Skip Navigation



Biometrika Advance Access published online on April 21, 2009
Biometrika, doi:10.1093/biomet/asp012
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
96/2/357    most recent
asp012v1
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Sentürk, D.
Right arrow Articles by Müller, H.-G.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 Biometrika Trust

Article

Covariate-adjusted generalized linear models

Damla Sentürk

Department of Statistics, Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A. dsenturk{at}stat.psu.edu

Hans-Georg Müller

Department of Statistics, University of California, Davis, One Shields Avenue, Davis, California 95616, U.S.A. mueller{at}wald.ucdavis.edu

Received for publication 1 April 2008. Revision received 1 October 2008.
  Abstract

We propose covariate adjustment methodology for a situation where one wishes to study the dependence of a generalized response on predictors while both predictors and response are distorted by an observable covariate. The distorting covariate is thought of as a size measurement that affects predictors in a multiplicative fashion. The generalized response is modelled by means of a random threshold, where the subject-specific thresholds are affected by a multiplicative factor that is a function of the distorting covariate. While the various factors are modelled as smooth unknown functions of the distorting covariate, the underlying relationship between response and covariates is assumed to be governed by a generalized linear model with a known link function. This model provides an extension of a covariate-adjusted regression approach to the case of a generalized linear model. We demonstrate that this contamination model leads to a semiparametric varying-coefficient model. Numerical implementation is straightforward by combining binning, quasilikelihood, and smoothing steps. The asymptotic distribution of the proposed estimators for the regression coefficients of the latent generalized linear model is derived by means of a martingale central limit theorem. Combining this result with consistent estimators for the asymptotic variance makes it then possible to obtain asymptotic inference for the targeted parameters. Both real and simulated data are used in illustrating the proposed methodology.

Key Words: Asymptotic inference • Confounding • Covariate-adjusted regression • Multiplicative effect • Quasilikelihood • Semiparametric modelling


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.