Principal component models for sparse functional data

Data often arrives as curves --- functions sampled at regular times or frequencies. Functional principal components (Ramsay and Silverman, 1997) can be used to describe the modes of variation of these functions. In many situations we do not get complete measurements of the individual curves. For example, growth curves are sampled functions, consisting of measurements such as bone density at different ages in a childs development. These measurements are often taken at an irregular and sparse set of time points, which can differ widely across individuals. We develop principal component models for representing the modes of variation of these curves. These models are estimated in a reduced-rank mixed-effects framework. 1 The problem In this paper we present a technique for estimating principal component curves for data such as those illustrated in Figure 1. The data consists of partial growth curves for 48 females measured at various ages. Even though there are only partial curves for ea...