Finite Mixture Distributions, Sequential Likelihood and the EM Algorithm

By P. Arcidiacono, John Bailey Jones. 2003

202 citations recorded by the source corpus.

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. Copyright Econometric Society, 2002.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f149c9950ed601a055a3cca5c3f68243285b6341

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Citations in the corpus

Using Angler Characteristics and Attitudinal Data to Identify Environmental Preference Classes: A Latent-Class Model (2006, unknown): “M algorithm is seeing increased use in economics (Arcidiacono and Jones 2003).”
Ability Sorting and the Returns to College Major (2004, unknown): “Arcidiacono and Jones (2003) show this method produces consistent estimates of the parameters with large computational savings.”
Nonlinear Panel Data Estimation via Quantile Regressions (2015, methodology): “Arcidiacono and Jones (2003). However, an additional difficulty in our case is that the posterior density depends on a continuum of parameters.”
Bayesian Estimation of Dynamic Discrete Choice Models (2009, background): “Another feature of our algorithm is that even though the number of grid points on the state variable is small per solution-estimation iteration, the number of effective grid points increases with the number of estimation iterations.”
Practical Methods for Estimation of Dynamic Discrete Choice Models (2011, methodology): “Arcidiacono and Jones (2003) show that the maximization step can once again be carried out in stages.”
On the ergodicity properties of some adaptive MCMC algorithms (2006, methodology): “Sequential implementations of the EM algorithm for estimating the parameters of a mixture when the data are observed sequentially in time have been considered by several authors (see [32], Chapter 6, [5] and the references therein). The version presented here is, in many respects, a standard adaptat”
The Pervasive Absence of Compensating Differentials (2009, methodology): “Arcidiacono and Jones (2003) propose to compute the asymptotic variance-covariance matrix by the usual GMM formula.”
The Structural Estimation of Behavioral Models: Discrete Choice Dynamic Programming Methods and Applications (2011, methodology): “v it = v (yit;zit; nit; it; it; it) (7)”
Dynamic Discrete Choice Structural Models: A Survey (2010, methodology): “Sequential EM algorithm (ESM): Arcidiacono and Jones (2003) propose a clever algorithm which makes the two-step partial likelihood approach compatible with the finite mixture model.”
Affirmative Action in Higher Education: How do Admission and Financial Aid Rules Affect Future Earnings? (2005, background): “Let v1ijk be the corresponding expected present discounted value of indirect utility: v1ijk = u1ijk + βE1(uwijk) (4)”