Reduced Rank Mixed Effects Models for Spatially Correlated Hierarchical Functional Data

Handle URI:
http://hdl.handle.net/10754/599475
Title:
Reduced Rank Mixed Effects Models for Spatially Correlated Hierarchical Functional Data
Authors:
Zhou, Lan; Huang, Jianhua Z.; Martinez, Josue G.; Maity, Arnab; Baladandayuthapani, Veerabhadran; Carroll, Raymond J.
Abstract:
Hierarchical functional data are widely seen in complex studies where sub-units are nested within units, which in turn are nested within treatment groups. We propose a general framework of functional mixed effects model for such data: within unit and within sub-unit variations are modeled through two separate sets of principal components; the sub-unit level functions are allowed to be correlated. Penalized splines are used to model both the mean functions and the principal components functions, where roughness penalties are used to regularize the spline fit. An EM algorithm is developed to fit the model, while the specific covariance structure of the model is utilized for computational efficiency to avoid storage and inversion of large matrices. Our dimension reduction with principal components provides an effective solution to the difficult tasks of modeling the covariance kernel of a random function and modeling the correlation between functions. The proposed methodology is illustrated using simulations and an empirical data set from a colon carcinogenesis study. Supplemental materials are available online.
Citation:
Zhou L, Huang JZ, Martinez JG, Maity A, Baladandayuthapani V, et al. (2010) Reduced Rank Mixed Effects Models for Spatially Correlated Hierarchical Functional Data. Journal of the American Statistical Association 105: 390–400. Available: http://dx.doi.org/10.1198/jasa.2010.tm08737.
Publisher:
Informa UK Limited
Journal:
Journal of the American Statistical Association
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Mar-2010
DOI:
10.1198/jasa.2010.tm08737
PubMed ID:
20396628
PubMed Central ID:
PMC2853971
Type:
Article
ISSN:
0162-1459; 1537-274X
Sponsors:
Zhou and Martinez were supported by a postdoctoral training grant from the National Cancer Institute (CA90301) Zhou was also supported by NSF grant DMS-0907170 Huang was partially supported by NSF grants DMS-0606580, DMS-0907170 and the NCI grant CA57030 Carroll was partially supported by NCI grants CA57030, CA104620 Huang and Carroll's work 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.authorZhou, Lanen
dc.contributor.authorHuang, Jianhua Z.en
dc.contributor.authorMartinez, Josue G.en
dc.contributor.authorMaity, Arnaben
dc.contributor.authorBaladandayuthapani, Veerabhadranen
dc.contributor.authorCarroll, Raymond J.en
dc.date.accessioned2016-02-28T05:51:49Zen
dc.date.available2016-02-28T05:51:49Zen
dc.date.issued2010-03en
dc.identifier.citationZhou L, Huang JZ, Martinez JG, Maity A, Baladandayuthapani V, et al. (2010) Reduced Rank Mixed Effects Models for Spatially Correlated Hierarchical Functional Data. Journal of the American Statistical Association 105: 390–400. Available: http://dx.doi.org/10.1198/jasa.2010.tm08737.en
dc.identifier.issn0162-1459en
dc.identifier.issn1537-274Xen
dc.identifier.pmid20396628en
dc.identifier.doi10.1198/jasa.2010.tm08737en
dc.identifier.urihttp://hdl.handle.net/10754/599475en
dc.description.abstractHierarchical functional data are widely seen in complex studies where sub-units are nested within units, which in turn are nested within treatment groups. We propose a general framework of functional mixed effects model for such data: within unit and within sub-unit variations are modeled through two separate sets of principal components; the sub-unit level functions are allowed to be correlated. Penalized splines are used to model both the mean functions and the principal components functions, where roughness penalties are used to regularize the spline fit. An EM algorithm is developed to fit the model, while the specific covariance structure of the model is utilized for computational efficiency to avoid storage and inversion of large matrices. Our dimension reduction with principal components provides an effective solution to the difficult tasks of modeling the covariance kernel of a random function and modeling the correlation between functions. The proposed methodology is illustrated using simulations and an empirical data set from a colon carcinogenesis study. Supplemental materials are available online.en
dc.description.sponsorshipZhou and Martinez were supported by a postdoctoral training grant from the National Cancer Institute (CA90301) Zhou was also supported by NSF grant DMS-0907170 Huang was partially supported by NSF grants DMS-0606580, DMS-0907170 and the NCI grant CA57030 Carroll was partially supported by NCI grants CA57030, CA104620 Huang and Carroll's work was also supported by award number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherInforma UK Limiteden
dc.subjectLongitudinal dataen
dc.subjectPenalized splinesen
dc.subjectPrincipal componentsen
dc.subjectReduced rank modelsen
dc.titleReduced Rank Mixed Effects Models for Spatially Correlated Hierarchical Functional Dataen
dc.typeArticleen
dc.identifier.journalJournal of the American Statistical Associationen
dc.identifier.pmcidPMC2853971en
dc.contributor.institutionDepartment of Statistics, Texas A&M University, College Station, TX 77843-3143.en
kaust.grant.numberKUS-CI-016-04en
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