Finite Mixture Distribution, Sequential Likelihood, and the EM Algorithm

The use of finite mixture distributions to control for unobserved heterogeneity has become increasingly popular among those estimating dynamic discrete choice models. One of the barriers to using mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log likelihood function. The EM algorithm reintroduces additive separability, however, thus allowing the option of estimating parameters sequentially during each maximization step. We show that, relative to full information maximum likelihood, the EM algorithm with sequential maximization (ESM) can generate large computational savings with little loss of efficiency.