Journal
JOURNAL OF THE ROYAL SOCIETY INTERFACE
Volume 14, Issue 134, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsif.2017.0213
Keywords
repeatability; heritability; goodness of fit; model fit; variance decomposition; reliability analysis
Categories
Funding
- Australian Research Council Future Fellowship [FT130100268]
- UK BBSRC Zoonoses and Emerging Livestock Systems (ZELS) Initiative [BB/L018926/1]
- Emmy Noether fellowship from the German Research Foundation (DFG) [SCHI 1188/1-1]
- Biotechnology and Biological Sciences Research Council [BB/L018926/1] Funding Source: researchfish
Ask authors/readers for more resources
The coefficient of determination R-2 quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R-2 for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R-2 that we called R-2 GLMM for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs. In this paper, we generalize our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen's inequality has important implications for biologically meaningful interpretation of GLMMs, whereas the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked examples from the field of ecology and evolution in the R environment. However, our method can be used across disciplines and regardless of statistical environments.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available