Testing variance components in balanced linear growth curve models

Abstract

It is well known that the testing of zero variance components is a non-standard problem since the null hypothesis is on the boundary of the parameter space. The usual asymptotic chi-square distribution of the likelihood ratio and score statistics under the null does not necessarily hold because of this null hypothesis. To circumvent this difficulty in balanced linear growth curve models, we introduce an appropriate test statistic and suggest a permutation procedure to approximate its finite-sample distribution. The proposed test alleviates the necessity of any distributional assumptions for the random effects and errors and can easily be applied for testing multiple variance components. Our simulation studies show that the proposed test has Type I error rate close to the nominal level. The power of the proposed test is also compared with the likelihood ratio test in the simulations. An application on data from an orthodontic study is presented and discussed.

Keywords:

• balanced linear growth curve model
• efficiency
• likelihood ratio
• linear mixed effects model
• permutation test
• variance components

Acknowledgements

R.D. would like to thank Professor M. Asgharian and the Department of Mathematics and Statistics, McGill University for their hospitality. His research was partially funded by Prof. Asgharian through his research grant from NSERC, Canada. The authors are grateful to the editor and the referees for their helpful comments which significantly improved the presentation of the paper.