Pairwise profile sketch

This routine approximates a pairwise confidence region for a nonlinear regression model.

Usage

# S3 method for profile.nls
ellipse(x, which = c(1, 2), level = 0.95, 
          t = sqrt(2 * qf(level, 2, attr(x, "summary")$df[2])), 
          npoints = 100, ...)

Arguments

x: An object of class profile.nls.
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.
npoints: How many points to use in the ellipse.
...: 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

# 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'])