nlstools (version 2.1-0)

nlsConfRegions: Confidence regions

Description

Draws parameter values in the Beale's 95 percent unlinearized confidence region

Usage

nlsConfRegions (nls, length = 1000, exp = 1.5)
    # S3 method for nlsConfRegions
plot (x, bounds = FALSE, ask = FALSE, ...)
    # S3 method for nlsConfRegions
print (x, ...)

Value

nlsConfRegions returns a list of four objects:

cr

a data frame containing the sample drawn in the Beale's confidence region

rss

a vector containing the residual sums of squares corresponding to cr

rss95

the 95 percent residual sum of squares threshold according to Beale (1960)

bounds

lower and upper bounds of the hypercube in which random values of parameters have been drawn

Arguments

nls

an object of class 'nls'

length

number of points to draw in the confidence region

exp

expansion factor of the hypercube in which random values of parameters are drawn

x

an object of class 'nlsConfRegions'

bounds

logical defining whether bounds of the drawing hypercube are plotted

ask

if TRUE, draw plot interactively

...

further arguments passed to or from other methods

Author

Florent Baty, Marie-Laure Delignette-Muller

Details

A sample of points in the 95 percent confidence region is computed according to Beale's criterion (Beale, 1960). This region is also named the joint parameter likelihood region (Bates and Watts, 1988). The method used consists in a random sampling of parameters values in a hypercube centered on the least squares estimate and rejecting the parameters values whose residual sum of squares do not verify the Beale criterion. The confidence region is plotted by projection of the sampled points in each plane defined by a couple of parameters. Bounds of the hypercube in which random values of parameters are drawn may be plotted in order to check if the confidence region was totally included in the hypercube defined by default. If not the hypercube should be expanded in order to obtain the full confidence region

References

Beale EML (1960) Confidence regions in non-linear estimations. Journal of the Royal Statistical Society, 22B, 41-88.

Bates DM and Watts DG (1988) Nonlinear regression analysis and its applications. Wiley, Chichester, UK.

See Also

ellipse.nls in the ellipse library

Examples

formulaExp <- as.formula(VO2 ~ (t <= 5.883) * VO2rest + (t > 5.883) * 
                        (VO2rest + (VO2peak - VO2rest) * 
                        (1 - exp(-(t - 5.883) / mu))))
O2K.nls1 <- nls(formulaExp, start = list(VO2rest = 400, VO2peak = 1600, 
                mu = 1), data = O2K)
O2K.conf1 <- nlsConfRegions(O2K.nls1, exp = 2, length = 200)
plot(O2K.conf1, bounds = TRUE)