partR2: partitioning R²in generalized linear mixed models

Abstract

The coefficient of determination R2 quantifies the amount of variance explained by regression coefficients in a linear model. It can be seen as the fixed-effects complement to the repeatability R (intra-class correlation) for the variance explained by random effects and thus as a tool for variance decomposition. The R2 of a model can be further partitioned into the variance explained by a particular predictor or a combination of predictors using semi-partial (part) R2 and structure coefficients, but this is rarely done due to a lack of software implementing these statistics. Here, we introduce partR2, an R package that quantifies part R2 for fixed effect predictors based on (generalized) linear mixed-effect model fits. The package iteratively removes predictors of interest from the model and monitors the change in the variance of the linear predictor. The difference to the full model gives a measure of the amount of variance explained uniquely by a particular predictor or a set of predictors. partR2 also estimates structure coefficients as the correlation between a predictor and fitted values, which provide an estimate of the total contribution of a fixed effect to the overall prediction, independent of other predictors. Structure coefficients can be converted to the total variance explained by a predictor, here called ‘inclusive’ R2, as the square of the structure coefficients times total R2. Furthermore, the package reports beta weights (standardized regression coefficients). Finally, partR2 implements parametric bootstrapping to quantify confidence intervals for each estimate. We illustrate the use of partR2 with real example datasets for Gaussian and binomial GLMMs and discuss interactions, which pose a specific challenge for partitioning the explained variance among predictors.

Paternal care effects outweigh gamete-mediated and personal environment effects during the transgenerational estimation of risk in fathead minnows

“…All analyses were conducted with R 4.0.3 [ 103 ], accompanied by the packages lme4 1.1-26 [ 104 ], lmerTest 3.1-3 [ 105 ], emmeans 1.5.4 [ 106 ], effsize 0.8.1 [ 107 ] and partR2 0.9.1 [ 108 ]. We applied linear mixed-effect models with family identity as a random intercept using maximum likelihood parameter estimation throughout; full models were then subject to stepwise reduction using backward elimination procedures with Satterthwaite approximations (retaining random factors) until only significant fixed effects remained in final models.…”

Genetic coupling of life-history and aerobic performance in Atlantic salmon

“…One outlier was identified and removed from each of SMR and MMR (using outlierTest in package car, Bonferroni-corrected p < 0.05). The proportion of variance explained by genotypes was calculated with partR2 68 . Predicted means were obtained with ggpredict in package ggeffects 69 .…”

A hydrological model skill score and revised R-squared

“…It is intuitive that the acceptability of model predictability is synonymous with the model's performance or quality. In this line, there is a large number of recent studies which has focused on metrics for assessing model performance and examples of the relevant papers include Bai et al (2021), Clark et al (2021), Stoffel et al (2021), Ye et al (2021), Lamontagne et al (2020), Liu (2020), Barber et al (2019), Jackson et al (2019), Mizukami et al (2019), Rose & McGuire (2019), Towner et al (2019, Pool et al (2018), Lin et al (2017) and Jie et al (2016). Due to efforts in improving how to judge model performance, several 'goodness-of-fit' metrics exist in the literature.…”