fit_DoseResponseCurve: Fit a dose-response curve for luminescence data (Lx/Tx...
In R-Lum/Luminescence: Comprehensive Luminescence Dating Data Analysis
View source: R/fit_DoseResponseCurve.R
fit_DoseResponseCurve R Documentation
Fit a dose-response curve for luminescence data (Lx/Tx against dose)
Description
A dose-response curve is produced for luminescence measurements using a
regenerative or additive protocol. The function supports interpolation and
extrapolation to calculate the equivalent dose.
Usage
fit_DoseResponseCurve(
object,
mode = "interpolation",
fit.method = "EXP",
fit.force_through_origin = FALSE,
fit.weights = TRUE,
fit.includingRepeatedRegPoints = TRUE,
fit.NumberRegPoints = NULL,
fit.NumberRegPointsReal = NULL,
fit.bounds = TRUE,
n.MC = 100,
txtProgressBar = TRUE,
verbose = TRUE,
...
)
Arguments
object
data.frame or a list of such objects (required):
data frame with columns for Dose, LxTx, LxTx.Error and TnTx.
The column for the test dose response is optional, but requires 'TnTx' as
column name if used. For exponential fits at least three dose points
(including the natural) should be provided. If object is a list,
the function is called on each of its elements.
mode
character (with default):
selects calculation mode of the function.
-
"interpolation" (default) calculates the De by interpolation,
-
"extrapolation" calculates the equivalent dose by extrapolation (useful for MAAD measurements) and
-
"alternate" calculates no equivalent dose and just fits the data points.
Please note that for option "interpolation" the first point is considered
as natural dose
fit.method
character (with default):
function used for fitting. Possible options are:
-
LIN,
-
QDR,
-
EXP,
-
EXP OR LIN,
-
EXP+LIN,
-
EXP+EXP,
-
GOK,
-
LambertW
See details.
fit.force_through_origin
logical (with default)
allow to force the fitted function through the origin.
For method = "EXP+EXP" the function will be fixed through
the origin in either case, so this option will have no effect.
fit.weights
logical (with default):
option whether the fitting is done with or without weights. See details.
fit.includingRepeatedRegPoints
logical (with default):
includes repeated points for fitting (TRUE/FALSE).
fit.NumberRegPoints
integer (optional):
set number of regeneration points manually. By default the number of all (!)
regeneration points is used automatically.
fit.NumberRegPointsReal
integer (optional):
if the number of regeneration points is provided manually, the value of the
real, regeneration points = all points (repeated points) including reg 0,
has to be inserted.
fit.bounds
logical (with default):
set lower fit bounds for all fitting parameters to 0. Limited for the use
with the fit methods EXP, EXP+LIN, EXP OR LIN, GOK, LambertW
Argument to be inserted for experimental application only!
n.MC
integer (with default): number of Monte Carlo simulations
for error estimation, see details.
txtProgressBar
logical (with default):
enable/disable the progress bar. If verbose = FALSE also no
txtProgressBar is shown.
verbose
logical (with default):
enable/disable output to the terminal.
...
Further arguments to be passed (currently ignored).
Details
Fitting methods
For all options (except for the LIN, QDR and the EXP OR LIN),
the minpack.lm::nlsLM function with the LM (Levenberg-Marquardt algorithm)
algorithm is used. Note: For historical reasons for the Monte Carlo
simulations partly the function nls using the port algorithm.
The solution is found by transforming the function or using stats::uniroot.
LIN: fits a linear function to the data using
lm:
y = mx + n
QDR: fits a linear function with a quadratic term to the data using
lm:
y = a + bx + cx^2
EXP: tries to fit a function of the form
y = a(1 - exp(-\frac{(x+c)}{b}))
Parameters b and c are approximated by a linear fit using lm. Note: b = D0
EXP OR LIN: works for some cases where an EXP fit fails.
If the EXP fit fails, a LIN fit is done instead.
EXP+LIN: tries to fit an exponential plus linear function of the
form:
y = a(1-exp(-\frac{x+c}{b}) + (gx))
The D_e is calculated by iteration.
Note: In the context of luminescence dating, this
function has no physical meaning. Therefore, no D0 value is returned.
EXP+EXP: tries to fit a double exponential function of the form
y = (a_1 (1-exp(-\frac{x}{b_1}))) + (a_2 (1 - exp(-\frac{x}{b_2})))
This fitting procedure is not robust against wrong start parameters and
should be further improved.
GOK: tries to fit the general-order kinetics function after
Guralnik et al. (2015) of the form of
y = a (d - (1 + (\frac{1}{b}) x c)^{(-1/c)})
where c > 0 is a kinetic order modifier
(not to be confused with c in EXP or EXP+LIN!).
LambertW: tries to fit a dose-response curve based on the Lambert W function
according to Pagonis et al. (2020). The function has the form
y ~ (1 + (W((R - 1) * exp(R - 1 - ((x + D_{int}) / D_{c}))) / (1 - R))) * N
with W the Lambert W function, calculated using the package lamW::lambertW0,
R the dimensionless retrapping ratio, N the total concentration
of trappings states in cm^-3 and D_{c} = N/R a constant. D_{int} is
the offset on the x-axis. Please note that finding the root in mode = "extrapolation"
is a non-easy task due to the shape of the function and the results might be
unexpected.
Fit weighting
If the option fit.weights = TRUE is chosen, weights are calculated using
provided signal errors (Lx/Tx error):
fit.weights = \frac{\frac{1}{error}}{\Sigma{\frac{1}{error}}}
Error estimation using Monte Carlo simulation
Error estimation is done using a parametric bootstrapping approach. A set of
Lx/Tx values is constructed by randomly drawing curve data sampled from normal
distributions. The normal distribution is defined by the input values (mean = value, sd = value.error). Then, a dose-response curve fit is attempted for each
dataset resulting in a new distribution of single De values. The standard
deviation of this distribution becomes then the error of the De. With increasing
iterations, the error value becomes more stable. However, naturally the error
will not decrease with more MC runs.
Alternatively, the function returns highest probability density interval
estimates as output, users may find more useful under certain circumstances.
Note: It may take some calculation time with increasing MC runs,
especially for the composed functions (EXP+LIN and EXP+EXP).
Each error estimation is done with the function of the chosen fitting method.
Value
An RLum.Results object is returned containing the slot data with the
following elements:
Overview elements
DATA.OBJECT TYPE DESCRIPTION
..$De : data.frame Table with De values
..$De.MC : numeric Table with De values from MC runs
..$Fit : nls or lm object from the fitting for EXP, EXP+LIN and EXP+EXP.
In case of a resulting linear fit when using LIN, QDR or EXP OR LIN
..Fit.Args : list Arguments to the function
..$Formula : expression Fitting formula as R expression
..$call : call The original function call
If object is a list, then the function returns a list of RLum.Results
objects as defined above.
Details - DATA.OBJECT$De
This object is a data.frame with the following columns
De numeric equivalent dose
De.Error numeric standard error the equivalent dose
D01 numeric D-naught value, curvature parameter of the exponential
D01.ERROR numeric standard error of the D-naught value
D02 numeric 2nd D-naught value, only for EXP+EXP
D02.ERROR numeric standard error for 2nd D-naught; only for EXP+EXP
Dc numeric value indicating saturation level; only for LambertW
n_N numeric saturation level of dose-response curve derived via integration from the used function; it compares the full integral of the curves (N) to the integral until De (n) (e.g., Guralnik et al., 2015)
De.MC numeric equivalent dose derived by Monte-Carlo simulation; ideally identical to De
De.plot numeric equivalent dose use for plotting
Fig character applied fit function
HPDI68_L numeric highest probability density of approximated equivalent dose probability curve representing the lower boundary of 68% probability
HPDI68_U numeric same as HPDI68_L for the upper bound
HPDI95_L numeric same as HPDI68_L but for 95% probability
HPDI95_U numeric same as HPDI95_L but for the upper bound
Function version
1.2.1
Author(s)
Sebastian Kreutzer, Institute of Geography, Heidelberg University (Germany)
Michael Dietze, GFZ Potsdam (Germany)
Marco Colombo, Institute of Geography, Heidelberg University (Germany)
References
Berger, G.W., Huntley, D.J., 1989. Test data for exponential fits. Ancient TL 7, 43-46.
Guralnik, B., Li, B., Jain, M., Chen, R., Paris, R.B., Murray, A.S., Li, S.-H., Pagonis, P.,
Herman, F., 2015. Radiation-induced growth and isothermal decay of infrared-stimulated luminescence
from feldspar. Radiation Measurements 81, 224-231.
Pagonis, V., Kitis, G., Chen, R., 2020. A new analytical equation for the dose response of dosimetric materials,
based on the Lambert W function. Journal of Luminescence 225, 117333. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jlumin.2020.117333")}
See Also
plot_GrowthCurve, nls, RLum.Results, get_RLum,
minpack.lm::nlsLM, lm, uniroot, lamW::lambertW0
Examples
##(1) fit growth curve for a dummy data.set and show De value
data(ExampleData.LxTxData, envir = environment())
temp <- fit_DoseResponseCurve(LxTxData)
get_RLum(temp)
##(1b) to access the fitting value try
get_RLum(temp, data.object = "Fit")
##(2) fit using the 'extrapolation' mode
LxTxData[1,2:3] <- c(0.5, 0.001)
print(fit_DoseResponseCurve(LxTxData, mode = "extrapolation"))
##(3) fit using the 'alternate' mode
LxTxData[1,2:3] <- c(0.5, 0.001)
print(fit_DoseResponseCurve(LxTxData, mode = "alternate"))
##(4) import and fit test data set by Berger & Huntley 1989
QNL84_2_unbleached <-
read.table(system.file("extdata/QNL84_2_unbleached.txt", package = "Luminescence"))
results <- fit_DoseResponseCurve(
QNL84_2_unbleached,
mode = "extrapolation",
verbose = FALSE)
#calculate confidence interval for the parameters
#as alternative error estimation
confint(results$Fit, level = 0.68)
## Not run:
QNL84_2_bleached <-
read.table(system.file("extdata/QNL84_2_bleached.txt", package = "Luminescence"))
STRB87_1_unbleached <-
read.table(system.file("extdata/STRB87_1_unbleached.txt", package = "Luminescence"))
STRB87_1_bleached <-
read.table(system.file("extdata/STRB87_1_bleached.txt", package = "Luminescence"))
print(
fit_DoseResponseCurve(
QNL84_2_bleached,
mode = "alternate",
verbose = FALSE)$Fit)
print(
fit_DoseResponseCurve(
STRB87_1_unbleached,
mode = "alternate",
verbose = FALSE)$Fit)
print(
fit_DoseResponseCurve(
STRB87_1_bleached,
mode = "alternate",
verbose = FALSE)$Fit)
## End(Not run)
R-Lum/Luminescence documentation built on March 1, 2025, 12:43 a.m.
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View source: R/fit_DoseResponseCurve.R
| fit_DoseResponseCurve | R Documentation |
Fit a dose-response curve for luminescence data (Lx/Tx against dose)
Description
A dose-response curve is produced for luminescence measurements using a regenerative or additive protocol. The function supports interpolation and extrapolation to calculate the equivalent dose.
Usage
fit_DoseResponseCurve(
object,
mode = "interpolation",
fit.method = "EXP",
fit.force_through_origin = FALSE,
fit.weights = TRUE,
fit.includingRepeatedRegPoints = TRUE,
fit.NumberRegPoints = NULL,
fit.NumberRegPointsReal = NULL,
fit.bounds = TRUE,
n.MC = 100,
txtProgressBar = TRUE,
verbose = TRUE,
...
)
Arguments
object |
data.frame or a list of such objects (required):
data frame with columns for |
mode |
character (with default): selects calculation mode of the function.
Please note that for option |
fit.method |
character (with default): function used for fitting. Possible options are:
See details. |
fit.force_through_origin |
logical (with default)
allow to force the fitted function through the origin.
For |
fit.weights |
logical (with default): option whether the fitting is done with or without weights. See details. |
fit.includingRepeatedRegPoints |
logical (with default):
includes repeated points for fitting ( |
fit.NumberRegPoints |
integer (optional): set number of regeneration points manually. By default the number of all (!) regeneration points is used automatically. |
fit.NumberRegPointsReal |
integer (optional): if the number of regeneration points is provided manually, the value of the real, regeneration points = all points (repeated points) including reg 0, has to be inserted. |
fit.bounds |
logical (with default):
set lower fit bounds for all fitting parameters to 0. Limited for the use
with the fit methods |
n.MC |
integer (with default): number of Monte Carlo simulations for error estimation, see details. |
txtProgressBar |
logical (with default):
enable/disable the progress bar. If |
verbose |
logical (with default): enable/disable output to the terminal. |
... |
Further arguments to be passed (currently ignored). |
Details
Fitting methods
For all options (except for the LIN, QDR and the EXP OR LIN),
the minpack.lm::nlsLM function with the LM (Levenberg-Marquardt algorithm)
algorithm is used. Note: For historical reasons for the Monte Carlo
simulations partly the function nls using the port algorithm.
The solution is found by transforming the function or using stats::uniroot.
LIN: fits a linear function to the data using
lm:
y = mx + n
QDR: fits a linear function with a quadratic term to the data using
lm:
y = a + bx + cx^2
EXP: tries to fit a function of the form
y = a(1 - exp(-\frac{(x+c)}{b}))
Parameters b and c are approximated by a linear fit using lm. Note: b = D0
EXP OR LIN: works for some cases where an EXP fit fails.
If the EXP fit fails, a LIN fit is done instead.
EXP+LIN: tries to fit an exponential plus linear function of the
form:
y = a(1-exp(-\frac{x+c}{b}) + (gx))
The D_e is calculated by iteration.
Note: In the context of luminescence dating, this function has no physical meaning. Therefore, no D0 value is returned.
EXP+EXP: tries to fit a double exponential function of the form
y = (a_1 (1-exp(-\frac{x}{b_1}))) + (a_2 (1 - exp(-\frac{x}{b_2})))
This fitting procedure is not robust against wrong start parameters and should be further improved.
GOK: tries to fit the general-order kinetics function after
Guralnik et al. (2015) of the form of
y = a (d - (1 + (\frac{1}{b}) x c)^{(-1/c)})
where c > 0 is a kinetic order modifier
(not to be confused with c in EXP or EXP+LIN!).
LambertW: tries to fit a dose-response curve based on the Lambert W function
according to Pagonis et al. (2020). The function has the form
y ~ (1 + (W((R - 1) * exp(R - 1 - ((x + D_{int}) / D_{c}))) / (1 - R))) * N
with W the Lambert W function, calculated using the package lamW::lambertW0,
R the dimensionless retrapping ratio, N the total concentration
of trappings states in cm^-3 and D_{c} = N/R a constant. D_{int} is
the offset on the x-axis. Please note that finding the root in mode = "extrapolation"
is a non-easy task due to the shape of the function and the results might be
unexpected.
Fit weighting
If the option fit.weights = TRUE is chosen, weights are calculated using
provided signal errors (Lx/Tx error):
fit.weights = \frac{\frac{1}{error}}{\Sigma{\frac{1}{error}}}
Error estimation using Monte Carlo simulation
Error estimation is done using a parametric bootstrapping approach. A set of
Lx/Tx values is constructed by randomly drawing curve data sampled from normal
distributions. The normal distribution is defined by the input values (mean = value, sd = value.error). Then, a dose-response curve fit is attempted for each
dataset resulting in a new distribution of single De values. The standard
deviation of this distribution becomes then the error of the De. With increasing
iterations, the error value becomes more stable. However, naturally the error
will not decrease with more MC runs.
Alternatively, the function returns highest probability density interval estimates as output, users may find more useful under certain circumstances.
Note: It may take some calculation time with increasing MC runs,
especially for the composed functions (EXP+LIN and EXP+EXP).
Each error estimation is done with the function of the chosen fitting method.
Value
An RLum.Results object is returned containing the slot data with the
following elements:
Overview elements
| DATA.OBJECT | TYPE | DESCRIPTION |
..$De : | data.frame | Table with De values |
..$De.MC : | numeric | Table with De values from MC runs |
..$Fit : | nls or lm | object from the fitting for EXP, EXP+LIN and EXP+EXP.
In case of a resulting linear fit when using LIN, QDR or EXP OR LIN |
..Fit.Args : | list | Arguments to the function |
..$Formula : | expression | Fitting formula as R expression |
..$call : | call | The original function call |
If object is a list, then the function returns a list of RLum.Results
objects as defined above.
Details - DATA.OBJECT$De
This object is a data.frame with the following columns
De | numeric | equivalent dose |
De.Error | numeric | standard error the equivalent dose |
D01 | numeric | D-naught value, curvature parameter of the exponential |
D01.ERROR | numeric | standard error of the D-naught value |
D02 | numeric | 2nd D-naught value, only for EXP+EXP |
D02.ERROR | numeric | standard error for 2nd D-naught; only for EXP+EXP |
Dc | numeric | value indicating saturation level; only for LambertW |
n_N | numeric | saturation level of dose-response curve derived via integration from the used function; it compares the full integral of the curves (N) to the integral until De (n) (e.g., Guralnik et al., 2015) |
De.MC | numeric | equivalent dose derived by Monte-Carlo simulation; ideally identical to De |
De.plot | numeric | equivalent dose use for plotting |
Fig | character | applied fit function |
HPDI68_L | numeric | highest probability density of approximated equivalent dose probability curve representing the lower boundary of 68% probability |
HPDI68_U | numeric | same as HPDI68_L for the upper bound |
HPDI95_L | numeric | same as HPDI68_L but for 95% probability |
HPDI95_U | numeric | same as HPDI95_L but for the upper bound |
Function version
1.2.1
Author(s)
Sebastian Kreutzer, Institute of Geography, Heidelberg University (Germany)
Michael Dietze, GFZ Potsdam (Germany)
Marco Colombo, Institute of Geography, Heidelberg University (Germany)
References
Berger, G.W., Huntley, D.J., 1989. Test data for exponential fits. Ancient TL 7, 43-46.
Guralnik, B., Li, B., Jain, M., Chen, R., Paris, R.B., Murray, A.S., Li, S.-H., Pagonis, P., Herman, F., 2015. Radiation-induced growth and isothermal decay of infrared-stimulated luminescence from feldspar. Radiation Measurements 81, 224-231.
Pagonis, V., Kitis, G., Chen, R., 2020. A new analytical equation for the dose response of dosimetric materials, based on the Lambert W function. Journal of Luminescence 225, 117333. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jlumin.2020.117333")}
See Also
plot_GrowthCurve, nls, RLum.Results, get_RLum, minpack.lm::nlsLM, lm, uniroot, lamW::lambertW0
Examples
##(1) fit growth curve for a dummy data.set and show De value
data(ExampleData.LxTxData, envir = environment())
temp <- fit_DoseResponseCurve(LxTxData)
get_RLum(temp)
##(1b) to access the fitting value try
get_RLum(temp, data.object = "Fit")
##(2) fit using the 'extrapolation' mode
LxTxData[1,2:3] <- c(0.5, 0.001)
print(fit_DoseResponseCurve(LxTxData, mode = "extrapolation"))
##(3) fit using the 'alternate' mode
LxTxData[1,2:3] <- c(0.5, 0.001)
print(fit_DoseResponseCurve(LxTxData, mode = "alternate"))
##(4) import and fit test data set by Berger & Huntley 1989
QNL84_2_unbleached <-
read.table(system.file("extdata/QNL84_2_unbleached.txt", package = "Luminescence"))
results <- fit_DoseResponseCurve(
QNL84_2_unbleached,
mode = "extrapolation",
verbose = FALSE)
#calculate confidence interval for the parameters
#as alternative error estimation
confint(results$Fit, level = 0.68)
## Not run:
QNL84_2_bleached <-
read.table(system.file("extdata/QNL84_2_bleached.txt", package = "Luminescence"))
STRB87_1_unbleached <-
read.table(system.file("extdata/STRB87_1_unbleached.txt", package = "Luminescence"))
STRB87_1_bleached <-
read.table(system.file("extdata/STRB87_1_bleached.txt", package = "Luminescence"))
print(
fit_DoseResponseCurve(
QNL84_2_bleached,
mode = "alternate",
verbose = FALSE)$Fit)
print(
fit_DoseResponseCurve(
STRB87_1_unbleached,
mode = "alternate",
verbose = FALSE)$Fit)
print(
fit_DoseResponseCurve(
STRB87_1_bleached,
mode = "alternate",
verbose = FALSE)$Fit)
## End(Not run)
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