A central point of disagreement, in certain long-standing discussions about a particular whaling dataset in the Scientific Committee of the International Whaling Commission, has directly involved model selection issues for linear mixed effect models. The biological question under discussion is associated with a clearly defined parameter of primary interest, a focus parameter, which makes model selection with the Focused Information Criterion (FIC) more appropriate than other selection methods. Since the existing FIC methodology has not covered the case of linear mixed effects models, this article sets up the required framework and develops the necessary formulae for the relevant FIC. Our new criterion requires the asymptotic distribution of estimators derived for a given candidate linear mixed model but with behaviour examined under a wider linear mixed model. These results, needed here to build our FIC, also have independent interest.

中文翻译：

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线性混合模型的聚焦模型选择及其在鲸鱼生态学中的应用

在国际捕鲸委员会科学委员会关于特定捕鲸数据集的某些长期讨论中，分歧的中心点直接涉及线性混合效应模型的模型选择问题。所讨论的生物学问题与一个明确定义的主要关注参数（焦点参数）相关联，这使使用焦点信息标准（FIC）进行的模型选择比其他选择方法更合适。由于现有的FIC方法尚未涵盖线性混合效应模型的情况，因此本文建立了所需的框架并为相关的FIC开发了必要的公式。我们的新标准要求为给定的候选线性混合模型导出估计量的渐近分布，但在更广泛的线性混合模型下检查行为。建立FIC所需的这些结果也具有独立利益。