A general and simple method for obtaining R 2 from generalized linear mixed‐effects models

作者：Shinichi Nakagawa, Holger Schielzeth · 发表于：Methods in Ecology and Evolution · 年份：2012 · DOI：10.1111/j.2041-210x.2012.00261.x · 被引用次数：10490 · 研究领域：Plant and animal studies、Ecology and Vegetation Dynamics Studies、Animal Behavior and Reproduction

Summary The use of both linear and generalized linear mixed‐effects models ( LMM s and GLMM s) 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’ ( R 2 ) as a relevant summarizing statistic of mixed‐effects models, however, is rare, even though R 2 is routinely reported for linear models ( LM s) and also generalized linear models ( GLM s). R 2 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, R 2 can also be a quantity of biological interest. One reason for the under‐appreciation of R 2 for mixed‐effects models lies in the fact that R 2 can be defined in a number of ways. Furthermore, most definitions of R 2 for mixed‐effects have theoretical problems (e.g. decreased or negative R 2 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 R 2 for mixed‐effects models. We first provide the common definitions of R 2 for LM s and GLM s and discuss the key problems associated with calculating R 2 for mixed‐effects models. We then recommend a ...