  We study an EM algorithm for estimating product-term regression models with
missing data. The study of such problems in the likelihood tradition has thus
far been restricted to an EM algorithm method using full numerical integration.
However, under most missing data patterns, we show that this problem can be
solved analytically, and numerical approximations are only needed under
specific conditions. Thus we propose a hybrid EM algorithm, which uses analytic
solutions when available and approximate solutions only when needed. The
theoretical framework of our algorithm is described herein, along with two
numerical experiments using both simulated and real data. We show that our
algorithm confers higher accuracy to the estimation process, relative to the
existing full numerical integration method. We conclude with a discussion of
applications, extensions, and topics of further research.
