numOSL (version 1.6)

fitGrowth: Fitting a growth curve

Description

Fitting a growth curve using the Levenberg-Marquardt algorithm.

Usage

fitGrowth(Curvedata, model = c("line","exp","lexp","dexp"), 
          origin = FALSE, nstart = 100, upb = 0.5, plot = TRUE)

Arguments

Curvedata

matrix(required): three columns, i.e., regenerative doses, standardised OSL signals, and standard errors of standardised OSL signals

model

character(with default): a fitting model, default model="line", see details

origin

logical(optional): force the fitting to pass the origin or not

nstart

numeric(with default): the maximum number of attempts of initializing the non-linear growth curve fitting, see details

upb

numeric(with default): the upper limit on b value (the reciprocal of the saturating dose), initial b value is generated uniformly from the space (0,upb), see details

plot

logical(with default): draw a plot or not

Value

• Return an list that contains following elements:
• LMpars
  parameters and standard errors of the growth curve
• value
  the minimized chi-square value of the fitted growth curve
• fit.value
  observations and fitted values

Details

For fitting a growth curve, four models are available: (1) "line": a linear model, y=a*x+b; (2) "exp": an exponential model, y=a*[1-exp(-b*x)]+c; (3) "lexp": an exponential plus linear model, y=a*[1-exp(-b*x)]+c*x+d; (4) "dexp": an double exponential model, y=a*[1-exp(-b*x)]+c*[1-exp(-d*x)]+e. The weighted curve fitting is performed using the Levenberg-Marquardt algorithm by J.J. More (available at http://ftp.netlib.org/minpack). When fitting a non-linear model, a series of b(d) values (i.e., the reciprocal of the saturating dose) are initialized randomly with a uniform distribution in the space (0,upb), then other parameters are estimated with a Linear Algebra method. For a growth curve that shows high saturating dose, it is more reasonable to use a smaller upb value. For example, a double saturating exponential model with a upb value less than 0.05 or 0.01 usually works better. The fitting process will be performed repeatedly with nstart times to find an optimal estimate. User is advised to set argument plot to be TRUE if possible in order to see if the fitted growth curve is correct.

References

More JJ, 1978. "The Levenberg-Marquardt algorithm: implementation and theory," in Lecture Notes in Mathematics: Numerical Analysis, Springer-Verlag: Berlin. 105-116.

See Also

analyst; calED; fastED

Examples

data(Signaldata) 
 dat<-analyst(Signaldata[[1]], Redose=c(80,160,240,320,0,80)*0.13, 
              model="line", origin=TRUE, plot=FALSE, nsim=100)
 fitGrowth(dat$Curvedata, model="exp", origin=FALSE, plot=TRUE)