nl_r2: Multilevel R-squared decomposition for nl_fit models

In MultiSpline: Spline-Based Nonlinear Modeling for Multilevel and Longitudinal Data

Multilevel R-squared decomposition for nl_fit models

Description

Computes a suite of R-squared statistics for models fitted by nl_fit. For single-level models the standard R-squared and adjusted R-squared are returned. For multilevel models (lmerMod / glmerMod) two quantities are reported: the Nakagawa-Schielzeth marginal R-squared (variance explained by fixed effects only) and the conditional R-squared (fixed plus all random effects), together with a level-specific variance partition table analogous to the r2_mlm / Raudenbush-Bryk approach.

Usage

nl_r2(object, digits = 4L)

Arguments

object	An nl_fit object returned by nl_fit.
digits	Integer; decimal places for display. Default 4.

Details

Marginal and conditional R-squared for LMMs follow the Nakagawa and Schielzeth (2013) formulae extended to multiple random effects by Nakagawa, Johnson and Schielzeth (2017). The fixed-effects variance \sigma^2_f is computed as the variance of the linear predictor from fixed effects only (\hat{\mu} = X\hat{\beta}).

The level-specific variance partition (r2_mlm-style) decomposes the total modelled variance (\sigma^2_f + \sum \sigma^2_j + \sigma^2_\epsilon) to show how much each source contributes, printed as a breakdown table.

Value

A list of class "nl_r2" returned invisibly and pretty-printed automatically. It contains type (one of "OLS", "GAM", "LMM", or "GLMM"), r2 (a named numeric vector: R2 and R2_adj for OLS; R2_dev for GAM; R2m and R2c for LMM/GLMM), and variance_partition (a data frame with columns component, variance, and proportion for multilevel models, or NULL for single-level models).

References

Nakagawa, S., & Schielzeth, H. (2013). A general and simple method for obtaining R-squared from generalized linear mixed-effects models. Methods in Ecology and Evolution, 4(2), 133–142.

Nakagawa, S., Johnson, P. C. D., & Schielzeth, H. (2017). The coefficient of determination R-squared and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded. Journal of the Royal Society Interface, 14(134), 20170213.

Rights, J. D., & Sterba, S. K. (2019). Quantifying explained variance in multilevel models: An integrative framework for defining R-squared measures. Psychological Methods, 24(3), 309–338.

See Also

nl_fit, nl_icc

MultiSpline documentation built on April 16, 2026, 9:06 a.m.