nls with the port algorithm.fit_LMCurve(values,
values.bg,
n.components = 3,
start_values,
input.dataType = "LM",
main = "Default",
sample_code = "",
sample_ID = "",
LED.power = 36, LED.wavelength = 470,
log_scale = "", cex.global = 0.8,
fit.trace = FALSE,
fit.advanced = FALSE,
fit.calcError = FALSE,
bg.subtraction = "polynomial",
output.path,
output.terminal = TRUE, output.terminaladvanced = TRUE,
output.plot = TRUE, output.plotBG = FALSE
)polynomial,
linear, channel, see Details). Note: input for values.bgoutput.terminal = TRUE.
If output.terminal = FALSE no advanced output is possible.output.path is set.list objectnls object ($fit) for which generic R functions are prov,
e.g. summary, confint, profile. For more details, see nls.
(b) a data.frame containing the summarised parameters including the
error ($output.table).The function for the fitting has the general form : $$y = exp(0.5)*Im_1*x/xm_1)*exp(-x^2/(2*xm_1^2)) + ,\ldots, + exp(0.5)*Im_i*x/xm_i)*exp(-x^2/(2*xm_i^2))$$ where $1>= i <= 7$="" this="" function="" and="" the="" equations="" for="" conversion="" to="" b="" (detrapping="" probability)="" n0="" (proportional="" initially="" trapped="" charge)="" have="" been="" taken="" from="" kitis="" et="" al.="" (2008):<="" p="">
$$xm_i=\sqrt{max(t)/b_i}$$ $$Im_i=exp(-0.5)n0/xm_i$$ Background subtraction
Three methods for background subtraction are provided for a given background signal (values.bg).
polynomial: default method. A polynomial function is fitted using glm and the resulting function
is used for the background subtraction:
$$y = a*x^4 + b*x^3 + c*x^2 + d*x + e$$
linear: a linear function is fitted using glm and the resulting function
is used for the background subtraction:
$$y = a*x + b$$
channel: the measured background signal is subtracted channelwise from the measured signal.
Start values
The choice of the initial parameters for the nls-fitting is a crucial point and the fitting procedure may mainly fail due to ill chosen start parameters. Here, three options are provided:
(a) If no start values (start_values) are provided by the user, a cheap guess is made by using
the detrapping values found by Jain et al. (2003) for quartz for a maximum of 7 components. Based
on these values, the pseudo start parameters xm and Im are recalculated for the given data set.
In all cases, the fitting starts with the ultra-fast component and (depending on n.components)
steps through the following values. If no fit could be achieved, an error plot
(for output.plot = TRUE) with the pseudo curve (based on the pseudo start parameters) is provided.
This may give the opportunity to identify appropriate start parameters visually.
(b) If start values are provided, the function works like a simple nls fitting approach.
(c) If no start parameters are provided and the option fit.advanced == TRUE is chosen, an
advanced start paramter estimation is applied using a stochastical attempt. Therefore the recalculated start parameters (a)
are used to construct a normal distribution. The start parameters are then sampled randomly from this distribution.
A maximum of 100 attempts will be made. Note: This process may be really time consuming.
Goodness of fit
The goodness of the fit is given by a 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 more details on the nonlinear regression in R, see Ritz & Streibig (2008).
Jain, M., Murray, A.S., Boetter-Jensen, L., 2003. Characterisation of blue-light stimulated luminescence components in different quartz samples: implications for dose measurement. Radiation Measurements, 37 (4-5), pp. 441-449.
Kitis, G. & Pagonis, V., 2008. Computerized curve deconvolution analysis for LM-OSL. Radiation Measurements, 43, pp. 737-741.
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.
fit_CWCurve, plot,nls##(1) fit LM data without background subtraction
data(ExampleData.FittingLM)
fit_LMCurve(values = values.curve, n.components = 3, log_scale = "x")
##(2) fit LM data with background subtraction and export as JPEG
## -alter file path for your prefered system
##jpeg(file = "~/Desktop/Fit_Output\%03d.jpg", quality = 100,
## height = 3000, width = 3000, res = 300)
data(ExampleData.FittingLM)
fit_LMCurve(values = values.curve, values.bg = values.curveBG,
n.components = 2, log_scale = "x", output.plotBG = TRUE)
##dev.off()
##(3) fit LM data with manual start parameters
data(ExampleData.FittingLM)
fit_LMCurve(values = values.curve, values.bg = values.curveBG, n.components = 3, log_scale = "x",
start_values = data.frame(Im = c(170,25,400), xm = c(56,200,1500)))Run the code above in your browser using DataLab