rptR: repeatability estimation and variance decomposition by generalized linear mixed‐effects models

• Published in: Methods in ecology and evolution Vol. 8; no. 11; pp. 1639 - 1644
• Main Authors: Stoffel, Martin A., Nakagawa, Shinichi, Schielzeth, Holger, Goslee, Sarah
• Format: Journal Article
• Language: English
• Published: London John Wiley & Sons, Inc 01-11-2017
• Subjects: animal personality; Biological effects; coefficient of determination; generalized linear mixed‐effects models; Generalized linear models; Likelihood ratio; Mathematical models; nonparametric bootstrapping; Nonparametric statistics; Reproducibility; software application; Statistical analysis; Statistical models; Statistical significance; Uncertainty; Variance; variance component analysis
• ISSN: 2041-210X; 2041-210X
• DOI: 10.1111/2041-210X.12797

Summary
Intra‐class correlations (ICC) and repeatabilities (R) are fundamental statistics for quantifying the reproducibility of measurements and for understanding the structure of biological variation. Linear mixed effects models offer a versatile framework for estimating ICC and R. However, while point estimation and significance testing by likelihood ratio tests is straightforward, the quantification of uncertainty is not as easily achieved.
A further complication arises when the analysis is conducted on data with non‐Gaussian distributions because the separation of the mean and the variance is less clear‐cut for non‐Gaussian than for Gaussian models. Nonetheless, there are solutions to approximate repeatability for the most widely used families of generalized linear mixed models (GLMMs).
Here, we introduce the R package rptR for the estimation of ICC and R for Gaussian, binomial and Poisson‐distributed data. Uncertainty in estimators is quantified by parametric bootstrapping and significance testing is implemented by likelihood ratio tests and through permutation of residuals. The package allows control for fixed effects and thus the estimation of adjusted repeatabilities (that remove fixed effect variance from the estimate) and enhanced agreement repeatabilities (that add fixed effect variance to the denominator). Furthermore, repeatability can be estimated from random‐slope models. The package features convenient summary and plotting functions.
Besides repeatabilities, the package also allows the quantification of coefficients of determination R2 as well as of raw variance components. We present an example analysis to demonstrate the core features and discuss some of the limitations of rptR.