Finite mixture distributions, sequential likelihood and the EM algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite 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. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.

Does higher hospital cost imply higher quality of care?

This study investigates whether higher input use per stay in the hospital (treatment intensity) and longer length of stay improve outcomes of care. We allow for endogeneity of intensity and length of stay by estimating a quasi-maximum-likelihood discrete factor model, where the distribution of the unmeasured variable is modeled using a discrete distribution. Data on elderly persons come from several waves of the National Long-Term Care Survey merged with Medicare claims data for 1984-1995 and the National Death Index. We find that higher intensity improves patient survival and some dimensions of functional status among those who survive.