Reduced Rank Mixed Effects Models for Spatially Correlated Hierarchical Functional Data.
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.
Zhou
Lan
L
Department of Statistics, Texas A&M University, College Station, TX 77843-3143.
Huang
Jianhua Z
JZ
Martinez
Josue G
JG
Maity
Arnab
A
Baladandayuthapani
Veerabhadran
V
Carroll
Raymond J
RJ
Biometrika. 2008;95(3):601-619
19396364
J R Stat Soc Series B Stat Methodol. 2006 Apr 1;68(2):179-199
19759841
Biostatistics. 2003 Apr;4(2):297-312
12925523
Biometrics. 2008 Mar;64(1):64-73
17608780
Biometrics. 1982 Dec;38(4):963-74
7168798
Biometrics. 2001 Mar;57(1):253-9
11252607
Electron J Stat. 2009 Jan 1;3:1193-1256
20305800
Ann Appl Stat. 2009 Mar 1;3(1):458-488
20221415
Nutr Cancer. 1997;28(1):20-9
9200146