A general and simple method for obtaining R2 from generalized linear mixed-effects models
A general and simple method for obtaining R2 from generalized linear mixed-effects models
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DOI：
10.1111/j.2041-210x.2012.00261.x
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发表时间：
2013-02-01
影响因子：
6.6
通讯作者：
Schielzeth, Holger
中科院分区：
文献类型：
--
作者：
Nakagawa, Shinichi;Schielzeth, Holger
线性和广义线性混合效应模型（LIFE和GLIFE）的使用不仅在社会科学和医学科学中，而且在生物科学中，特别是在生态学和进化领域中，都很流行。信息准则，如赤池信息准则（AIC），通常作为混合效应模型的模型比较工具。然而，将方差解释（R2）作为混合效应模型的相关汇总统计量的呈现是罕见的，尽管R2通常用于线性模型（LM）和广义线性模型（GLM）。R2具有为模型的拟合优度提供绝对值的极其有用的性质，这不能由信息准则给出。作为描述解释的方差量的汇总统计量，R2也可以是生物学感兴趣的量。R2在混合效应模型中被低估的一个原因在于，R2可以以多种方式定义。此外，大多数混合效应的R2定义都存在理论问题（例如，在较大的模型中R2值降低或为负值），并且/或者它们的使用受到实际困难（例如，实施）的阻碍。在这里，我们说明了报告混合效应模型R2的重要性。我们首先提供LM和GLM的R2的常见定义，并讨论与计算混合效应模型的R2相关的关键问题。然后，我们建议一个通用的和简单的方法来计算两种类型的R2（边际和条件R2）的Lingdom和GLingdom，这是不太容易受到常见的问题。这种方法是由例子说明，并可以广泛采用的研究人员在任何研究领域，无论用于拟合混合效应模型的软件包。所提出的方法有可能促进R2的介绍范围广泛的情况。
The use of both linear and generalized linear mixed-effects models (LMMs and GLMMs) has become popular not only in social and medical sciences, but also in biological sciences, especially in the field of ecology and evolution. Information criteria, such as Akaike Information Criterion (AIC), are usually presented as model comparison tools for mixed-effects models. The presentation of variance explained' (R2) as a relevant summarizing statistic of mixed-effects models, however, is rare, even though R2 is routinely reported for linear models (LMs) and also generalized linear models (GLMs). R2 has the extremely useful property of providing an absolute value for the goodness-of-fit of a model, which cannot be given by the information criteria. As a summary statistic that describes the amount of variance explained, R2 can also be a quantity of biological interest. One reason for the under-appreciation of R2 for mixed-effects models lies in the fact that R2 can be defined in a number of ways. Furthermore, most definitions of R2 for mixed-effects have theoretical problems (e.g. decreased or negative R2 values in larger models) and/or their use is hindered by practical difficulties (e.g. implementation). Here, we make a case for the importance of reporting R2 for mixed-effects models. We first provide the common definitions of R2 for LMs and GLMs and discuss the key problems associated with calculating R2 for mixed-effects models. We then recommend a general and simple method for calculating two types of R2 (marginal and conditional R2) for both LMMs and GLMMs, which are less susceptible to common problems. This method is illustrated by examples and can be widely employed by researchers in any fields of research, regardless of software packages used for fitting mixed-effects models. The proposed method has the potential to facilitate the presentation of R2 for a wide range of circumstances.