Principal Component Analysis in the Presence of Missing Data

The aim of this chapter is to provide an overview of recent developments in principal component analysis (PCA) methods when the data are incomplete. Missing data bring uncertainty into the analysis and their treatment requires statistical approaches that are tailored to cope with specific missing data processes (i.e., ignorable and nonignorable mechanisms). Since the publication of the classic textbook by Jolliffe, which includes a short, same-titled section on the missing data problem in PCA, there have been a few methodological contributions that hinge upon a probabilistic approach to PCA. In this chapter, we unify methods for ignorable and nonignorable missing data in a general likelihood framework. We also provide real data examples to illustrate the application of these methods using the R language and environment for statistical computing and graphics.