ellipse.profile.nls {ellipse}

Pairwise profile sketch

Description

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

Usage

## S3 method for class '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).

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.

Value

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

References

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

See Also

profile, ellipse.nls

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'])