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FunBootBand

The FunBootBand package contains one function band(), which generates statistical (prediction or confidence) bands from time series or curve data using a functional approach and bootstrapping.

Acknowledgments

At its core, this package is an implementation of the method developed by Sutherland et al. (1988) and Olshen et al. (1989), described in detail in Lenhoff et al. (1999). The method was originally written as a MATLAB program by Doris Oriwol and later translated into R and extended with an approach to handle nested/hierarchical data (see also https://github.com/koda86/floa).

For more theoretical background, see this publication:

Koska, D., Oriwol, D., & Maiwald, C. (2023). Comparison of statistical models for characterizing continuous differences between two biomechanical measurement systems. Journal of Biomechanics 149, https://doi.org/10.1016/j.jbiomech.2023.111506.

Installation

You can install the development version of FunBootBand from GitHub with:

# install.packages("devtools")
devtools::install_github("koda86/FunBootBand")

Usage

The package comes with a built-in data set (named data) of dimension [101, 110], meaning 110 curves are arranged in columns of length 101 (each column represents a curve). Your data set should be structured the same way.

Here’s how to use the band() function with the built-in data set (iid case).

library(FunBootBand)

# In the example, the number of bootstrap iterations `B` is set to only 5 to guarantee a fast calculation.
# In reality, this value would be too low (package default: 400).
prediction.band <- band(data,
                        type = "prediction",
                        B = 5,
                        alpha = 0.05,
                        iid = TRUE)

# Function output:
rownames(prediction.band)
#> [1] "upper" "mean"  "lower"
str(prediction.band)
#>  num [1:3, 1:101] 0.766 0.153 -0.461 0.81 0.196 ...
#>  - attr(*, "dimnames")=List of 2
#>   ..$ : chr [1:3] "upper" "mean" "lower"
#>   ..$ : NULL

You may, i.e., print the calculated limits alongside the original curves.

plot(data[, 1], type = "l", ylim = c(-3, 3), ylab = "Amplitude")
apply(data, 2, function(x) lines(x))
apply(prediction.band, 1, function(x) lines(x, col = "red", lwd = 4))

Function arguments

type

Setting type to “prediction” or “confidence” will generate the respective statistical bands.

alpha

When constructing prediction intervals, the significance level alpha will affect the band width. Lower values of alpha will result in wider bands.

iid

As in many empirical data sets, the curves in the built-in data set data have a hierarchical structure, which means that curves are arranged in clusters. These clusters may e.g. represent subjects, within which several curves are nested. The header in data specifies this cluster structure by assigning curves of the same cluster the same letter. The function argument iid, as in independent and identically distributed, specifies if the cluster structure is accounted for (iid=FALSE), or if curves are treated as independent (iid=TRUE). In the iid=TRUE case, no header is required. For the other function arguments, please see the function description or Function Arguments. They should be self-explanatory.

k.coef

In the applied functional approach, curves are approximated using Fourier series. k.coef sets the number of Fourier coefficients and depends on the smoothness of the curves. The default value of 50 is rather high for smooth curves and may be reduced. This, however, should be accompanied by some sort of (graphical) plausibility check. If curves are too rough, or if curves are generated by a non-stationary process, the functional approach may fail altogether.

B

The distribution of the curves and thus the band width is estimated using a bootstrap procedure. Larger values typically provide better estimates, but will take longer to compute. The band width is likely to converge to a certain value. Therefore, different values of B may be tested to investigate the convergence behavior. By default, B is set to 400.

Issues and contributing

You can use the “Issues” tab in the Github repo or write me an E-Mail ().

Licence

LGPL (>= 3)

References

  • Lenhoff, M.W., Santner, T.J., Otis, J.C., Peterson, M.G., Williams, B.J., Backus, S.I., 1999. Bootstrap prediction and confidence bands: a superior statistical method for analysis of gait data. Gait Posture 9 (1), 10–17. http://dx.doi.org/10.1016/s0966- 6362(98)00043-5.

  • Olshen, R.A., Biden, E.N., Wyatt, M.P., Sutherland, D.H., 1989. Gait analysis and the bootstrap. Ann. Statist. 17 (4), http://dx.doi.org/10.1214/aos/1176347372.

  • Sutherland, D., Olshen, R., Biden, E., Wyatt, M., 1988. Development of Mature Walking. Mac Keith Press.