numOSL (version 1.8)

calED: Equivalent dose calculation and error assessment

Description

Calculating an equivalent dose value and assessing its standard error using methods described in Duller (2007).

Usage

calED(Curvedata, Ltx, model = c("line","exp","lexp","dexp"), 
      origin = FALSE, nstart = 100, upb = 0.5, ErrorMethod = c("mc","sp"),
      nsim = 1000, weight = TRUE, plot = TRUE, outfile = NULL)

Arguments

Curvedata

matrix(required): three columns, i.e., regenerative doses, sensitivity-corrected OSLs, and standard errors of sensitivity-corrected OSLs

Ltx

vector or matrix(required): sensitivity-corrected natural OSL(s) and associated standard error(s)

model

character(with default): fitting model for a growth curve, default model="line", see fitGrowth for available models

origin

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

nstart

integer(with default): maximum number of attempts for initializing the non-linear growth curve, see function fitGrowth for details

upb

double(with default): upper limit on b value (i.e., the reciprocal of the saturating dose), initial b value is generated uniformly from the space (0,upb), see function

ErrorMethod

character(with default): method used for assessing the standard error of an equivalent dose, default ErrorMethod="mc", see details

nsim

integer(with default): maximum number of simulations if a Monte Carlo method is applied to assessing the standard error of an equivalent dose

weight

logical(with default): fit the growth curve using a weighted or an un-weighted procedure, see function fitGrowth for details

plot

logical(with default): draw a plot or not

outfile

character(with default): if specified, simulated equivalent dose values will be written to a file named "outfile" in ".csv" format and saved to the current work directory

Value

• Return a list that contains the following elements:
• LMpars
  parameters of the growth curve
• value
  minimized objective of the growth curve
• fit.value
  observations and fitted values
• ED
  equivalent dose(s) and standard error(s)

Details

Function calED can be used for calculating a single equivalent dose value (Duller, 2007) (if Ltx is a two-element vector) or a series of equivalent dose values using the "Standardised Growth Curve" method (i.e. "SGC" used by Roberts and Duller, 2004; or "gSGC" proposed by Li et al., 2015) (if Ltx is a row matrix). Standard error of an equivalent dose can be assessd using two methods outlined by Duller (2007): (1) "sp": a simple transformation from error of a sensitivity-corrected OSL (i.e., s(Lx/Tx)) to error of an equivalent dose (i.e., s(ED)); (2) "mc": a Monte Carlo method (a "parametric bootstrap" protocol). Interpolation is performed using a combination of golden section search and successive parabolic interpolation (using freely available subroutine at http://www.netlib.org/fmm/fmin.f). See function fitGrowth for more details on growth curve fitting.

References

Duller GAT, 2007. Assessing the error on equivalent dose estimates derived from single aliquot regenerative dose measurements. Ancient TL, 25(1): 15-24.

Li B, Roberts RG, Jacobs Z, Li SH, 2015. Potential of establishing a "global standardised growth curve" (gSGC) for optical dating of quartz from sediments. Quaternary Geochronology, 27: 94-104.

Roberts HM, Duller GAT, 2004. Standardised growth curves for optical dating of sediment using multiple-grain aliquots. Radiation Measurements, 38(2): 241-252.

See Also

analyst; fastED; fitGrowth

Examples

# In SGC method application, if aliquots have different test 
  # dose values, their sensitivity-corrected OSL (Lx/Tx) need be 
  # normalized using their test dose Dt so as to reduce the between-aliquot
  # scatter. But in the following example, normalization is unnecessary, 
  # as the two aliquots share a common test dose. 
  data1<-cbind(c(0, 18, 36, 54, 72, 0, 18),               
               c(0.026, 1.55, 2.39, 3.46, 4.13, 0.023, 1.61),  
               c(0.005, 0.11, 0.27, 0.22, 0.20, 0.008, 0.24)) 
  data2<-cbind(c(0, 18, 36, 54, 72, 0, 18),                
               c(0.021, 1.47, 2.51, 3.37, 4.31, 0.028, 1.52),  
               c(0.003, 0.09, 0.35, 0.21, 0.29, 0.01, 0.17))  
  data <- rbind(data1, data2)  
  # data3, data4, ... can be added in the same way.                         
  Ltx<-cbind(c(0.5, 1.0, 1.8, 2.3, 2.8, 3.1, 3.6, 4.0),         
             c(0.02, 0.08, 0.11, 0.12, 0.23, 0.31, 0.33, 0.51)) 
  calED(Curvedata=data, Ltx=Ltx, model= "exp", origin=FALSE)