r2beta {r2glmm}

r2beta Compute R Squared for Mixed Models

Description

Computes coefficient of determination (R squared) from edwards et al., 2008 and the generalized R squared from Jaeger et al., 2016. Currently implemented for linear mixed models with lmer and lme objects. For generalized linear mixed models, only glmmPQL are supported.

Usage

r2beta(model, partial = TRUE, method = "sgv", data = NULL)

Arguments

model

a fitted mermod, lme, or glmmPQL model.

partial

if TRUE, semi-partial R squared are calculated for each fixed effect in the mixed model.

method

Specifies the method of computation for R squared beta: if method = 'sgv' then the standardized generalized variance approach is applied. This method is recommended for covariance model selection. if method = 'kr', then the Kenward Roger approach is applied. This option is only available for lme models. if method = 'nsj',then the Nakagawa and Schielzeth approach is applied. This option is available for lmer and lme objects. if method = 'lm', the classical R squared from the linear model is computed. This method should only be used on glm and lm object.

data

The data used by the fitted model. This argument is required for models with special expressions in their formula, such as offset, log, cbind(sucesses, trials), etc.

Value

A dataframe containing the model F statistic, numerator and denominator degrees of freedom, non-centrality parameter, and R squared statistic with 95 If partial = TRUE, then the dataframe also contains partial R squared statistics for all fixed effects in the model.

References

Edwards, Lloyd J., et al. "An R2 statistic for fixed effects in the linear mixed model." Statistics in medicine 27.29 (2008): 6137-6157.

Nakagawa, Shinichi, and Holger Schielzeth. "A general and simple method for obtaining R2 from generalized linear mixed effects models." Methods in Ecology and Evolution 4.2 (2013): 133-142.

Jaeger, Byron C., et al., "An R Squared Statistic for Fixed Effects in the Generalized Linear Mixed Model." Journal of Applied Statistics (2016).

Examples

library(nlme)
library(lme4)
data(Orthodont)

# Linear mixed models
mermod = lmer(distance ~ age*Sex + (1|Subject), data = Orthodont)
lmemod = lme(distance ~ age*Sex, random = ~1|Subject, data = Orthodont)

# The Kenward-Roger approach
r2beta(mermod, method = 'kr')

# Standardized Generalized Variance
r2beta(mermod, method = 'sgv')
r2beta(lmemod, method = 'sgv')

# The marginal R squared by Nakagawa and Schielzeth (extended by Johnson)
r2beta(mermod, method = 'nsj')

# linear and generalized linear models

library(datasets)
dis = data.frame(discoveries)
dis$year = 1:nrow(dis)

lmod = lm(discoveries ~ year + I(year^2), data = dis)
glmod = glm(discoveries ~ year + I(year^2), family = 'poisson', data = dis)

# Using an inappropriate link function (normal) leads to
# a poor fit relative to the poisson link function.

r2beta(lmod)
r2beta(glmod)

# PQL models
# Currently only SGV method is supported
library(MASS)
PQL_bac = glmmPQL(y ~ trt + I(week > 2), random = ~ 1 | ID,
                  family = binomial, data = bacteria,
                  verbose = FALSE)

r2beta(PQL_bac, method='sgv')