Acceleration of the EM and ECM algorithms using the Aitken δ2 method for log-linear models with partially classified data

In this paper, we discuss the MLEs for log-linear models with partially classified data. We propose to apply the Aitken δ2δ2 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 δ2δ2 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 δ2δ2 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.