Estimation in mixed models through three step minimization

ABSTRACT

The aim of this article is to present an estimation procedure for both fixed effects and variance components in linear mixed models. This procedure consists of a maximum-likelihood method which we call Three Step Minimization (TSM). The major contribution of this method is that when variances tend to be null standard algorithms behave badly, unlike the TSM method, which uses a grid search algorithm in a compact set. A numerical application with real and simulated data is provided.

KEYWORDS:

• Inference
• Maximum-likelihood
• Mixed models
• Newton–Raphson
• Variance components

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J10
• 62F12

Acknowledgments

The authors gratefully acknowledge the reviewers for their very valuable comments.

This work was partially supported by the Center of Mathematics, University of Beira Interior through the project PEst-OE/MAT/UI0212/2014 and by CMA, Faculty of Science and Technology, New University of Lisbon, through the project PEst- OE/MAT/UI0297/2011.