breakage (version 1.1-1)

fit.breakage: Fit a tip geometry model to breakage resistance data

Description

Estimates pipette tip half-cone angle and initial inner radius from the resistance vs breakage distance data. Fitting is performed by minimisation of the residual sum of squares calculated by err.breakage. By default, a plot of the data and the fitted model is drawn.

Usage

fit.breakage(data, start = list(theta = 3 * pi/180, r = 0.05), rho = 51, l = 1000, do.plot = TRUE, ...)

Arguments

data

Measured breakage data as an XY list or data frame, with data$x holding the breakage distances in microns, and data$y the corresponding resistance in megohms. For compatibility with breakage.plot and break.clust, these columns may instead by named Z and Mohm respectively.

start

List of initial values for the optimisation parameters. Must contain values for theta and r. The error function typically has a well-behaved minimum and the default start values should converge in most cases.

rho

Resistivity of the filler solution, in ohm centimetres. The default value of 51 ohm cm corresponds to a 150 mM solution of KCl.

l

The initial length of the pipette tip, in microns. Because the resistance is dominated by the narrower tip region, the precise value of this is not usually important provided it is much greater than the breakage distance.

do.plot

Whether to plot a graph of the data and fit results if successful.

...

Additional parameters passed to the plotting functions.

Value

theta

The fitted estimate of the half-cone angle, in radians; or NA if the optimisation failed.

r

The fitted estimate of the tip inner radius, in microns; or NA if the optimisation failed.

degrees

The fitted estimate of the half-cone angle, in degrees; or NA if the optimisation failed.

theta.sd

A crude estimate of the standard error in theta, calculated from the Hessian returned by optim; or NA if optimisation failed.

r.sd

A crude estimate of the standard error in r, calculated from the Hessian returned by optim; or NA if optimisation failed.

degrees.sd

A crude estimate of the standard error in degrees, calculated from the Hessian returned by optim; or NA if optimisation failed.

err

The residual sum of squares error between the fitted model predictions and the data; or NA if the optimisation failed.

opt

The result structure returned by optim. If the optimisation failed, this may provide some useful information as to why.

Details

Optimisation is performed using the L-BFGS-B method of optim, constraining the possible values of r and theta to physically plausible ranges.

References

Caldwell, M., Del Linz, S. J. L., Smart, T. G. S. and Moss, G. W. J. 2012 Method for estimating the tip geometry of scanning ion conductance microscope pipets. Anal. Chem. 84(21):8980--8984

See Also

fit.breakage

Examples

# fake up some breakage data
brks <- sort(abs(0.5 + rnorm(n=15, sd=0.5) * 1:15))
res <- resist.breakage(brks, theta=3*pi/180, r=0.04, rho=64) + rnorm(15)

# fit it
fit.breakage(list(x=brks, y=res))