sjstats (version 0.10.2)

r2: Compute r-squared of (generalized) linear (mixed) models

Description

Compute R-squared values of linear (mixed) models, or pseudo-R-squared values for generalized linear (mixed) models.

Usage

r2(x, n = NULL)

Arguments

x

Fitted model of class lm, glm, lmerMod/lme or glmerMod.

n

Optional, a lmerMod object, representing the fitted null-model (unconditional model) to x. If n is given, the pseudo-r-squared for random intercept and random slope variances are computed (Kwok et al. 2008) as well as the Omega squared value (Xu 2003). See 'Examples' and 'Details'.

Value

• For linear models, the r-squared and adjusted r-squared values.

• For linear mixed models, the r-squared and Omega-squared values.

• For glm objects, Cox & Snell's and Nagelkerke's pseudo r-squared values.

• For glmerMod objects, Tjur's coefficient of determination.

Details

For linear models, the r-squared and adjusted r-squared value is returned, as provided by the summary-function.

For linear mixed models, an r-squared approximation by computing the correlation between the fitted and observed values, as suggested by Byrnes (2008), is returned as well as a simplified version of the Omega-squared value (1 - (residual variance / response variance), Xu (2003), Nakagawa, Schielzeth 2013), unless n is specified.

If n is given, for linear mixed models pseudo r-squared measures based on the variances of random intercept (tau 00, between-group-variance) and random slope (tau 11, random-slope-variance), as well as the r-squared statistics as proposed by Snijders and Bosker 2012 and the Omega-squared value (1 - (residual variance full model / residual variance null model)) as suggested by Xu (2003) are returned.

For generalized linear models, Cox & Snell's and Nagelkerke's pseudo r-squared values are returned.

For generalized linear mixed models, the coefficient of determination as suggested by Tjur (2009) (see also cod). Note that Tjur's D is restricted to models with binary response.

More ways to compute coefficients of determination are shown in this great GLMM faq. Furthermore, see r.squaredGLMM or rsquared for conditional and marginal r-squared values for GLMM's.

References

• DRAFT r-sig-mixed-models FAQ

• Byrnes, J. 2008. Re: Coefficient of determination (R^2) when using lme() (https://stat.ethz.ch/pipermail/r-sig-mixed-models/2008q2/000713.html)

• Kwok OM, Underhill AT, Berry JW, Luo W, Elliott TR, Yoon M. 2008. Analyzing Longitudinal Data with Multilevel Models: An Example with Individuals Living with Lower Extremity Intra-Articular Fractures. Rehabilitation Psychology 53(3): 370<U+2013>86. 10.1037/a0012765

• 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<U+2013>142. 10.1111/j.2041-210x.2012.00261.x

• Rabe-Hesketh S, Skrondal A. 2012. Multilevel and longitudinal modeling using Stata. 3rd ed. College Station, Tex: Stata Press Publication

• Raudenbush SW, Bryk AS. 2002. Hierarchical linear models: applications and data analysis methods. 2nd ed. Thousand Oaks: Sage Publications

• Snijders TAB, Bosker RJ. 2012. Multilevel analysis: an introduction to basic and advanced multilevel modeling. 2nd ed. Los Angeles: Sage

• Xu, R. 2003. Measuring explained variation in linear mixed effects models. Statist. Med. 22:3527-3541. 10.1002/sim.1572

• Tjur T. 2009. Coefficients of determination in logistic regression models - a new proposal: The coefficient of discrimination. The American Statistician, 63(4): 366-372

See Also

rmse for more methods to assess model quality.

Examples

# NOT RUN {
library(sjmisc)
library(lme4)
fit <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
r2(fit)

data(efc)
fit <- lm(barthtot ~ c160age + c12hour, data = efc)
r2(fit)

# Pseudo-R-squared values
efc$services <- ifelse(efc$tot_sc_e > 0, 1, 0)
fit <- glm(services ~ neg_c_7 + c161sex + e42dep,
           data = efc, family = binomial(link = "logit"))
r2(fit)

# Pseudo-R-squared values for random effect variances
fit <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
fit.null <- lmer(Reaction ~ 1 + (Days | Subject), sleepstudy)
r2(fit, fit.null)


# }