Acceleration of the EM and ECM algorithms using the Aitken delta(2) method for log-linear models with partially classified data

摘要

In this paper, we discuss the MLEs for log-linear models with partially classified data. We propose to apply the Aitken delta(2) method of Aitken [Aitken, A.C., 1926. On Bernoulli's numerical solution of algebraic equations. Proc. R. Soc. Edinburgh 46, 289-305] to the EM and ECM algorithms to accelerate their convergence. The Aitken 2 accelerated algorithm shares desirable properties of the EM algorithm, such as numerical stability, computational simplicity and flexibility in interpreting the incompleteness of data. We show the convergence of the Aitken delta(2) accelerated algorithm and compare its speed of convergence with that of the EM algorithm, and we also illustrate their performance by means of a simulation.