rsq (version 2.7)

vresidual: Variance-Function-Based Residuals

Description

Calculate the variance-function-based residuals for generalized linear models, which are used to calculate the variance-function-based R-squared.

Usage

vresidual(y,yfit,family=binomial(),variance=NULL)

Value

Variance-function-based residuals.

Arguments

y

a vector of observed values.

yfit

a vector of fitted values.

family

family of the distribution.

variance

variance function (specified by family by default).

Author

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

Details

The calcualted residual relies on the variance function, and is well-defined for quasi models. It reduces to the classical residual when the variance function is constant or linear. Note that only the variance function is required to specify, via either "family"" or "variance".

References

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

See Also

rsq.v, rsq.

Examples

data(hcrabs)
attach(hcrabs)
y <- ifelse(num.satellites>0,1,0)
bnfit <- glm(y~color+spine+width+weight,family="binomial")
vresidual(y,bnfit$fitted.values,family="binomial")

# 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")
yfit <- cbind(tbn$fitted.values, 1-tbn$fitted.values)
vr0 <- vresidual(matrix(0,2,1),yfit[,1],family="binomial")
vr1 <- vresidual(matrix(1,2,1),yfit[,2],family="binomial")
y[,1]*vr0+y[,2]*vr1