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Likelihood Ratio Tests in Linear Mixed Models with One Variance Component
Abstract
Summary: We consider the problem of testing null hypotheses that include restrictions on the variance component in a linear mixed model with one variance component and we derive the finite sample and asymptotic distribution of the likelihood ratio test and the restricted likelihood ratio test. The spectral representations of the likelihood ratio test and the restricted likelihood ratio test statistics are used as the basis of efficient simulation algorithms of their null distributions. The large sample χ2 mixture approximations using the usual asymptotic theory for a null hypothesis on the boundary of the parameter space have been shown to be poor in simulation studies. Our asymptotic calculations explain these empirical results. The theory of Self and Liang applies only to linear mixed models for which the data vector can be partitioned into a large number of independent and identically distributed subvectors. One-way analysis of variance and penalized splines models illustrate the results.
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Cites
Mixed-Effects Models in S and S-PLUS
(2001) · Technometrics · doi:10.1198/tech.2001.s574 · Cited by 9,278
Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems
Harville, D. A. (1977) · Journal of the American Statistical Association · doi:10.1080/01621459.1977.10480998 · Cited by 2,667
Searle, S. R., Casella, G., & McCulloch, C. E. (1992) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316856 · Cited by 1,926
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Tufford (2017) · doi:10.1007/s · Cited by 2,003
Zhao, N., Chen, J., Carroll, I. M., Ringel-Kulka, T., Epstein, M. P., Zhou, H., Zhou, J. J., Ringel, Y., Li, H., & Wu, M. C. (2015) · The American Journal of Human Genetics · doi:10.1016/j.ajhg.2015.04.003 · Cited by 306
Metadata
- Authors
- Crainiceanu, C. M., & Ruppert, D.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 2003-12-22
- Volume
- 66
- Issue
- 1
- Pages
- 165-185
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2051138734
- Cited by
- 445
- References
- 3
- FWCI
- 10.11
- Type
- journal article
- Language
- en
- Open access
- closed
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- Crainiceanu, C. M., & Ruppert, D. (2004). Likelihood Ratio Tests in Linear Mixed Models with One Variance Component. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.1467-9868.2004.00438.x
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