glmtoolbox (version 0.1.12)

adjR2.glm: Adjusted R-squared in Generalized Linear Models

Description

Computes the adjusted deviance-based R-squared in generalized linear models.

Usage

# S3 method for glm
adjR2(..., digits = max(3, getOption("digits") - 2), verbose = TRUE)

Value

a matrix with the following columns

Deviance	value of the residual deviance,
R-squared	value of the deviance-based R-squared,
df	number of parameters in the linear predictor,
adj.R-squared	value of the adjusted deviance-based R-squared,

Arguments

...

one or several objects of the class glm, which are obtained from the fit of generalized linear models.

digits

an (optional) integer value indicating the number of decimal places to be used. As default, digits is set to max(3, getOption("digits") - 2).

verbose

an (optional) logical indicating if should the report of results be printed. As default, verbose is set to TRUE.

Details

The deviance-based R-squared is computed as \(R^2=1 - Deviance/Null.Deviance\). Then, the adjusted deviance-based R-squared is computed as \(1 - \frac{n-1}{n-p}(1-R^2)\), where \(p\) is the number of parameters in the linear predictor and \(n\) is the sample size.

Examples

###### Example 1: Fuel efficiency of cars
Auto <- ISLR::Auto
fit1 <- glm(mpg ~ horsepower*weight, family=Gamma(inverse), data=Auto)
fit2 <- update(fit1, formula=mpg ~ horsepower*weight*cylinders)
fit3 <- update(fit1, family=Gamma(log))
fit4 <- update(fit2, family=Gamma(log))
fit5 <- update(fit1, family=inverse.gaussian(log))
fit6 <- update(fit2, family=inverse.gaussian(log))

AIC(fit1,fit2,fit3,fit4,fit5,fit6)
BIC(fit1,fit2,fit3,fit4,fit5,fit6)
adjR2(fit1,fit2,fit3,fit4,fit5,fit6)