Luminescence (version 0.2.2)

fit_CWCurve: Nonlinear Least Squares Fit for CW-OSL curves

Description

The function determines the weighted least-squares estimates of the component parameters of a CW-OSL for a given maximum number of components and returns various component parameters. The fitting procedure uses the nls function with the port algorithm.

Usage

fit_CWCurve(values, 
            n.components.max, 
            fit.failure_threshold = 3, 
            fit.trace = FALSE, 
            fit.calcError = FALSE, 
            LED.power = 36, 
            LED.wavelength = 470, 
            log = "", 
            cex.global = 0.6, 
            main = "CW-OSL Curve Fit", 
            sample_code = "Default", 
            ylab, xlab, 
            output.path, 
            output.terminal = TRUE, 
            output.terminalAdvanced = TRUE, 
            output.plot = TRUE)

Arguments

values

data.frame (required): x,y data of measured values (time and counts). See examples.

n.components.max

vector (optional): maximum number of components that are to be used for fitting. The upper limit is 7.

fit.failure_threshold

vector (with default): limits the failed fitting attempts.

fit.trace

logical (with default): trace the fitting process on the terminal.

fit.calcError

logical (with default): calculate 1-sigma error range of components using confint

LED.power

numeric (with default): LED power (max.) used for intensity ramping in mW/cm^2. Note: The value is used for the calculation of the absolute photoionisation cross section.

LED.wavelength

numeric (with default): LED wavelength used for stimulation in nm. Note: The value is used for the calculation of the absolute photoionisation cross section.

log

character (optional): option for log-scaled axis, works as in plot

cex.global

numeric (with default): global scaling factor.

main

character (with default): header for plot output.

sample_code

character (optional): sample code used for the plot and the optional output table (mtext).

ylab

character (with default): alternative y-axis labelling

xlab

character (with default): alternative x-axis labelling

output.path

character (optional): output path for table output containing the results of the fit. The file name is set automatically. If the file already exists in the directory, the values are appended.

output.terminal

logical (with default): terminal ouput with fitting results.

output.terminalAdvanced

logical (with default): enhanced terminal output. Requires output.terminal = TRUE. If output.terminal = FALSE no advanced output is possible.

output.plot

logical (with default): returns a plot of the fitted curves.

Value

• plot
  (optional) the fitted CW-OSL curves are returned as plot.
• table
  (optional) an output table (*.csv) with the fitted components is provided if the output.path is set.
• list object
  beside the plot and table output options a list is returned. The list contains: (a) a nls object ($fit) for which generic R functions are provided, e.g. summary, confint, profile. For more details, see nls. (b) a data.frame containing the summarized parameters including the error ($output.table).

Details

Fitting function

The function for the fitting has the general form : $$y = I0_1*exp(-lambda_1*x) + ,\ldots, + I0_i*exp(-lambda_i*x)$$ where $1>= i <= 7$<="" p="">

Start values

Start values are estimated automatically by fitting a linear function on the log input data set. Currently, there is no option to manually provide start parameters.

goodness of fit

The goodness of the fit is given by a expression(pseudo-R^2) value (pseudo coefficient of determination). According to Lave (1970), the value is calculated as:

$$pseudoR^2 = 1 - RSS/TSS$$ where $RSS = Residual~Sum~of~Squares$ and $TSS = Total~Sum~of~Squares$

Error of fitted component parameters

The 1-sigma error for the components is calculated using the function confint. Due to considerable calculation time, this option is deactived by default. In addition, the error for the components can be estimated by using internal R functions like summary. See the nls help page for more information.

For details on the nonlinear regression in R, see Ritz & Streibig (2008).

References

Lave, C.A.T., 1970. The Demand for Urban Mass Transportation. The Review of Economics and Statistics, 52 (3), pp. 320-323.

Ritz, C. & Streibig, J.C., 2008. Nonlinear Regression with R R. Gentleman, K. Hornik, & G. Parmigiani, eds., Springer.

See Also

fit_LMCurve, plot,nls

Examples

##load data
data(ExampleData.CW_OSL_Curve)

##fit data
fit <- fit_CWCurve(values = ExampleData.CW_OSL_Curve,
                   main = "CW Curve Fit",
                   n.components.max = 4,
                   log = "x")