# plot_GrowthCurve

##### Fit and plot a growth curve for luminescence data (Lx/Tx against dose)

A dose response curve is produced for luminescence measurements using a regenerative or additive protocol. The function supports interpolation and extraxpolation to calculate the equivalent dose.

##### Usage

```
plot_GrowthCurve(sample, na.rm = TRUE, 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, NumberIterations.MC = 100, output.plot = TRUE,
output.plotExtended = TRUE, output.plotExtended.single = FALSE,
cex.global = 1, txtProgressBar = TRUE, verbose = TRUE, ...)
```

##### Arguments

- sample
data.frame (

**required**): data frame with three columns for x=Dose,y=LxTx,z=LxTx.Error, y1=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.- na.rm
logical (

*with default*): excludes`NA`

values from the data set prior to any further operations.- mode
character (

*with default*): selects calculation mode of the function.`"interpolation"`

(default) calculates the De by interpolation,`"extrapolation"`

calculates the De by extrapolation and`"alternate"`

calculates no De and just fits the data points.

Please note that for option

`"regenrative"`

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`

or`GOK`

.

See details.

- fit.force_through_origin
logical (

*with default*) allow to force the fitted function through the origin. For`method = "EXP+EXP"`

and`method = "GOK"`

the function will go 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`

and`GOK`

. Argument to be inserted for experimental application only!- NumberIterations.MC
integer (

*with default*): number of Monte Carlo simulations for error estimation. See details.- output.plot
logical (

*with default*): plot output (`TRUE/FALSE`

).- output.plotExtended
logical (

*with default*): If'`TRUE`

, 3 plots on one plot area are provided:growth curve,

histogram from Monte Carlo error simulation and

a test dose response plot.

If

`FALSE`

, just the growth curve will be plotted.**Requires:**`output.plot = TRUE`

.- output.plotExtended.single
logical (

*with default*): single plot output (`TRUE/FALSE`

) to allow for plotting the results in single plot windows. Requires`output.plot = TRUE`

and`output.plotExtended = TRUE`

.- cex.global
numeric (

*with default*): global scaling factor.- txtProgressBar
logical (

*with default*): enables or disables txtProgressBar. If`verbose = FALSE`

also no txtProgressBar is shown.- verbose
logical (

*with default*): enables or disables terminal feedback.- ...
Further arguments and graphical parameters to be passed. Note: Standard arguments will only be passed to the growth curve plot. Supported:

`xlim`

,`ylim`

,`main`

,`xlab`

,`ylab`

##### 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 uniroot.

`LIN`

: fits a linear function to the data using
lm: $$y = m*x+n$$

`QDR`

: fits a linear function to the data using
lm: $$y = a + b * x + c * x^2$$

`EXP`

: try to fit a function of the form
$$y = a*(1-exp(-(x+c)/b))$$
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:
$$y = a*(1-exp(-(x+c)/b)+(g*x))$$
The De 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
$$y = (a1*(1-exp(-(x)/b1)))+(a2*(1-exp(-(x)/b2)))$$
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

$$y = a*(1-(1+(1/b)*x*c)^(-1/c))$$

where **c > 0** is a kinetic order modifier
(not to be confused with **c** in `EXP`

or `EXP+LIN`

!).

**Fit weighting**

If the option `fit.weights = TRUE`

is chosen, weights are calculated using
provided signal errors (Lx/Tx error):
$$fit.weights = 1/error/(sum(1/error))$$

**Error estimation using Monte Carlo simulation**

Error estimation is done using a Monte Carlo (MC) simulation approach. A set of Lx/Tx values is
constructed by randomly drawing curve data from samled from normal
distributions. The normal distribution is defined by the input values (mean
= value, sd = value.error). Then, a growth curve fit is attempted for each
dataset resulting in a new distribution of single De values. The sd
of this distribution is becomes then the error of the De. With increasing
iterations, the error value becomes more stable.
**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.

**Subtitle information**

To avoid plotting the subtitle information, provide an empty user mtext
`mtext = ""`

. To plot any other subtitle text, use `mtext`

.

##### Value

Along with a plot (so far wanted) an `RLum.Results`

object is returned containing,
the slot `data`

contains the following 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` |

`..$Formula` : |
expression | Fitting formula as R expression |

`..$call` : |
`call` |
The original function call |

##### Function version

1.10.5 (2018-08-03 10:46:48)

##### How to cite

Kreutzer, S., Dietze, M. (2018). plot_GrowthCurve(): Fit and plot a growth curve for luminescence data (Lx/Tx against dose). Function version 1.10.5. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J. (2018). Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 0.8.6. https://CRAN.R-project.org/package=Luminescence

##### 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.

##### See Also

nls, '>RLum.Results, get_RLum, minpack.lm::nlsLM, lm, uniroot

##### Examples

```
# NOT RUN {
##(1) plot growth curve for a dummy data.set and show De value
data(ExampleData.LxTxData, envir = environment())
temp <- plot_GrowthCurve(LxTxData)
get_RLum(temp)
##(1a) to access the fitting value try
get_RLum(temp, data.object = "Fit")
##(2) plot the growth curve only - uncomment to use
##pdf(file = "~/Desktop/Growth_Curve_Dummy.pdf", paper = "special")
plot_GrowthCurve(LxTxData)
##dev.off()
##(3) plot growth curve with pdf output - uncomment to use, single output
##pdf(file = "~/Desktop/Growth_Curve_Dummy.pdf", paper = "special")
plot_GrowthCurve(LxTxData, output.plotExtended.single = TRUE)
##dev.off()
##(4) plot resulting function for given intervall x
x <- seq(1,10000, by = 100)
plot(
x = x,
y = eval(temp$Formula),
type = "l"
)
##(5) plot using the 'extrapolation' mode
LxTxData[1,2:3] <- c(0.5, 0.001)
print(plot_GrowthCurve(LxTxData,mode = "extrapolation"))
##(6) plot using the 'alternate' mode
LxTxData[1,2:3] <- c(0.5, 0.001)
print(plot_GrowthCurve(LxTxData,mode = "alternate"))
##(7) import and fit test data set by Berger & Huntley 1989
QNL84_2_unbleached <-
read.table(system.file("extdata/QNL84_2_unbleached.txt", package = "Luminescence"))
results <- plot_GrowthCurve(
QNL84_2_unbleached,
mode = "extrapolation",
plot = FALSE,
verbose = FALSE)
#calculate confidence interval for the parameters
#as alternative error estimation
confint(results$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(
plot_GrowthCurve(
QNL84_2_bleached,
mode = "alternate",
plot = FALSE,
verbose = FALSE)$Fit)
print(
plot_GrowthCurve(
STRB87_1_unbleached,
mode = "alternate",
plot = FALSE,
verbose = FALSE)$Fit)
print(
plot_GrowthCurve(
STRB87_1_bleached,
mode = "alternate",
plot = FALSE,
verbose = FALSE)$Fit)
# }
# NOT RUN {
# }
```

*Documentation reproduced from package Luminescence, version 0.8.6, License: GPL-3*