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.
|Original language||English (US)|
|Number of pages||11|
|Journal||Journal of the American Statistical Association|
|State||Published - Mar 2010|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.