Apply the central age model (CAM) after Galbraith et al. (1999) to a given De distribution

This function calculates the central dose and dispersion of the De distribution, their standard errors and the profile log likelihood function for sigma.

Usage

calc_CentralDose(data, sigmab, log = TRUE, na.rm = FALSE, plot = TRUE, ...)

Arguments

data: RLum.Results or data.frame (required): for data.frame: two columns with De (data[,1]) and De error (data[,2])
sigmab: numeric (with default): additional spread in De values. This value represents the expected overdispersion in the data should the sample be well-bleached (Cunningham & Walling 2012, p. 100). NOTE: For the logged model (log = TRUE) this value must be a fraction, e.g. 0.2 (= 20 \ sigmab must be provided in the same absolute units of the De values (seconds or Gray).
log: logical (with default): fit the (un-)logged central age model to De data
na.rm: logical (with default): strip NA values before the computation proceeds
plot: logical (with default): plot output
...: further arguments (trace, verbose).

Value

Returns a plot (optional) and terminal output. In addition an RLum.Results object is returned containing the following elements:

.$summary: data.frame summary of all relevant model results.
.$data: data.frame original input data
.$args: list used arguments
.$call: call the function call
.$profile: data.frame the log likelihood profile for sigma

The output should be accessed using the function get_RLum

Details

This function uses the equations of Galbraith & Roberts (2012). The parameters delta and sigma are estimated by numerically solving eq. 15 and 16. Their standard errors are approximated using eq. 17. In addition, the profile log-likelihood function for sigma is calculated using eq. 18 and presented as a plot. Numerical values of the maximum likelihood approach are only presented in the plot and not in the console. A detailed explanation on maximum likelihood estimation can be found in the appendix of Galbraith & Laslett (1993, 468-470) and Galbraith & Roberts (2012, 15)

Function version

1.4.1

How to cite

Burow, C., 2024. calc_CentralDose(): Apply the central age model (CAM) after Galbraith et al. (1999) to a given De distribution. Function version 1.4.1. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J., Mercier, N., Philippe, A., Riedesel, S., Autzen, M., Mittelstrass, D., Gray, H.J., Galharret, J., Colombo, M., 2024. Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.9.26. https://r-lum.github.io/Luminescence/

References

Galbraith, R.F. & Laslett, G.M., 1993. Statistical models for mixed fission track ages. Nuclear Tracks Radiation Measurements 4, 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, 339-364.

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, 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, 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, 2475-2502.

Cunningham, A.C. & Wallinga, J., 2012. Realizing the potential of fluvial archives using robust OSL chronologies. Quaternary Geochronology 12, 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, 1 109-120.

Rodnight, H., 2008. How many equivalent dose values are needed to obtain a reproducible distribution?. Ancient TL 26, 3-10.

Author

Christoph Burow, University of Cologne (Germany)
Based on a rewritten S script of Rex Galbraith, 2010 , RLum Developer Team

Examples


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

##apply the central dose model
calc_CentralDose(ExampleData.DeValues$CA1)
#> 
#>  [calc_CentralDose]
#> 
#> ----------- meta data ----------------
#>  n:                       62
#>  log:                     TRUE
#> ----------- dose estimate ------------
#>  abs. central dose:       65.71
#>  abs. SE:                 3.05
#>  rel. SE [%]:             4.65
#> ----------- overdispersion -----------
#>  abs. OD:                 22.79
#>  abs. SE:                 2.27
#>  OD [%]:                  34.69
#>  SE [%]:                  3.46
#> -------------------------------------
#>