Computes the Rights and Sterba (2019) integrative framework of R-squared measures for a fitted two-level linear mixed-effects (multilevel) model. The model implied outcome variance is fully decomposed into five sources: variance due to level-1 predictors via fixed slopes (\(f_1\)), level-2 predictors via fixed slopes (\(f_2\)), predictors via random slope (co)variation (\(v\)), cluster-specific outcome means via random intercept variation (\(m\)), and level-1 residuals (\(\sigma^2\)). Proportions of the total, within-cluster, and between-cluster outcome variance attributable to combinations of these sources give the family of R-squared measures.
R2_mixed_effects_decomposition(model)A data.frame (dmar_tbl) with columns term and
value. When the level-1 predictors are cluster-mean-centered, the
full set of 12 measures is returned, named total_f1, total_f2,
total_v, total_m, total_f, total_fv,
total_fvm, within_f1, within_v, within_fv,
between_f2, and between_m; otherwise the five total-variance
measures total_f, total_v, total_m, total_fv,
and total_fvm are returned (the within/between split requires
cluster-mean-centering). The returned object carries the source-by-target
variance decomposition in attr(x, "decomposition").
Ken Kelley [email protected]
The companion R2_mixed_effects returns the Nakagawa and
Schielzeth marginal and conditional R-squared; this function contains those
two as special cases (total_f and total_fvm) within the fuller
source decomposition.
The measure superscripts index the variance sources in the numerator and the
subscripts index the outcome variance in the denominator: total_* use
the total outcome variance, within_* the within-cluster variance
(\(f_1 + v + \sigma^2\)), and between_* the between-cluster variance
(\(f_2 + m\)). total_fvm is the omnibus measure (all explained
sources over the total variance) and, for a random-intercept model, coincides
with the Nakagawa and Schielzeth conditional R-squared computed by
R2_mixed_effects; total_f coincides with their marginal
R-squared. See Rights and Sterba (2019, Table 1) for the definitions.
The measures were derived under the assumption that the fitted model uses cluster-mean-centering of the level-1 predictors (with the cluster means entered as level-2 predictors). When that centering is not detected, only the total-variance measures are returned, matching the reference implementation.
Fitting the model requires lme4 (for a merMod fit) or nlme
(for an lme fit) to be installed.
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. tools:::Rd_expr_doi("10.1037/met0000184")
Nakagawa, S., & Schielzeth, H. (2013). A general and simple method for obtaining \(R^2\) from generalized linear mixed-effects models. Methods in Ecology and Evolution, 4(2), 133--142. tools:::Rd_expr_doi("10.1111/j.2041-210x.2012.00261.x")
R2_mixed_effects, icc_lmer
Other mixed models:
R2_mixed_effects(),
icc_lmer(),
manova_split_plot(),
mixed_anova(),
ss_aipe_mixed_effects(),
ss_aipe_mixed_effects_sensitivity(),
ss_power_mixed_effects(),
ss_power_split_plot_anova()
fit <- lme4::lmer(Reaction ~ Days + (Days | Subject),
data = lme4::sleepstudy)
R2_mixed_effects_decomposition(fit)
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