Pairwise profile sketch for GLM profiles

This routine approximates a pairwise confidence region for a glm model.

Usage

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

Arguments

x: An object of class profile.glm.
which: Which pair of parameters to use.
level: The level argument specifies the confidence level for an asymptotic confidence region.
t: The square root of the value to be contoured. By default, this is qchisq(level, 2) for models with fixed dispersion (i.e. binomial and Poisson), and 2 * qf(level, 2, df) for other models, where df is the residual degrees of freedom.
npoints: How many points to use in the ellipse.
dispersion: If specified, fixed dispersion is assumed, otherwise the dispersion is taken from the model.
...: Extra parameters which are not used (for compatibility with the generic).

Value

An npoints x 2 matrix with columns having the chosen parameter names, which approximates a contour of the function that was profiled.

Details

This function uses the 4 point approximation to the contour as described in Appendix 6 of Bates and Watts (1988). It produces the exact contour for quadratic surfaces, and good approximations for mild deviations from quadratic. If the surface is multimodal, the algorithm is likely to produce nonsense.

References

Bates and Watts (1988). Nonlinear Regression Analysis and Its Applications. Wiley. doi:10.1002/9780470316757 .

Examples

## MASS has a pairs.profile function that conflicts with ours, so
## do a little trickery here
   noMASS <- is.na(match('package:MASS', search()))
   if (noMASS) require(MASS)
#> Loading required package: MASS

## 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 variables
     prof.D93 <- profile(glm.D93)
     plot(ellipse(prof.D93, which = 2:3), type = 'l')
     lines(ellipse(glm.D93, which = 2:3), lty = 2)
     params <- glm.D93$coefficients
     points(params[2],params[3])

     
##  Clean up our trickery
   if (noMASS) detach('package:MASS')