MLE for LME Model

  1. Eugene Demidenko

Published Online: 28 JAN 2005

DOI: 10.1002/0471728438.ch2

Mixed Models: Theory and Applications

Mixed Models: Theory and Applications

How to Cite

Demidenko, E. (2004) MLE for LME Model, in Mixed Models: Theory and Applications, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471728438.ch2

Publication History

  1. Published Online: 28 JAN 2005
  2. Published Print: 28 JUL 2004

ISBN Information

Print ISBN: 9780471601616

Online ISBN: 9780471728436



  • mixed models;
  • linear mixed effect models;
  • matrix algebra;
  • variance;
  • statistical analysis


This chapter includes the following topics:

  • Example: Height Versus Weight

  • The Model and Log-Likelihood Functions

  • Balanced Random-Coefficient Model

  • LME Model with Random Intercepts

  • Criterion for the MLE Existence

  • Criterion for Positive Definiteness of Matrix D

  • Preestimation Bounds for Variance Parameters

  • Maximization Algorithms

  • Derivatives of the Log-Likelihood Function

  • Newton–Raphson Algorithm

  • Fisher Scoring Algorithm

  • EM Algorithm

  • Starting Point

  • Algorithms for Restricted MLE

  • Optimization on Nonnegative Definite Matrices

  • Appendix: Proof of the LILE Existence

  • Summary Points