Assessing the predictive ability of a multilevel binary regression model
AbstractAn adaptation of the Brier score and the concordance probability is proposed for the two-level and the three-level random intercept binary regression model. This results in 2 different Brier scores and 3 different C-indices for the two-level binary regression model and 4 different Brier scores and 7 different C-indices for the three-level binary regression model. The ensemble of these measures offers a better view on how the different elements of the random effects model, i.e. the covariates and the random effects, affect the predictive ability of the model separately, evaluated on a within-cluster, between-cluster and global level. For all measures, an estimation procedure using Bayesian and likelihood estimation methods was developed, including a percentile and a BCa non-parametric bootstrap step to construct credible/confidence intervals. In a simulation study, the likelihood estimation procedure showed difficulties in estimating unbiasedly the predictive ability of the random effects, while the Bayesian estimation procedure resulted in good estimation properties for all of the developed measures. The BCa non-parametric bootstrap method resulted in confidence/credible intervals with better coverage properties than the percentile non-parametric bootstrap method. The proposals are applied to a real-life binary data set with a three-level structure using the Bayesian estimation procedure.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 56 (2012)
Issue (Month): 6 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/csda
Brier score; C-index; Concordance probability; Multilevel; Binary regression;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- C. A. Field & A. H. Welsh, 2007. "Bootstrapping clustered data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 369-390.
- Anders Skrondal & Sophia Rabe-Hesketh, 2009. "Prediction in multilevel generalized linear models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(3), pages 659-687.
- Germán Rodríguez & Noreen Goldman, 2001. "Improved estimation procedures for multilevel models with binary response: a case-study," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 339-355.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.