Luminescence (version 0.2.2)

Calc_MinDose3: Apply the (un-)logged three parameter minimum age model (MAM 3) after Galbraith et al. (1999) to a given De distribution

Description

Function to fit the (un-)logged three parameter minimum dose model (MAM 3) to De data.

Usage

Calc_MinDose3(input.data, 
              sigmab,
              log = TRUE,
              sample.id = "unknown sample",
              gamma.xlb = 0.1,
              gamma.xub = 100,
              sigma.xlb = 0.001,
              sigma.xub = 5.00,
              init.gamma = 10,
              init.sigma = 1.2,
              init.p0 = 0.01,
              calc.ProfileLikelihoods = TRUE, 
              console.ProfileLikelihoods=FALSE,
              console.extendedOutput=FALSE,
              output.file = FALSE, 
              output.filename = "default", 
              output.plot = FALSE, 
              output.indices = 3)

Arguments

input.data

data.frame (required): two column data frame with De values and corresponding De errors

sigmab

numeric (required): spread in De values given as a fraction (e.g. 0.2). This value represents the expected overdispersion in the data should the sample be well-bleached (Cunningham & Walling 2012, p. 100).

log

logical (with default): fit the (un-)logged three parameter minimum dose model to De data

sample.id

character (with default): sample id

gamma.xlb

numeric (with default): lower boundary of gamma

gamma.xub

numeric (with default): upper boundary of gamma

sigma.xlb

numeric (with default): lower boundary of sigma

sigma.xub

numeric (with default): upper boundary of sigma

init.gamma

numeric (with default): starting value of gamma

init.sigma

numeric (with default): starting value of sigma

init.p0

numeric (with default): starting value of p0

calc.ProfileLikelihoods

logical (with default): calculate profile log likelihood functions for gamma, sigma, p0. See output.indices.

console.ProfileLikelihoods

logical (with default): print profile log likelihood functions for gamma, sigma, p0 to console.

console.extendedOutput

logical (with default): extended terminal output

output.file

logical (with default): save results to file. See output.filename.

output.filename

character (with default): desired filename, else results are saved to default-3R(-UL).res

output.plot

logical (with default): plot output (TRUE/FALSE)

output.indices

numeric (with default): requires calc.ProfileLikelihoods = TRUE. Indices: 1 = gamma, 2 = gamma/sigma, 3 = gamma/sigma/p0.

Value

• A terminal output is provided. A plot (postscript) and a file containing statistical results are provided if desired. In addition a list is returned containing the following element:
• results
  data frame containing statistical results.

Details

Parameters This model has three parameters: rl{ gamma: minimum dose on the log scale sigma: spread in ages above the minimum p0: proportion of grains at gamma } (Un-)logged model In the original version of the three-parameter minimum dose model, the basic data are the natural logarithms of the De estimates and relative standard errors of the De estimates. This model will be applied if log = TRUE. If log = FALSE, the modified un-logged model will be applied instead. This has essentially the same form as the original version. gamma and sigma are in Gy and gamma becomes the minimum true dose in the population. While the original (logged) version of the mimimum dose model may be appropriate for most samples (i.e. De distributions), the modified (un-logged) version is specially designed for modern-age and young samples containing negative, zero or near-zero De estimates (Arnold et al. 2009, p. 323). Boundaries Depending on the data, the upper and lower bounds for gamma (gamma.xlb and gamma.xub) need to be specified. If the final estimate of gamma is on the boundary, gamma.xlb and gamma.xub need to be adjusted appropriately, so that gamma lies within the bounds. The same applies for sigma boundaries (sigma.xlb and sigma.xub). Initial values The log likelihood calculations use the nlminb function. Accordingly, initial values for the three parameters init.gamma, init.sigma and init.p0 need to be specified.

References

Arnold, L.J., Roberts, R.G., Galbraith, R.F. & DeLong, S.B., 2009. A revised burial dose estimation procedure for optical dating of young and modern-age sediments. Quaternary Geochronology, 4, pp. 306-325. Galbraith, R.F. & Laslett, G.M., 1993. Statistical models for mixed fission track ages. Nuclear Tracks Radiation Measurements, 4, pp. 459-470. Galbraith, R.F., Roberts, R.G., Laslett, G.M., Yoshida, H. & Olley, J.M., 1999. Optical dating of single grains of quartz from Jinmium rock shelter, northern Australia. Part I: experimental design and statistical models. Archaeometry, 41, pp. 339-364. Galbraith, R.F., 2005. Statistics for Fission Track Analysis, Chapman & Hall/CRC, Boca Raton. Galbraith, R.F. & Roberts, R.G., 2012. Statistical aspects of equivalent dose and error calculation and display in OSL dating: An overview and some recommendations. Quaternary Geochronology, 11, pp. 1-27. Further reading Arnold, L.J. & Roberts, R.G., 2009. Stochastic modelling of multi-grain equivalent dose (De) distributions: Implications for OSL dating of sediment mixtures. Quaternary Geochronology, 4, pp. 204-230. Bailey, R.M. & Arnold, L.J., 2006. Statistical modelling of single grain quartz De distributions and an assessment of procedures for estimating burial dose. Quaternary Science Reviews, 25, pp. 2475-2502. Cunningham, A.C. & Wallinga, J., 2012. Realizing the potential of fluvial archives using robust OSL chronologies. Quaternary Geochronology, 12, pp. 98-106. Rodnight, H., Duller, G.A.T., Wintle, A.G. & Tooth, S., 2006. Assessing the reproducibility and accuracy of optical dating of fluvial deposits. Quaternary Geochronology, 1, pp. 109-120. Rodnight, H., 2008. How many equivalent dose values are needed to obtain a reproducible distribution?. Ancient TL, 26, pp. 3-10.

See Also

nlminb, postscript, Calc_CentralDose, Calc_CommonDose, Calc_FiniteMixture, Calc_FuchsLang2001, Calc_MinDose4

Examples

## load example data
data(ExampleData.DeValues)

## apply the logged minimum dose model
Calc_MinDose3(ExampleData.DeValues,
              sigmab = 0.3,gamma.xub = 7000, 
              output.file = FALSE, output.plot = FALSE)

## apply the un-logged minimum dose model
## note that the example data set does not meet the un-logged model requirements
Calc_MinDose3(ExampleData.DeValues, log = FALSE,
              sigmab = 0.3,gamma.xub = 5000, 
              output.file = FALSE, output.plot = FALSE)