Likelihood Ratio Tests in Linear Mixed Models with One Variance Component
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- 22 December 2003
- journal article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 66 (1) , 165-185
- https://doi.org/10.1111/j.1467-9868.2004.00438.x
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.Keywords
This publication has 20 references indexed in Scilit:
- Selecting the Number of Knots for Penalized SplinesJournal of Computational and Graphical Statistics, 2002
- Selecting the Number of Knots for Penalized SplinesJournal of Computational and Graphical Statistics, 2002
- Degrees-of-freedom tests for smoothing splinesBiometrika, 2002
- ASYMPTOTICS OF ML ESTIMATOR FOR REGRESSION MODELS WITH A STOCHASTIC TREND COMPONENTEconometric Theory, 1999
- Maximum Likelihood Estimation of Regression Models with Stochastic Trend ComponentsJournal of the American Statistical Association, 1993
- ON THE PROBABILITY OF ESTIMATING A DETERMINISTIC COMPONENT IN THE LOCAL LEVEL MODELJournal of Time Series Analysis, 1990
- Locally Weighted Regression: An Approach to Regression Analysis by Local FittingJournal of the American Statistical Association, 1988
- Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard ConditionsJournal of the American Statistical Association, 1987
- Maximum Likelihood Approaches to Variance Component Estimation and to Related ProblemsJournal of the American Statistical Association, 1977
- Recovery of inter-block information when block sizes are unequalBiometrika, 1971