Outline an approximate pairwise confidence region

This function produces the ellipsoidal outline of an approximate pairwise confidence region for a generalized linear model fit.

Usage

# S3 method for glm
ellipse(x, which = c(1, 2), level = 0.95, t, npoints = 100, 
        dispersion, ...)

Arguments

x: The first argument should be a glm object, usually resulting from a call to glm().
which: Which selects the pair of parameters to be plotted. The default is the first two.
level: The confidence level of the region. Default 95%.
t: The t statistic on the boundary of the ellipse. For Binomial or Poisson families, sqrt(qchisq(level, 2)) is used; for other distributions, sqrt(2*qf(level, 2, df)) where df is the residual degrees of freedom.
npoints: How many points to return in the ellipse.
dispersion: The value of dispersion to use. If specified, it is treated as fixed, and the chi-square limits for t are used. If missing, it is taken from summary(x).
...: Other ellipse.default parameters may also be used.

Value

A matrix with columns named according to which to outline the confidence region.

Details

The summary function is used to obtain the approximate covariance matrix of the fitted parameters, the dispersion estimate, and the degrees of freedom.

Examples

## Dobson (1990) Page 93: Randomized Controlled Trial :

     counts <- c(18,17,15,20,10,20,25,13,12)
     outcome <- gl(3,1,9)
     treatment <- gl(3,3)
     glm.D93 <- glm(counts ~ outcome + treatment, family=poisson())

# Plot an approximate 95 % confidence region for the two Outcome parameters

  plot(ellipse(glm.D93, which = c(2,3)), type = 'l')
  points(glm.D93$coefficients[2], glm.D93$coefficients[3])