rsq.partial: Partial R-Squared for Generalized Linear Models

In rsq: R-Squared and Related Measures

Partial R-Squared for Generalized Linear Models

Description

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

Usage

rsq.partial(objF,objR=NULL,adj=FALSE,type=c('v','kl','sse','lr','n'))

Arguments

objF	an object of class "lm" or "glm", a result of a call to lm, glm, or glm.nb to fit the full model.
objR	an object of class "lm" or "glm", a result of a call to lm, glm, or glm.nb to fit the reduced model.
adj	logical; if TRUE, calculate the adjusted partial 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.

Details

When the fitting object of the reduced model is not specified, the partial R^2 of each term in the model will be calculated.

Value

Returned values include adjustment and partial.rsq. When objR is not NULL, variable.full and variable.reduced are returned; otherwise variable is returned.

adjustment	logical; if TRUE, calculate the adjusted partial R^2.
variable.full	all covariates in the full model.
variable.reduced	all covariates in the reduced model.
variable	all covariates in the full model.
partial.rsq	partial R^2 or the adjusted partial R^2.

Author(s)

Dabao Zhang, Department of Statistics, Purdue University

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. (2017). A coefficient of determination for generalized linear models. The American Statistician, 71(4): 310-316.

See Also

rsq, pcor.

Examples

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

bnfitr <- glm(y~color+weight,family=binomial)
rsq.partial(bnfit,bnfitr)

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

quasibnr <- glm(y~color+weight,family=binomial)
rsq.partial(quasibn,quasibnr)

rsq documentation built on Oct. 22, 2023, 5:07 p.m.