Abstract

This note describes an algorithm for maximization of a conditional likelihood function in the situation where the corresponding unconditional likelihood function can be more easily maximized. The algorithm is dual to the EM algorithm in the sense that the parameters rather than the data are augmented and that the conditional rather than the marginal likelihood function is maximized. In exponential families the algorithm takes a particular simple form and the specic computations involved in the steps of the algorithm are identical to computations in the EM algorithm. To reflect the structure of the algorithm and the above-mentioned duality, we have chosen to refer to the algorithm as the ME algorithm. The algorithm applies to mixed graphical chain models (Lauritzen and Wermuth 1989) and their generalizations (Edwards 1990), and it was developed with these as motivation, but we believe it to have potential applications beyond these. The algorithm has been implemented in the most recent version of the MIM software (Edwards 1995).

Citations