Prediction in multilevel generalized linear models

Anders Skrondal and Sophia Rabe-Hesketh ()

Journal Of The Royal Statistical Society Series A, 2009, vol. 172, issue 3, pages 659-687

Abstract: We discuss prediction of random effects and of expected responses in multilevel generalized linear models. Prediction of random effects is useful for instance in small area estimation and disease mapping, effectiveness studies and model diagnostics. Prediction of expected responses is useful for planning, model interpretation and diagnostics. For prediction of random effects, we concentrate on empirical Bayes prediction and discuss three different kinds of standard errors; the posterior standard deviation and the marginal prediction error standard deviation (comparative standard errors) and the marginal sampling standard deviation (diagnostic standard error). Analytical expressions are available only for linear models and are provided in an appendix. For other multilevel generalized linear models we present approximations and suggest using parametric bootstrapping to obtain standard errors. We also discuss prediction of expectations of responses or probabilities for a new unit in a hypothetical cluster, or in a new (randomly sampled) cluster or in an existing cluster. The methods are implemented in gllamm and illustrated by applying them to survey data on reading proficiency of children nested in schools. Simulations are used to assess the performance of various predictions and associated standard errors for logistic random-intercept models under a range of conditions. Copyright (c) 2009 Royal Statistical Society.

Date: 2009

Downloads: (external link)
http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-985X.2009.00587.x link to full text (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:bla:jorssa:v:172:y:2009:i:3:p:659-687

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0964-1998

Access Statistics for this article

Journal Of The Royal Statistical Society Series A is edited by A. Fielding and G. Verbeke

More articles in Journal Of The Royal Statistical Society Series A from Royal Statistical Society
Series data maintained by Christopher F. Baum ().