Copula‐based regression models for a bivariate mixed discrete and continuous outcome

Statistics in Medicine - Tập 30 Số 2 - Trang 175-185 - 2011
Alexander R. de Leon1, Bin Wu1
1Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4

Tóm tắt

AbstractThis paper is concerned with regression models for correlated mixed discrete and continuous outcomes constructed using copulas. Our approach entails specifying marginal regression models for the outcomes, and combining them via a copula to form a joint model. Specifically, we propose marginal regression models (e.g. generalized linear models) to link the outcomes' marginal means to covariates. To account for associations between outcomes, we adopt the Gaussian copula to indirectly specify their joint distributions. Our approach has two advantages over current methods: one, regression parameters in models for both outcomes are marginally meaningful, and two, the association is ‘margin‐free’, in the sense that it is characterized by the copula alone. By assuming a latent variable framework to describe discrete outcomes, the copula used still uniquely determines the joint distribution. In addition, association measures between outcomes can be interpreted in the usual way. We report results of simulations concerning the bias and efficiency of two likelihood‐based estimation methods for the model. Finally, we illustrate the model using data on burn injuries. Copyright © 2010 John Wiley & Sons, Ltd.

Từ khóa


Tài liệu tham khảo

10.1016/j.csda.2007.07.018

10.1177/0962280207081240

10.1002/sim.3588

10.1214/aoms/1177705052

10.2307/2533101

10.1080/01621459.1995.10476583

10.1093/biomet/79.3.441

Regan MM, 2002, Topics in Modelling of Clustered Data, 233

10.1080/01621459.1992.10475264

10.1002/sim.923

10.1002/cjs.5550350405

10.1016/j.jspi.2007.03.024

10.1002/sim.2776

10.1111/1368-423X.00019

10.1002/sim.3082

10.1093/biostatistics/kxi036

10.1002/sim.3314

10.1016/j.jspi.2009.05.023

10.1111/j.1541-0420.2008.01058.x

10.1198/073500105000000153

Song PXK, 2007, Correlated Data Analysis: Modeling, Analytics, and Applications

10.1016/j.csda.2007.08.012

10.1016/j.jempfin.2006.07.004

10.2143/AST.37.2.2024077

de Leon AR, 2010, Encyclopedia of Biopharmaceutical Statistics

10.1002/0470090456.ch21

JoeH XuJJ.The estimation method of inference functions for margins for multivariate models. Technical Report Department of Statistics University of British Columbia 1996.

10.1093/biomet/93.3.537

10.1007/s11336-007-9005-4

Drasgow F, 1986, Encyclopedia of Statistical Sciences, 68

10.1198/016214501753208762

10.1002/sim.3449

10.1017/CBO9780511550683

10.1111/j.0006-341X.1999.00258.x

Song PXK, 2007, Maximum likelihood inference in robust linear mixed‐effects models using multivariate t distributions, Statistica Sinica, 17, 929

Thông tin
Thông tin xuất bản

Statistics in Medicine

Tập 30 Số 2

175-185

Thông tin tác giả