partR2 {partR2}

Partitioning R2 (R-square) in mixed models

Description

R2, semi-partial (part) R2 for predictors and their combinations as well as inclusive R2, structure coefficients and beta weights for Gaussian, Poisson and binomial mixed models.

Usage

partR2(
  mod,
  partvars = NULL,
  data = NULL,
  R2_type = "marginal",
  max_level = NULL,
  nboot = NULL,
  CI = 0.95,
  parallel = FALSE,
  expct = "meanobs",
  olre = TRUE,
  partbatch = NULL,
  allow_neg_r2 = FALSE
)

Arguments

mod

Fitted lme4 model (a merMod object).

partvars

Character vector specifying the predictors (fixed effects) for which to partition the R2. Can be main effects like c("Var1", "Var2") and interactions ("Var1:Var2"). Predictors specified in partvars have to be named precisely like the terms in the formula to fit the model.

data

The data.frame used to fit the lme4 model. If not provided, partR2 will try to fetch it.

R2_type

"marginal" or "conditional" R2. With "marginal", the variance explained by fixed effects is calculated. With "conditional", the variance explained by both fixed and random effects is calculated.

max_level

Level up to which shared semi-partial R2s are calculated. The number of sets for which to calculate R2 increases exponentially, i.e. for 10 variables 2^10 - 1 R2s can be calculated. If you are only interested in the unique but not the shared effects, use max_level = 1. If interested in unique effects and combinations of two terms, use max_level = 2 etc.

nboot

Number of parametric bootstrap iterations for confidence interval estimation (defaults to NULL, i.e. no bootstrapping). Larger numbers of bootstraps give a better asymptotic CI, but may be time-consuming. Bootstrapping can be switched on by setting nboot = 1000.

CI

Width of the required confidence interval between 0 and 1 (defaults to 0.95).

parallel

If TRUE, computation uses future within furrr::map which allows parallelisation. However, it is necessary to specify a plan before running partR2(). To see which options you have, check ?future::plan and have a look at our vignette for details. When running RStudio, usually plan(multisession, workers = 4) is a good choice, when you want to use 4 cores. To detect how many cores you have, use parallel::detectCores(). If no plan is specified, partR2 will simply run sequentially.

expct

A string specifying the method for estimating the expectation in Poisson models with log link and in Binomial models with logit link (in all other cases the argument is ignored). The only valid terms are 'meanobs', 'latent', 'none' (and 'liability for binary and proportion data). With the default 'meanobs', the expectation is estimated as the mean of the observations in the sample. With 'latent', the expectation is estimated from estimates of the intercept and variances on the link scale. While this is a preferred solution, it is susceptible to the distribution of fixed effect covariates and gives appropriate results typically only when all covariances are centered to zero. With 'liability' estimates follow formulae as presented in Nakagawa & Schielzeth (2010). With 'none', R2 is calculated without distribution specific variance in the denominator.

olre

Logical, defaults to TRUE. This argument allows the user to prevent the automatic fitting of an observation level random effect (by setting it to FALSE) in Poisson and binomial models. The OLRE is used to account for overdispersion.

partbatch

List of character vectors with predictors that should be fitted and removed together. For example, partbatch = list(batch1 = c("V1", "V2", "V3"), batch2 = c("V4", "V5", "V6")) would calculate part R2 only for combinations of predictors which contain the variables V1, V2, V3 together or/and V4,V5,V6 together. This is useful when the number of potential subsets gets too large to be computationally practical, for example when dummy coding is used. See our vignette for details. This feature is still experimental and should be used with caution.

allow_neg_r2

Calculating part R2 involves fitting two models, one with and one without the predictor of interest. In cases where the predictor has little association with the response, the resulting part R2 value can become negative. By default we set negative values to 0, but by setting this parameter to TRUE, R2 values can become negative.

Value

Returns an object of class partR2 that is a a list with the following elements:

call

model call

R2_type

Marginal or conditional R2

R2

R2 and confidence intervals for full model and semi-partial R2 for predictors and their combinations

SC

Structure coefficients and confidence intervals. SC are the correlation between a predictor and the predicted response.

IR2

Inclusive R2. This is SC^2 * R2_full.

BW

Standardised model estimates (beta weights) for fixed effects. Beta weights for Gaussian models are calculated as beta * sd(x)/sd(y), with beta being the estimated slope of a fixed effect for predictor x and response y. Beta weight for Non-Gaussian models are calculated as beta * sd(x). Beta weights for interactions or polynomial terms are not informative at the moment and we recommend users to standardise variables themselves before fitting the model and to look at the model estimates (Ests) instead of beta weights (BW) in the partR2 output. See vignette for details.

Ests

Model estimates and confidence intervals.

R2_boot

Parametric bootstrap samples for R2 for full model and partitions

SC_boot

Parametric bootstrap samples for structure coefficients

IR2_boot

Parametric bootstrap samples for inclusive R2 values

BW_boot

Parametric bootstrap samples for beta weights

Ests_boot

Parametric bootstrap samples for model estimates

partvars

Predictors to partition

CI

Coverage of the confidence interval as specified by the CI argument.

boot_warnings

Potential warnings from estimating partial R2s during parametric bootstrapping

boot_message

Potential messages from estimating partial R2s during parametric bootstrapping. Common are for example singularity messages in lme4.

References

Nakagawa, S., & Schielzeth, H. (2013). A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution, 4(2), 133-142.

Nakagawa, S., Johnson, P. C., & Schielzeth, H. (2017). The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded. Journal of the Royal Society Interface, 14(134), 20170213.

Examples

data(biomass)
library(lme4)

# scale data
biomass[] <- lapply(biomass, function(x) if (is.double(x)) scale(x) else x)

# Gaussian data
mod <- lmer(Biomass ~ Year + Temperature + Precipitation + SpeciesDiversity + (1 | Population),
  data = biomass)

# R2
(R2_1 <- partR2(mod))

# R2 with CI
(R2_2 <- partR2(mod, R2_type = "marginal", nboot = 15, CI = 0.95))

# Part (semi-partial) R2s with CIs
(R2_3 <- partR2(mod,
  partvars = c("SpeciesDiversity", "Temperature", "Precipitation"),
  R2_type = "marginal", nboot = 10, CI = 0.95
))