Methods for constructing confidence intervals for variance component ratios in general unbalanced mixed models are developed. The methods are based on inverting the distribution of the signed root of the log‐likelihood ratio statistic constructed from either the restricted maximum likelihood or the full likelihood. As this distribution is intractable, the inversion is rather based on using a saddlepoint approximation to its distribution. Apart from Wald's exact method, the resulting intervals are unrivalled in terms of achieving accuracy in overall coverage, underage, and overage. Issues related to the proper “reference set” with which to judge the coverage as well as issues connected to variance ratios being nonnegative with lower bound 0 are addressed. Applications include an unbalanced nested design and an unbalanced crossed design.

中文翻译：

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不平衡线性混合模型中方差成分比率的置信区间

开发了在一般不平衡混合模型中构建方差分量比置信区间的方法。这些方法是基于对数似然比统计量的有符号根的分布进行反转的，该对数似然比统计量是从受限最大似然或完全似然构造的。由于这种分布是难处理的，因此反演是基于对它的分布使用鞍点近似进行的。除了Wald的精确方法外，在总体覆盖率，未成年人和超龄乘客的准确性方面，最终的间隔也是无与伦比的。解决了与用于判断覆盖率的正确“参考集”有关的问题，以及与下限为0的方差比非负相关的问题。应用包括不平衡的嵌套设计和不平衡的交叉设计。