ABSTRACT
This chapter introduces analytic methods for multilevel functional data, which is functional data that has at least two levels of functional variability. This includes nested, crossed, and longitudinal functional data structures. Such data structures are different from traditional longitudinal data where the individual observation is scalar and the collection of observations across individuals can be analyzed using single-level functional approaches. They are also different from functional ANOVA, which allows for different functional means of groups, but have only one source of functional variability around these means. Methods are illustrated using the NHANES data, where functions are observed for multiple individuals (Level 1 variability) over multiple days (Level 2 variability). Multilevel, longitudinal, and structured functional principal component analysis (MFPCA/LFPCA/SFPCA) are introduced. Functional Additive Mixed Models (FAMM) and Fast Univariate Inference (FUI) are described and compared. Several extensions and generalizations are mentioned together with current advances and limitations of computational methods.
