Compute R squared — r2 • lvmisc

Returns the R squared values according to the model class.

r2(model)

# S3 method for default
r2(model)

# S3 method for lm
r2(model)

# S3 method for lmerMod
r2(model)

Arguments

model	An object containing a model.

Value

If the model is a linear model, it returns a data.frame with the R squared and adjusted R squared values. If the model is a linear mixed model it return a data.frame with the marginal and conditional R squared values as described by Nakagawa and Schielzeth (2013). See the formulas for the computations in "Details".

Details

R squared computations.

R squared

$$R^2 = \frac{var(\hat{y})}{var(\epsilon)}$$ Where $var(\hat{y})$ is the variance explained by the model and $var(\epsilon)$ is the residual variance.

Adjusted R squared

$$R_{adj}^{2} = 1 - (1 - R^2)\frac{n - 1}{n - p - 1}$$ Where $n$ is the number of data points and $p$ is the number of predictors in the model.

Marginal R squared

$$R_{marg}^{2} = \frac{var(f)}{var(f) + var(r) + var(\epsilon)}$$ Where $var(f)$ is the variance of the fixed effects, $var(r)$ is the variance of the random effects and $var(\epsilon)$ is the residual variance.

Conditional R squared

$$R_{cond}^{2} = \frac{var(f) + var(r)}{var(f) + var(r) + var(\epsilon)}$$

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. doi: 10.1111/j.2041-210x.2012.00261.x .

Examples

m1 <- lm(Sepal.Length ~ Species, data = iris)
r2(m1)
#>          R2    R2_adj
#> 1 0.6187057 0.6135181
if (require(lme4, quietly = TRUE)) {
  m2 <- lmer(
    Sepal.Length ~ Sepal.Width + Petal.Length + (1 | Species), data = iris
  )
  r2(m2)
}
#>     R2_marg   R2_cond
#> 1 0.7437646 0.9541472