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Luminescence (version 0.3.4)

calc_MinDose4: Apply the (un-)logged four parameter minimum age model (MAM 4) after Galbraith et al. (1999) to a given De distribution

Description

Function to fit the (un-)logged four parameter minimum dose model (MAM 4) to De data.

Usage

calc_MinDose4(input.data, sigmab, log = TRUE, sample.id = "unknown sample", 
    gamma.xlb = 0.1, gamma.xub = 100, mu.xlb = 1, mu.xub = 100, 
    sigma.xlb = 0.001, sigma.xub = 5, init.gamma = 10, init.mu = 10, 
    init.sigma = 0.6, init.p0 = 0.01, ignore.NA = FALSE, calc.ProfileLikelihoods = TRUE, 
    console.ProfileLikelihoods = FALSE, console.extendedOutput = FALSE, 
    output.plot = TRUE, output.indices = 4)

Arguments

input.data
RLum.Results or data.frame (required): for data.frame: two columns with De (input.data[,1]) and De error (values[,2])
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
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
mu.xlb
numeric (with default): lower boundary of mu
mu.xub
numeric (with default): upper boundary of mu
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.mu
numeric (with default): starting value of mu
init.sigma
numeric (with default): starting value of sigma
init.p0
numeric (with default): starting value of p0
ignore.NA
logical (with default): ignore NA values during log likelihood calculations. See details.
calc.ProfileLikelihoods
logical (with default): calculate profile log likelihood functions for gamma, mu, sigma, p0. See output.indices.
console.ProfileLikelihoods
logical (with default): print profile log likelihood functions for gamma, mu, sigma, p0 to console.
console.extendedOutput
logical (with default): extended terminal output
output.plot
logical (with default): plot output (TRUE/FALSE)
output.indices
numeric (with default): requires calc.ProfileLikelihoods = TRUE. Indices: 1 = gamma, 2 = gamma/mu, 3 = gamma/mu/sigma, 4 = gamma/mu/sigma/p0

Value

  • Returns a plot (optional) and terminal output. A file containing statistical results is provided if desired. In addition an RLum.Results object is returned containing the following element:
  • resultsdata.frame with statistical parameters.
  • The output should be accessed using the function get_RLum.Results

Function version

0.22 (2014-04-13 14:28:35)

Details

Parameters This model has four parameters: rl{ gamma: minimum dose on the log scale mu: mean of the non-truncated normal distribution 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) and mu (mu.xlb and mu.xub) need to be specified. If the final estimate of gamma or mu is on the boundary, gamma.xlb and gamma.xub (mu.xlb and mu.xub respectively) need to be adjusted appropriately, so that gamma and mu lie 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 four parameters init.gamma, init.sigma, init.mu and init.p0 need to be specified. Ignore NA values In some cases during the calculation of the log likelihoods NA values are produced instantly terminating the minimum age model. It is advised to adjust some of the values provided for any argument. If the model still produces NA values it is possible to omit these values by setting ignore.NA = TRUE. While the model is then usually able to finish all calculations the integrity of the final estimates cannot be ensured. Use this argument at own risk.

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, calc_CentralDose, calc_CommonDose, calc_FiniteMixture, calc_FuchsLang2001, calc_MinDose3

Examples

Run this code
## load example data
data(ExampleData.DeValues, envir = environment())

## apply the logged minimum dose model
calc_MinDose4(ExampleData.DeValues, 
              sigmab = 0.05, gamma.xub = 10000, mu.xub = 10000, init.p0 = 0.4,
              output.plot = FALSE)

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