rsq (version 2.7)

rsq.partial: 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'))

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.

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, 2017), 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.

Author

Dabao Zhang, Department of Epidemiology and Biostatistics, University of California, Irvine

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.

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)