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

Handle URI:
http://hdl.handle.net/10754/599868
Title:
Testing for constant nonparametric effects in general semiparametric regression models with interactions
Authors:
Wei, Jiawei; Carroll, Raymond J.; Maity, Arnab
Abstract:
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.
Citation:
Wei J, Carroll RJ, Maity A (2011) Testing for constant nonparametric effects in general semiparametric regression models with interactions. Statistics & Probability Letters 81: 717–723. Available: http://dx.doi.org/10.1016/j.spl.2010.11.002.
Publisher:
Elsevier BV
Journal:
Statistics & Probability Letters
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Jul-2011
DOI:
10.1016/j.spl.2010.11.002
PubMed ID:
21731151
PubMed Central ID:
PMC3124863
Type:
Article
ISSN:
0167-7152
Sponsors:
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).
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorWei, Jiaweien
dc.contributor.authorCarroll, Raymond J.en
dc.contributor.authorMaity, Arnaben
dc.date.accessioned2016-02-28T06:31:17Zen
dc.date.available2016-02-28T06:31:17Zen
dc.date.issued2011-07en
dc.identifier.citationWei J, Carroll RJ, Maity A (2011) Testing for constant nonparametric effects in general semiparametric regression models with interactions. Statistics & Probability Letters 81: 717–723. Available: http://dx.doi.org/10.1016/j.spl.2010.11.002.en
dc.identifier.issn0167-7152en
dc.identifier.pmid21731151en
dc.identifier.doi10.1016/j.spl.2010.11.002en
dc.identifier.urihttp://hdl.handle.net/10754/599868en
dc.description.abstractWe 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.en
dc.description.sponsorshipOur 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).en
dc.publisherElsevier BVen
dc.subjectFunction estimationen
dc.subjectGeneralized likelihood ratioen
dc.subjectInteractionsen
dc.subjectNonparametric regressionen
dc.subjectPartially linear logistic modelen
dc.titleTesting for constant nonparametric effects in general semiparametric regression models with interactionsen
dc.typeArticleen
dc.identifier.journalStatistics & Probability Lettersen
dc.identifier.pmcidPMC3124863en
dc.contributor.institutionDepartment of Statistics, 3143 TAMU, Texas A&M University, College Station, Texas 77843, USA.en
kaust.grant.numberKUS-CI-016-04en
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