Maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse
Roderick J. A. Little, Donald B. Rubin · Wiley series in probability and statistics · 2002
Patterns of incomplete data in practice often do not have the particular forms that allow explicit maximum likelihood (ML) estimates to be calculated by exploiting factorizations of the likelihood. This chapter considers the iterative methods of computation for situations without explicit ML estimates. An alternative computing strategy for incomplete-data problems, which does not require second derivatives to be calculated or approximated, is the Expectation Maximization (EM) algorithm. In many important cases, the EM algorithm is remarkably simple, both conceptually and computationally. The EM-type algorithms described in the chapter include ECM, ECME, AECM, and PX-EM. The chapter finally discusses versions of the second type of extension of EM with more focus on missing data applications.