TY - JOUR

T1 - Testing for constant nonparametric effects in general semiparametric regression models with interactions

AU - Wei, Jiawei

AU - Carroll, Raymond J.

AU - Maity, Arnab

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: Our research was supported by a grant from the National Cancer Institute (CA57030). Carroll's research was also supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2011/7

Y1 - 2011/7

N2 - We consider the problem of testing for a constant nonparametric effect in a general semi-parametric regression model when there is the potential for interaction between the parametrically and nonparametrically modeled variables. The work was originally motivated by a unique testing problem in genetic epidemiology (Chatterjee, et al., 2006) that involved a typical generalized linear model but with an additional term reminiscent of the Tukey one-degree-of-freedom formulation, and their interest was in testing for main effects of the genetic variables, while gaining statistical power by allowing for a possible interaction between genes and the environment. Later work (Maity, et al., 2009) involved the possibility of modeling the environmental variable nonparametrically, but they focused on whether there was a parametric main effect for the genetic variables. In this paper, we consider the complementary problem, where the interest is in testing for the main effect of the nonparametrically modeled environmental variable. We derive a generalized likelihood ratio test for this hypothesis, show how to implement it, and provide evidence that our method can improve statistical power when compared to standard partially linear models with main effects only. We use the method for the primary purpose of analyzing data from a case-control study of colorectal adenoma.

AB - We consider the problem of testing for a constant nonparametric effect in a general semi-parametric regression model when there is the potential for interaction between the parametrically and nonparametrically modeled variables. The work was originally motivated by a unique testing problem in genetic epidemiology (Chatterjee, et al., 2006) that involved a typical generalized linear model but with an additional term reminiscent of the Tukey one-degree-of-freedom formulation, and their interest was in testing for main effects of the genetic variables, while gaining statistical power by allowing for a possible interaction between genes and the environment. Later work (Maity, et al., 2009) involved the possibility of modeling the environmental variable nonparametrically, but they focused on whether there was a parametric main effect for the genetic variables. In this paper, we consider the complementary problem, where the interest is in testing for the main effect of the nonparametrically modeled environmental variable. We derive a generalized likelihood ratio test for this hypothesis, show how to implement it, and provide evidence that our method can improve statistical power when compared to standard partially linear models with main effects only. We use the method for the primary purpose of analyzing data from a case-control study of colorectal adenoma.

UR - http://hdl.handle.net/10754/599868

UR - https://linkinghub.elsevier.com/retrieve/pii/S016771521000310X

UR - http://www.scopus.com/inward/record.url?scp=79955146434&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2010.11.002

DO - 10.1016/j.spl.2010.11.002

M3 - Article

C2 - 21731151

SN - 0167-7152

VL - 81

SP - 717

EP - 723

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

IS - 7

ER -