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A modified EM algorithm for estimation in generalized mixed models

B M Steele1

  • 1Department of Mathematical Sciences, University of Montana, Missoula 59812-1032, USA.

Biometrics
|December 1, 1996
PubMed
Summary
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This study introduces a modified EM algorithm using Laplace's method for generalized mixed models. This approach overcomes the intractable E-step, offering a computationally efficient alternative for parameter estimation.

Area of Science:

  • Statistics
  • Computational Statistics

Background:

  • The Expectation-Maximization (EM) algorithm is often unsuccessful for generalized mixed models due to intractable E-steps.
  • The E-step involves a complex integral, especially with normal random effect distributions, hindering practical application.

Purpose of the Study:

  • To adapt Laplace's method for analytic approximation within the E-step of the EM algorithm.
  • To develop a computationally straightforward and conceptually simple algorithm for generalized mixed models.

Main Methods:

  • Laplace's method was employed to approximate the intractable integral in the E-step.
  • The modified EM algorithm was designed to handle multiple random factors and non-normal distributions like log-gamma.

Main Results:

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  • The proposed algorithm is computationally straightforward and retains the conceptual simplicity of the standard EM algorithm.
  • Parameter estimates from the modified EM algorithm favorably compare with existing methods for generalized mixed models.
  • Simulations and real data analyses demonstrate the efficacy of the new approach.

Conclusions:

  • The modified EM algorithm provides a viable solution for parameter estimation in generalized mixed models.
  • This method offers an improvement over traditional approaches by addressing the E-step intractability.
  • The algorithm's flexibility extends to various random effect distributions, enhancing its applicability.