Gilmour, Thompson, and Cullis (Biometrics, 1995, 51, 1440) presented the average information residual maximum likelihood (REML) algorithm for efficient variance parameter estimation in the linear mixed model. That paper dealt specifically with traditional variance component models, but the algorithm was quickly applied to more general models and implemented in several REML packages including ASReml (Gilmour et al., Biometrics, 2015, 51, 1440). This paper outlines the theory with respect to these more general models, describes the main issues encountered in fitting these models and how they have been addressed in the ASReml software. The issues covered are the basics steps in the implementation of the algorithm, keeping parameters within the parameter space, maximizing sparsity, avoiding issues associated with unstructured variance matrices by using the factor-analytic structure and handling singularities in marker-based relationship matrices and current work.

中文翻译：

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实践中的平均信息残差最大似然

Gilmour、Thompson 和 Cullis (Biometrics, 1995, 51, 1440) 提出了用于线性混合模型中有效方差参数估计的平均信息残差最大似然 (REML) 算法。该论文专门处理传统的方差分量模型，但该算法很快应用于更通用的模型，并在包括 ASReml 在内的几个 REML 包中实现（Gilmour 等人，Biometrics，2015, 51, 1440）。本文概述了关于这些更一般模型的理论，描述了拟合这些模型时遇到的主要问题，以及如何在 ASReml 软件中解决这些问题。涵盖的问题是算法实现的基本步骤，将参数保持在参数空间内，最大化稀疏性，