adjR2.gnm {glmtoolbox}

Adjusted R-squared in Generalized Nonlinear Models

Description

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

Usage

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

Arguments

...

one or several objects of the class gnm, which are obtained from the fit of generalized nonlinear 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.

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,

Examples

###### Example 1: The effects of fertilizers on coastal Bermuda grass
data(Grass)
fit1 <- gnm(Yield ~ b0 + b1/(Nitrogen + a1) + b2/(Phosphorus + a2) + b3/(Potassium + a3),
            family=gaussian(inverse), start=c(b0=0.1,b1=13,b2=1,b3=1,a1=45,a2=15,a3=30), data=Grass)
fit2 <- update(fit1, family=Gamma(inverse))
adjR2(fit1,fit2)

###### Example 2: Developmental rate of Drosophila melanogaster
data(Drosophila)
fit1 <- gnm(Duration ~ b0 + b1*Temp + b2/(Temp-a), family=Gamma(log),
            start=c(b0=3,b1=-0.25,b2=-210,a=55), weights=Size, data=Drosophila)
fit2 <- update(fit1, family=inverse.gaussian(log))
adjR2(fit1,fit2)

###### Example 3: Radioimmunological Assay of Cortisol
data(Cortisol)
fit1 <- gnm(Y ~ b0 + (b1-b0)/(1 + exp(b2+ b3*lDose))^b4, family=Gamma(identity),
            start=c(b0=130,b1=2800,b2=3,b3=3,b4=0.5), data=Cortisol)
fit2 <- update(fit1, family=gaussian(identity))
adjR2(fit1,fit2)

###### Example 4: Age and Eye Lens Weight of Rabbits in Australia
data(rabbits)
fit1 <- gnm(wlens ~ b1 - b2/(age + b3), family=Gamma(log),
            start=c(b1=5.5,b2=130,b3=35), data=rabbits)
fit2 <- update(fit1, family=gaussian(log))
adjR2(fit1,fit2)