rsq.lr {rsq}

Likelihood-Ratio-Based R-Squared

Description

Calculate the likelihood-ratio-based R^2 for generalized linear models.

Usage

rsq.lr(fitObj,adj=FALSE)

Arguments

fitObj

an object of class "lm" or "glm", usually, a result of a call to lm, glm, or glm.nb.

adj

logical; if TRUE, calculate the adjusted R^2.

Details

Proposed by Maddala (1983), Cox and Snell (1989), and Magee (1990), this version of R^2 is defined with the likelihood ratio statistics, so it is not defined for quasi models. It reduces to the classical R^2 when the variance function is constant or linear.

Value

The R^2 or adjusted R^2.

Author(s)

Dabao Zhang, Department of Statistics, Purdue University

References

Cox, D. R. and Snell, E. J. (1989) The Analysis of Binary Data, 2nd ed. London: Chapman and Hall.

Maddala, G. S. (1983) Limited-Dependent and Qualitative Variables in Econometrics. Cambridge University.

Magee, L. (1990) R^2 measures based on Wald and likelihood ratio joint significance tests. The American Statistician, 44: 250-253.

See Also

rsq, rsq.partial, pcor, rsq.n.

Examples

data(hcrabs)
attach(hcrabs)
y <- ifelse(num.satellites>0,1,0)
bnfit <- glm(y~color+spine+width+weight,family=binomial)
rsq.lr(bnfit)
rsq.lr(bnfit,adj=TRUE)

psfit <- glm(num.satellites~color+spine+width+weight,family=poisson)
rsq.lr(psfit)
rsq.lr(psfit,adj=TRUE)

# Effectiveness of Bycycle Safety Helmets in Thompson et al. (1989)
y <- matrix(c(17,218,233,758),2,2)
x <- factor(c("yes","no"))
tbn <- glm(y~x,family=binomial)
rsq.lr(tbn)
rsq.lr(tbn,adj=TRUE)