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.

Newly resolved relationships in an early land plant lineage: Bryophyta class Sphagnopsida (peat mosses).

UNLABELLED: PREMISE OF THE STUDY: The Sphagnopsida, an early-diverging lineage of mosses (phylum Bryophyta), are morphologically and ecologically unique and have profound impacts on global climate. The Sphagnopsida are currently classified in two genera, Sphagnum (peat mosses) with some 350-500 species and Ambuchanania with one species. An analysis of phylogenetic relationships among species and genera in the Sphagnopsida were conducted to resolve major lineages and relationships among species within the Sphagnopsida. • METHODS: Phylogenetic analyses of nucleotide sequences from the nuclear, plastid, and mitochondrial genomes (11 704 nucleotides total) were conducted and analyzed using maximum likelihood and Bayesian inference employing seven different substitution models of varying complexity. • KEY RESULTS: Phylogenetic analyses resolved three lineages within the Sphagnopsida: (1) Sphagnum sericeum, (2) S. inretortum plus Ambuchanania leucobryoides, and (3) all remaining species of Sphagnum. Sister group relationships among these three clades could not be resolved, but the phylogenetic results indicate that the highly divergent morphology of A. leucobryoides is derived within the Sphagnopsida rather than plesiomorphic. A new classification is proposed for class Sphagnopsida, with one order (Sphagnales), three families, and four genera. • CONCLUSIONS: The Sphagnopsida are an old lineage within the phylum Bryophyta, but the extant species of Sphagnum represent a relatively recent radiation. It is likely that additional species critical to understanding the evolution of peat mosses await discovery, especially in the southern hemisphere.