Seminar Details

Seminar Details


Monday

Nov 17

3:30 pm

Estimating Common Functional Principal Components in a Linear Mixed Effects Model Framework

Kevin Hayes

Seminar

University of Limerick

The emerging area of statistical science known as functional data analysis is concerned with evaluating information on curves or functions. In recent years much of the research emphasis has focused on extending statistical methods from classical settings into the functional domain. For example, functional principal component analysis (FPCA) is analogous to the traditional PCA, except that the observed data are entire functions rather than multivariate vectors. We show how FPCA can be extended to the case where grouping structures are evident in the data or replicated functions are available for each experimental unit. The resulting common-FPCA (CFPCA) methodology is an extension of ideas due Flury, from multivariate statistics. We use an estimation procedure based on the linear mixed effects model. Representing the smoothing problem via the linear mixed effects model allows us to determine smooth estimates of individual functions, while accounting for replicate observations, and grouping structure. Another advantage of the linear mixed effects framework is that the degree of smoothing is automatically controlled at a subject-specific level. This paper discusses an application of our method to a biomechanical data set studying Chronic Achilles tendon injury, which exhibits all of the multilevel features mentioned above.