ellipse.profile.nls | R Documentation |

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

```
## 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, ...)
```

`x` |
An object of class |

`which` |
Which pair of parameters to use. |

`level` |
The |

`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). |

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.

An `npoints`

x `2`

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

Bates and Watts (1988). Nonlinear Regression Analysis and Its Applications. Wiley. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/9780470316757")}.

`profile`

, `ellipse.nls`

```
# 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'])
```

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