for fitting multilevel models, Bayesian Analysis doi
  2. (2003). Approximate cross-validatory predictive checks in disease mapping, doi
  3. (2006). Bayesian modelling of differential gene expression, Biometrics doi
  4. (2000). Diagnostic checks for discreet data regression models using posterior predictive simulations, doi
  5. (2007). farm and management factors during the dry period that determine the rate of clinical mastitis after calving, J. Dairy Sci. doi
  6. (1984). Graphical methods for assessing logistic regression models (with discussion), doi
  7. (2005). MLwiN Version 2.02, Multilevel Models Project, Centre for Multilevel Modelling,
  8. (1995). Multilevel Statistical Models, doi
  9. (1998). Outliers in multilevel data, doi
  10. (1996). Posterior predictive assessment of model fitness via realized discrepancies, Statistica Sinica
  11. (2000). Posterior predictive model checks for disease mapping models, doi
  12. (2003). Veterinary epidemiologic research, Atlantic Veterinary College Inc.,
  13. (2004). WinBUGS Version 1.4.1., Imperial College and MRC,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.