Likelihood ratio tests in linear mixed models with one variance component
Likelihood ratio tests in linear mixed models with one variance component
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DOI：
10.1111/j.1467-9868.2004.00438.x
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发表时间：
2004-01-01
影响因子：
5.8
通讯作者：
Ruppert, D
中科院分区：
文献类型：
--
作者：
Crainiceanu, CM;Ruppert, D
本文研究了含有一个方差分量的线性混合模型中包含方差分量限制的原假设的检验问题，给出了似然比检验和限制似然比检验的有限样本和渐近分布。似然比检验统计量和限制似然比检验统计量的谱表示被用作其零分布的有效模拟算法的基础。在模拟研究中，对于参数空间边界上的零假设，使用通常的渐近理论的大样本χ（2）混合逼近已被证明是很差的。我们的渐近计算解释了这些经验结果。Self和Liang的理论仅适用于线性混合模型，其中数据向量可以划分为大量独立且同分布的子向量。单因素方差分析和惩罚样条模型说明了结果。
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 chi(2) 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.