Pairwise profile sketch

This routine approximates a contour of a function based on the profile of that function.

Usage

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

Arguments

x: An object of class profile, e.g. from profile.glm in the MASS package.
which: Which pair of parameters to use.
level: The ellipse.profile function defaults assume that the profiled function is -2 times the log likelihood of a regular model. With this assumption the level argument specifies the confidence level for an asymptotic confidence region.
t: The square root of the value to be contoured.
npoints: How many points to use in the ellipse.
...: Extra arguments are not used.

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

# Plot an approximate 95% confidence region for the Puromycin
# parameters Vm and K, and overlay the ellipsoidal region

data(Puromycin)
Purboth <- nls(formula = rate ~ ((Vm + delV * (state == "treated"))
  * conc)/(K + conc), data = Puromycin,
  start = list(Vm = 160, delV = 40, K = 0.05))
Pur.prof <- profile(Purboth)
plot(ellipse(Pur.prof, which = c('Vm', 'K')), type = 'l')
lines(ellipse(Purboth, which = c('Vm', 'K')), lty = 2)
params <- Purboth$m$getPars()
points(params['Vm'],params['K'])