Finite mixture distributions, sequential likelihood and the EM algorithm

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2003-01-01

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Abstract

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.

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Scholars@Duke

Arcidiacono

Peter S. Arcidiacono

William Henry Glasson Distinguished Professor of Economics

Professor Arcidiacono specializes in research involving applied microeconomics, applied economics, and labor economics. His research primarily focuses on education and discrimination. His work focuses specifically on the exploration of a variety of subjects, such as structural estimation, affirmative action, minimum wages, teen sex, discrimination, higher education, and dynamic discrete choice models, among others. He recently received funding from a National Science Foundation Grant for his project, “CCP Estimation of Dynamic Discrete Choice Models with Unobserved Heterogeneity.” He has also been awarded grants from NICHD for his work entitled, “A Dynamic Model of Teen Sex, Abortion, and Childbearing;” and from the Smith Richardson Foundation for his study, “Does the River Spill Over? Race and Peer Effects in the College & Beyond” with Jacob Vigdor. Other recent studies of his include, “The Distributional Effects of Minimum Wage Increases when Both Labor Supply and Labor Demand are Endogenous” with Tom Ahm and Walter Wessles; “Explaining Cross-racial Differences in Teenage Labor Force Participation: Results from a General Equilibrium Search Model” with Alvin Murphy and Omari Swinton; and “The Effects of Gender Interactions in the Lab and in the Field” in collaboration with Kate Antonovics and Randy Walsh.


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