cooks.distance.gnm {glmtoolbox}

Cook's Distance for Generalized Nonlinear Models

Description

Produces an approximation of the Cook's distance, better known as the one-step approximation, for measuring the effect of deleting each observation in turn on the estimates of the parameters in a linear predictor. Additionally, this function can produce an index plot of Cook's distance for all or a subset of the parameters in the linear predictor (via the argument coefs).

Usage

## S3 method for class 'gnm'
cooks.distance(model, plot.it = FALSE, dispersion = NULL, coefs, identify, ...)

Arguments

model

an object of class gnm.

plot.it

an (optional) logical indicating if the plot is required or just the data matrix in which that plot is based. As default, plot.it is set to FALSE.

dispersion

an (optional) value indicating the estimate of the dispersion parameter. As default, dispersion is set to summary(object)$dispersion.

coefs

an (optional) character string that matches (partially) some of the model parameter names.

identify

an (optional) integer indicating the number of individuals to identify on the plot of the Cook's distance. This is only appropriate if plot.it=TRUE.

...

further arguments passed to or from other methods. If plot.it=TRUE then ... may be used to include graphical parameters to customize the plot. For example, col, pch, cex, main, sub, xlab, ylab.

Details

The Cook's distance consists of the distance between two estimates of the parameters in the linear predictor using a metric based on the (estimate of the) variance-covariance matrix. The first one set of estimates is computed from a dataset including all individuals, and the second one is computed from a dataset in which the i-th individual is excluded. To avoid computational burden, the second set of estimates is replaced by its one-step approximation. See the dfbeta.overglm documentation.

Value

A matrix as many rows as individuals in the sample and one column with the values of the Cook's distance.

Examples

###### Example 1: The effects of fertilizers on coastal Bermuda grass
data(Grass)
fit1 <- gnm(Yield ~ b0 + b1/(Nitrogen + a1) + b2/(Phosphorus + a2) + b3/(Potassium + a3),
            family=gaussian(inverse), start=c(b0=0.1,b1=13,b2=1,b3=1,a1=45,a2=15,a3=30), data=Grass)

cooks.distance(fit1, plot.it=TRUE, col="red", lty=1, lwd=1,
  col.lab="blue", col.axis="blue", col.main="black", family="mono", cex=0.8)

###### Example 2: Assay of an Insecticide with a Synergist
data(Melanopus)
fit2 <- gnm(Killed/Exposed ~ b0 + b1*log(Insecticide-a1) + b2*Synergist/(a2 + Synergist),
            family=binomial(logit), weights=Exposed, start=c(b0=-3,b1=1.2,a1=1.7,b2=1.7,a2=2),
		   data=Melanopus)

### Cook's distance just for the parameter "b1"
cooks.distance(fit2, plot.it=TRUE, coef="b1", col="red", lty=1, lwd=1,
  col.lab="blue", col.axis="blue", col.main="black", family="mono", cex=0.8)

###### Example 3: Developmental rate of Drosophila melanogaster
data(Drosophila)
fit3 <- gnm(Duration ~ b0 + b1*Temp + b2/(Temp-a), family=Gamma(log),
            start=c(b0=3,b1=-0.25,b2=-210,a=55), weights=Size, data=Drosophila)

cooks.distance(fit3, plot.it=TRUE, col="red", lty=1, lwd=1,
  col.lab="blue", col.axis="blue", col.main="black", family="mono", cex=0.8)

###### Example 4: Radioimmunological Assay of Cortisol
data(Cortisol)
fit4 <- gnm(Y ~ b0 + (b1-b0)/(1 + exp(b2+ b3*lDose))^b4, family=Gamma(identity),
            start=c(b0=130,b1=2800,b2=3,b3=3,b4=0.5), data=Cortisol)

cooks.distance(fit4, plot.it=TRUE, col="red", lty=1, lwd=1,
  col.lab="blue", col.axis="blue", col.main="black", family="mono", cex=0.8)