Compute Goodness-of-fit measures for various regression models, including mixed and Bayesian regression models.
cod(x)r2(x, ...)
# S3 method for lme
r2(x, n = NULL, ...)
# S3 method for stanreg
r2(x, loo = FALSE, ...)
# S3 method for brmsfit
r2(x, loo = FALSE, ...)
Fitted model of class lm, glm, merMod,
glmmTMB, lme, plm, stanreg or brmsfit.
For method cod(), only a glm with binrary response.
Currently not used.
Optional, an lme 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'.
Logical, if TRUE and x is a stanreg or
brmsfit object, a LOO-adjusted r-squared is calculated. Else,
a rather "unadjusted" r-squared will be returned by calling
rstantools::bayes_R2().
For r2(), depending on the model, returns:
For linear models, the r-squared and adjusted r-squared values.
For mixed models, the marginal and conditional r-squared values.
For glm objects, Cox & Snell's and Nagelkerke's pseudo r-squared values.
For brmsfit or stanreg objects, the Bayesian version of r-squared is computed, calling rstantools::bayes_R2().
If loo = TRUE, for brmsfit or stanreg objects a LOO-adjusted version of r-squared is returned.
Models that are not currently supported return NULL.
For cod(), returns the D Coefficient of Discrimination,
also known as Tjur's R-squared value.
For linear models, the r-squared and adjusted r-squared value is returned,
as provided by the summary-function.
For mixed models (from lme4 or glmmTMB) marginal and
conditional r-squared values are calculated, based on
Nakagawa et al. 2017. The distributional variance
(or observation-level variance) is based on lognormal approximation,
log(1+var(x)/mu^2).
For lme-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 lme-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.
The ("unadjusted") r-squared value and its standard error for
brmsfit or stanreg objects are robust measures, i.e.
the median is used to compute r-squared, and the median absolute
deviation as the measure of variability. If loo = TRUE,
a LOO-adjusted r-squared is calculated, which comes conceptionally
closer to an adjusted r-squared measure.
Bolker B et al. (2017): GLMM 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): 370-86. 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):133-142. 10.1111/j.2041-210x.2012.00261.x
Nakagawa S, Johnson P, Schielzeth H (2017) The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisted and expanded. J. R. Soc. Interface 14. 10.1098/rsif.2017.0213
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
# NOT RUN {
data(efc)
# Tjur's R-squared value
efc$services <- ifelse(efc$tot_sc_e > 0, 1, 0)
fit <- glm(services ~ neg_c_7 + c161sex + e42dep,
data = efc, family = binomial(link = "logit"))
cod(fit)
library(lme4)
fit <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
r2(fit)
fit <- lm(barthtot ~ c160age + c12hour, data = efc)
r2(fit)
# Pseudo-R-squared values
fit <- glm(services ~ neg_c_7 + c161sex + e42dep,
data = efc, family = binomial(link = "logit"))
r2(fit)
# }
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