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Numerical Maximisation of Likelihood: A Neglected Alternative to EM?

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  • Iain L. MacDonald

Abstract

type="main" xml:id="insr12041-abs-0001"> There is by now a long tradition of using the EM algorithm to find maximum-likelihood estimates (MLEs) when the data are incomplete in any of a wide range of ways, even when the observed-data likelihood can easily be evaluated and numerical maximisation of that likelihood is available as a conceptually simple route to the MLEs. It is rare in the literature to see numerical maximisation employed if EM is possible. But with excellent general-purpose numerical optimisers now available free, there is no longer any reason, as a matter of course, to avoid direct numerical maximisation of likelihood. In this tutorial, I present seven examples of models in which numerical maximisation of likelihood appears to have some advantages over the use of EM as a route to MLEs. The mathematical and coding effort is minimal, as there is no need to derive and code the E and M steps, only a likelihood evaluator. In all the examples, the unconstrained optimiser nlm available in R is used, and transformations are used to impose constraints on parameters. I suggest therefore that the following question be asked of proposed new applications of EM: Can the MLEs be found more simply and directly by using a general-purpose numerical optimiser?

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  • Iain L. MacDonald, 2014. "Numerical Maximisation of Likelihood: A Neglected Alternative to EM?," International Statistical Review, International Statistical Institute, vol. 82(2), pages 296-308, August.
    • Handle: RePEc:bla:istatr:v:82:y:2014:i:2:p:296-308
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    13. Gordon Anderson & Alessio Farcomeni & Grazia Pittau & Roberto Zelli, 2017. "Rectangular latent Markov models for time-specific clustering," Working Papers tecipa-589, University of Toronto, Department of Economics.
    14. Iain L. MacDonald & Brendon M. Lapham, 2016. "Even More Direct Calculation of the Variance of a Maximum Penalized-Likelihood Estimator," The American Statistician, Taylor & Francis Journals, vol. 70(1), pages 114-118, February.
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