Standardised Dispersion Analysis (SDA).

Source: R/fd.R

fd_sda

fd_sda(
  y,
  fs = NULL,
  removeTrend = c("no", "poly", "adaptive", "bridge")[2],
  polyOrder = 1,
  standardise = c("none", "mean.sd", "median.mad")[2],
  adjustSumOrder = FALSE,
  scaleMin = 4,
  scaleMax = stats::nextn(floor(NROW(y)/2), factors = 2),
  scaleResolution = log2(scaleMax) - log2(scaleMin),
  dataMin = NA,
  scaleS = NA,
  overlap = 0,
  doPlot = FALSE,
  returnPlot = FALSE,
  returnPLAW = FALSE,
  returnInfo = FALSE,
  silent = FALSE,
  noTitle = FALSE,
  tsName = "y"
)

Arguments

y

A numeric vector or time series object.

fs

Sample rate

removeTrend

Method to use for global detrending (default = "poly")

polyOrder

Order of global polynomial trend to remove if removeTrend = "poly". If removeTrend = "adaptive" polynomials 1 to polyOrder will be evaluated and the best fitting curve (R squared) will be removed (default = 1)

standardise

Standardise the series using ts_standardise() with adjustN = FALSE (default = "mean.sd")

adjustSumOrder

Adjust the time series (summation or difference), based on the global scaling exponent, see e.g. Ihlen (2012) (default = FALSE)

scaleMin

Minimum scale (in data points) to use for log-log regression (default = 4)

scaleMax

Maximum scale (in data points) to use for log-log regression. This value will be ignored if dataMin is not NA, in which case bins of size < dataMin will be removed (default = stats::nextn(floor(NROW(y)/4), factors = 2))

scaleResolution

The scales at which detrended fluctuation will be evaluated are calculated as: seq(scaleMin, scaleMax, length.out = scaleResolution) (default = round(log2(scaleMax-scaleMin))). #' @param dataMin Minimum number of data points in a bin required for inclusion in calculation of the scaling relation. For example if length(y) = 1024 and dataMin = 4, the maximum scale used to calculate the slope will be 1024 / 4 = 256. This value will take precedence over the scaleMax (default = NA)

scaleS

If not NA, it should be a numeric vector listing the scales on which to evaluate the detrended fluctuations. Arguments scaleMax, scaleMin, scaleResolution and dataMin will be ignored (default = NA)

overlap

A number in [0 ... 1] representing the amount of 'bin overlap' when calculating the fluctuation. This reduces impact of arbitrary time series begin and end points. If length(y) = 1024 and overlap is .5, a scale of 4 will be considered a sliding window of size 4 with step-size floor(.5 * 4) = 2, so for scale 128 step-size will be 64 (default = NA)

doPlot

Output the log-log scale versus fluctuation plot with linear fit by calling function plotFD_loglog() (default = TRUE)

returnPlot

Return ggplot2 object (default = FALSE)

returnPLAW

Return the power law data (default = FALSE)

returnInfo

Return all the data used in SDA (default = FALSE)

silent

Silent-ish mode (default = FALSE)

noTitle

Do not generate a title (only the subtitle) (default = FALSE)

tsName

Name of y added as a subtitle to the plot (default = "y")

Value

A list object containing:

  • A data matrix PLAW with columns freq.norm, size and bulk.

  • Estimate of scaling exponent sap based on a fit over the standard range (fullRange), or on a user defined range fitRange.

  • Estimate of the the Fractal Dimension (FD) using conversion formula's reported in Hasselman(2013).

  • Information output by various functions.

References

Hasselman, F. (2013). When the blind curve is finite: dimension estimation and model inference based on empirical waveforms. Frontiers in Physiology, 4, 75. https://doi.org/10.3389/fphys.2013.00075

See also

Other Fluctuation Analyses: fd_RR(), fd_allan(), fd_dfa(), fd_mfdfa(), fd_psd(), fd_sev()

Author

Fred Hasselman