The Use of Permutation Tests for Variance Components in Linear Mixed Models

Abstract

Standard asymptotic chi-square distribution of the likelihood ratio and score statistics under the null hypothesis does not hold when the parameter value is on the boundary of the parameter space. In mixed models it is of interest to test for a zero random effect variance component. Some available tests for the variance component are reviewed and a new test within the permutation framework is presented. The power and significance level of the different tests are investigated by means of a Monte Carlo simulation study. The proposed test has a significance level closer to the nominal one and it is more powerful.

Keywords:

• Bootstrap test
• Likelihood ratio test
• Linear mixed model
• Permutation test
• Variance component

2000 Mathematics Subject Classification:

• Primary 62G09
• Secondary 62J12

Acknowledgments

The authors would like to thank Dr. Paolo Emilio Mazzon and Professor Gianfranco Bilardi of Department of Information Engineering – Univeristy of Padua for their helping to use their own computer clusters which facilitate and accelerate our computations. Moreover, the authors wish to thank the University of Padova (CPDA092350/09) and the Italian Ministry for University and Research MIUR project PRIN2008-CUP number C91J10000000001 (2008WKHJPK/002) for providing the financial support for this research.

Notes

LRT: Likelihood Ratio Test; ERLRT: Exact Restricted LRT; Boot: Bootstrap Test; Fitz: Fitzmaurice et al. (2007) Test; PT: our proposed Permutation Test.

LRT: Likelihood Ratio Test; ERLRT: Exact Restricted LRT; Boot: Bootstrap Test; Fitz: Fitzmaurice et al. (2007) Test; PT: our proposed Permutation Test.