glmtoolbox (version 0.1.12)

localInfluence.gnm: Local Influence for Generalized Nonlinear Models

Description

Computes some measures and, optionally, display graphs of them to perform influence analysis based on the approaches described by Cook (1986).

Usage

# S3 method for gnm
localInfluence(
  object,
  type = c("total", "local"),
  perturbation = c("case-weight", "response"),
  coefs,
  plot.it = FALSE,
  identify,
  ...
)

Value

A matrix as many rows as observations in the sample and one column with the values of the measures of local influence.

Arguments

object

an object of class gnm.

type

an (optional) character string indicating the type of approach to study the local influence. The options are: the absolute value of the elements of the eigenvector which corresponds to the maximum absolute eigenvalue ("local"); and the absolute value of the elements of the main diagonal ("total"). As default, type is set to "total".

perturbation

an (optional) character string indicating the perturbation scheme to apply. The options are: case weight perturbation of observations ("case-weight") and perturbation of response ("response"). As default, perturbation is set to "case-weight".

coefs

an (optional) character string which (partially) match with the names of some of the parameters in the 'linear' predictor.

plot.it

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

identify

an (optional) integer indicating the number of observations to identify on the plot of the measures of local influence. 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.

References

Cook D. (1986) Assessment of Local Influence. Journal of the Royal Statistical Society: Series B (Methodological) 48, 133-155.

Thomas W., Cook D. (1989) Assessing Influence on Regression Coefficients in Generalized Linear Models. Biometrika 76, 741-749.

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)

localInfluence(fit1, type="local", perturbation="case-weight", plot.it=TRUE, col="red",
               lty=1, lwd=1, col.lab="blue", col.axis="blue", col.main="black", family="mono")

###### 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)

### Local Influence just for the parameter "b1"
localInfluence(fit2, type="local", perturbation="case-weight", plot.it=TRUE, coefs="b1", col="red",
               lty=1, lwd=1, col.lab="blue", col.axis="blue", col.main="black", family="mono")

###### 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)

localInfluence(fit3, type="total", perturbation="case-weight", plot.it=TRUE, col="red",
               lty=1, lwd=1, col.lab="blue", col.axis="blue", col.main="black", family="mono")

###### 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)

localInfluence(fit4, type="total", perturbation="case-weight", plot.it=TRUE, col="red",
               lty=1, lwd=1, col.lab="blue", col.axis="blue", col.main="black", family="mono")