auc: Calculate the area under a line(curve).

Description Usage Arguments Details Value Author(s) See Also Examples

Description

Calculates the area under a curve (integral) following the trapezoid rule. With auc.mc several Monte Carlo methods can be applied to obtain error terms for estimating the interpolation error for the integration.

Usage

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auc(x, y, thresh = NULL, dens = 100, sort.x = TRUE)

auc.mc(x, y, method = "leave out", lo = 2, it = 100, ...)

Arguments

x

Numerical vector giving the x cordinates of the points of the line (curve).

y

Numerical vector giving the y cordinates of the points of the line (curve). One can calculate the integral of a fitted line through giving a vector to x that spans xlim with small intervals and predicting the y coordinates with predict and that x-vector as newdata. See example.

thresh

Threshold below which area is not calculated. Can be used to deal with unrealistically low flux data. By default thresh is set to NULL and therefore the complete area below the zero line is subtracted from the area above the zero line to integrate the area under the curve. When data below a certain value make no sense for your question, you are able to set thresh. Then, all y-values below thresh are set to the value of thresh and the regarding areas below thresh are not subtracted from the total area.

dens

By default the data density is artificially increased by adding 100 data points between given adjacent data points. These additional data points are calculated by linear interpolation along x and y. When a threshold is set, this procedure increases the accuracy of the result. Setting dens has no effect on the result when thresh is set to NULL.

sort.x

By default the vectors in x and y are ordered along increasing x because integration makes no sense with unordered data. You can override this by setting sort.x = FALSE

method

Specify how interpolation error should be estimated. Available methods include "leave out", "bootstrap", "sorted bootstrap", "constrained bootstrap", "jackknife", "jack-validate". True bootstrap is only effective when sort.x = FALSE. See details.

lo

When estimating interpolation error with "leave out" or "jack-validate", how many data points should be left out randomly? Defaults to 2. See method and details.

it

How many iterations should be run when using auc.mc to estimate the interpolation error. Defaults to 100.

...

Any arguments passed through to auc.

Details

During integration the underlying assumption is that values can be interpolated linearly between adjacent data points. In many cases this is questionable. For estimating the linear interpolation error from the data at hand one may use Monte Carlo resampling methods. In auc.mc the following approaches are available:

Value

auc returns a numeric value that expresses the area under the curve. The unit depends from the input.

auc.mc returns a numeric vector containing the auc values of the it permutations. Just calculate summary statistics from this as you like. Due to the sampling approaches means and medians are not stable for most of the methods. jackknife and jack-validate produce repeatable results, in the case of leave out it depends on n (length(x)) and it.

Author(s)

Gerald Jurasinski, gerald.jurasinski@uni-rostock.de

See Also

trapz, integrate

Examples

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## Construct a data set (Imagine 2-hourly ghg emission data
## (methane) measured during a day).
## The emission vector (data in mg CH4 / m2*h) as a time series.
ghg <- ts(c(12.3, 14.7, 17.3, 13.2, 8.5, 7.7, 6.4, 3.2, 19.8, 
22.3, 24.7, 15.6, 17.4), start=0, end=24, frequency=0.5)
## Have a look at the emission development.
plot(ghg)
## Calculate what has been emitted that day
## Assuming that emissions develop linearly between
## measurements
auc(time(ghg), ghg)

## Test some of the auc.mc approaches
## "leave out" as default
auc.rep <- auc.mc(time(ghg), ghg)
## mean and median are well below the original value
summary(auc.rep)
## results for "bootstrap" are unstable (run several times)
auc.rep <- auc.mc(time(ghg), ghg, "boot")
summary(auc.rep)
## results for "jack-validate" are stable (run several times)
auc.rep <- auc.mc(time(ghg), ghg, "jack-val", lo=3)
summary(auc.rep)

## The effect of below.zero:
## Shift data, so that we have negative emissions (immissions)
ghg <- ghg-10
## See the difference
plot(ghg)
abline(h=0)
## With thresh = NULL the negative emissions are subtracted
## from the positive emissions
auc(time(ghg), ghg)
## With thresh = -0.5 the negative emissions are set to -0.5
## and only the emissions >= -0.5 count.
auc(time(ghg), ghg, thresh = -0.5)

flux documentation built on May 2, 2019, 6:09 a.m.