标题： 线性混合模型的符号公式 显示英文标题

标题： Symbolic Formulae for Linear Mixed Models

摘要： 统计模型是对一个通常被简化或理想化的数据生成过程的数学表示。 在本文中，我们关注一种特定类型的统计模型，称为线性混合模型（LMMs），它在许多学科中被广泛使用，例如农业、生态学、计量经济学和心理学。 混合模型也常被称为多级、嵌套、分层或面板数据模型，它们结合了固定效应和随机效应，而LMMs是其中的一个特例。 特别是随机效应的引入，使LMMs在解释数据中常见的各种复杂相关结构方面具有相当大的灵活性。 然而，这种灵活性也导致了多种方式，使得最终用户可以在统计软件中指定他们希望拟合的LMM的确切形式。 在本文中，我们回顾了LMM（以及其特例，线性模型）的软件设计，特别关注高级符号模型公式以及lme4和asreml这两个流行但对比鲜明的R包的使用。 显示英文摘要

摘要： A statistical model is a mathematical representation of an often simplified or idealised data-generating process. In this paper, we focus on a particular type of statistical model, called linear mixed models (LMMs), that is widely used in many disciplines e.g.~agriculture, ecology, econometrics, psychology. Mixed models, also commonly known as multi-level, nested, hierarchical or panel data models, incorporate a combination of fixed and random effects, with LMMs being a special case. The inclusion of random effects in particular gives LMMs considerable flexibility in accounting for many types of complex correlated structures often found in data. This flexibility, however, has given rise to a number of ways by which an end-user can specify the precise form of the LMM that they wish to fit in statistical software. In this paper, we review the software design for specification of the LMM (and its special case, the linear model), focusing in particular on the use of high-level symbolic model formulae and two popular but contrasting R-packages in lme4 and asreml.