partR2: partitioning R² in generalized linear mixed models

Area of Science:

• Statistics
• Ecological Modeling
• Quantitative Biology

Background:

• The coefficient of determination (R²) measures variance explained by regression coefficients in linear models.
• R² is a crucial tool for variance decomposition, complementing repeatability (intra-class correlation) for random effects.
• Partitioning R² using semi-partial (part) R² and structure coefficients is challenging due to limited software availability.

Purpose of the Study:

• Introduce partR2, an R package for quantifying part R² for fixed effects in (generalized) linear mixed-effect models.
• Provide tools for detailed variance decomposition in complex statistical models.
• Facilitate the estimation of unique and total contributions of predictors.

Main Methods:

• The partR2 package iteratively removes predictors to assess changes in linear predictor variance.
• Estimates structure coefficients representing the correlation between predictors and fitted values.
• Implements parametric bootstrapping for confidence intervals of estimates.

Main Results:

• partR2 quantifies unique variance explained by individual or sets of fixed-effect predictors.
• Estimates structure coefficients and 'inclusive' R² for total predictor contribution.
• Provides beta weights and confidence intervals via bootstrapping.

Conclusions:

• partR2 offers a robust solution for variance partitioning in mixed-effects models.
• The package enhances the interpretability of complex statistical models by detailing predictor contributions.
• Demonstrates utility with Gaussian and binomial GLMMs, addressing challenges like interactions.