rsq (version 1.1)

rsq: R-Squared for Generalized Linear Models

Description

Calculate the coefficient of determination, aka R^2, for both linear and generalized linear models.

Usage

rsq(fitObj,adj=FALSE,type=c('v','kl','sse','lr','n'),data=NULL)

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.

type

the type of R-squared:

'v' (default) -- variance-function-based (Zhang, 2016), calling rsq.v;

'kl' -- KL-divergence-based (Cameron and Windmeijer, 1997), calling rsq.kl;

'sse' -- SSE-based (Efron, 1978), calling rsq.sse;

'lr' -- likelihood-ratio-based (Maddala, 1983; Cox and Snell, 1989; Magee, 1990), calling rsq.lr;

'n' -- corrected version of 'lr' (Nagelkerke, 1991), calling rsq.n.

data

an optional data frame used by fitObj.

Value

The R^2 or adjusted R^2.

Details

Calculate the R-squared for (generalized) linear models.

References

Cameron, A. C. and Windmeijer, A. G. (1997) An R-squared measure of goodness of fit for some common nonlinear regression models. Journal of Econometrics, 77: 329-342.

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

Efron, B. (1978) Regression and ANOVA with zero-one data: measures of residual variation. Journal of the American Statistical Association, 73: 113-121.

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.

Nagelkerke, N. J. D. (1991) A note on a general definition of the coefficient of determination. Biometrika, 78: 691-692.

Zhang, D. (2016). A coefficient of determination for generalized linear models. The American Statistician, accepted. <http://dx.doi.org/10.1080/00031305.2016.1256839>.

See Also

rsq.partial,pcor,simglm.

Examples

# NOT RUN {
data(hcrabs)
attach(hcrabs)
y <- ifelse(num.satellites>0,1,0)
bnfit <- glm(y~color+spine+width+weight,family=binomial)
rsq(bnfit)
rsq(bnfit,adj=TRUE)

quasibn <- glm(y~color+spine+width+weight,family=quasibinomial)
rsq(quasibn)
rsq(quasibn,adj=TRUE)

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

quasips <- glm(num.satellites~color+spine+width+weight,family=quasipoisson)
rsq(quasips)
rsq(quasips,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(tbn)
rsq(tbn,adj=TRUE)
# }