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On the simulation size and the convergence of the Monte Carlo EM algorithm via likelihood-based distances

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  • Eickhoff, Jens C.
  • Zhu, Jun
  • Amemiya, Yasuo

Abstract

When the conditional expectation of a complete-data likelihood in an EM algorithm is analytically intractable, Monte Carlo integration is often used to approximate the E-step. While the resulting Monte Carlo EM algorithm (MCEM) is flexible, assessing convergence of the algorithm is a more difficult task than the original EM algorithm, because of the uncertainty involved in the Monte Carlo approximation. In this note, we propose a convergence criterion using a likelihood-based distance. Because the likelihood is approximated by Monte Carlo integration, we make the distance small with a large probability by selecting the Monte Carlo sample size adaptively at each step of the MCEM algorithm. We implement the proposed convergence criterion along with the simulation size selection in a one-way random effects model. The result shows that our MCEM iterations match the exact EM iterations closely.

Suggested Citation

  • Eickhoff, Jens C. & Zhu, Jun & Amemiya, Yasuo, 2004. "On the simulation size and the convergence of the Monte Carlo EM algorithm via likelihood-based distances," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 161-171, April.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:2:p:161-171
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    References listed on IDEAS

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    1. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    2. J.‐Q. Shi & S.‐Y. Lee, 2000. "Latent variable models with mixed continuous and polytomous data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 77-87.
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    1. J. Zhu & J. C. Eickhoff & P. Yan, 2005. "Generalized Linear Latent Variable Models for Repeated Measures of Spatially Correlated Multivariate Data," Biometrics, The International Biometric Society, vol. 61(3), pages 674-683, September.
    2. Ricardo Smith Ramírez, 2007. "FIML estimation of treatment effect models with endogenous selection and multiple censored responses via a Monte Carlo EM Algorithm," Working Papers DTE 403, CIDE, División de Economía.
    3. Liu Yuan & Bottai Matteo, 2009. "Mixed-Effects Models for Conditional Quantiles with Longitudinal Data," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-24, November.

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