Maximization by parts in likelihood inference

Peter X.K. Song, Yanqin Fan, John D. Kalbfleisch, Jiming Jiang, Thomas A. Louis, J. G. Liao, Bahjat F. Qaqish, David Ruppert

Research output: Contribution to journalArticle


This article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second-order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log-likelihood from a simply analyzed model, and the second part is used to update estimates from the first part. Convergence properties of this iterative (fixed-point) algorithm are examined, and asymptotics are derived for estimators obtained using only a finite number of iterations. Illustrative examples considered in the article include multivariate Gaussian copula models, nonnormal random-effects models, generalized linear mixed models, and state-space models. Properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal linear random-effects model.

Original languageEnglish (US)
Pages (from-to)1145-1158
Number of pages14
JournalJournal of the American Statistical Association
Issue number472
StatePublished - Dec 2005


  • Copula model
  • Fixed-point algorithm
  • Generalized linear mixed model
  • Information dominance
  • Iterative algorithm
  • Non-normal random effects
  • Score equation
  • State-space model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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  • Cite this

    Song, P. X. K., Fan, Y., Kalbfleisch, J. D., Jiang, J., Louis, T. A., Liao, J. G., Qaqish, B. F., & Ruppert, D. (2005). Maximization by parts in likelihood inference. Journal of the American Statistical Association, 100(472), 1145-1158.