ATS function

Akritas-Theil-Sen line for censored data

Computes Kendall's tau and the Akritas-Theil-Sen (ATS) line for censored data, along with the test that the slope (and Kendall's tau) equal zero. For one x variable regression.

ATS(
  y.var,
  y.cen,
  x.var,
  x.cen = rep(0, times = length(x.var)),
  LOG = TRUE,
  retrans = FALSE,
  xlabel = NULL,
  ylabel = NULL,
  printstat = TRUE,
  drawplot = TRUE
)

Arguments

• y.var: The column of y (response variable) values plus detection limits
• y.cen: The y-variable indicators, where 1 (or TRUE) indicates a detection limit in the y.var column, and 0 (or FALSE) indicates a detected value in y.var.
• x.var: The column of x (explanatory variable) values plus detection limits
• x.cen: The x-variable indicators, where 1 (or TRUE) indicates a detection limit in the x.var column, and 0 (or FALSE) indicates a detected value in x.var.
• LOG: Indicator of whether to compute the ATS line in the original y units, or for their logarithms. The default is to use the logarithms (LOG = TRUE). To compute in original units, specify the option LOG = FALSE (or LOG = 0).
• retrans: Indicator of whether to retransform the plot and line back to original Y-variable units. Not needed when LOG = FALSE. When retrans = FALSE & LOG = TRUE the plot is drawn with logY units (default). When retrans = TRUE & LOG = TRUE the plot is drawn with original Y units.
• xlabel: Custom label for the x axis of plots. Default is x variable column name.
• ylabel: Custom label for the y axis of plots. Default is y variable column name.
• printstat: Logical TRUE/FALSE option of whether to print the resulting statistics in the console window, or not. Default is TRUE.
• drawplot: Logical TRUE/FALSE option of whether to draw plots or not. Default is TRUE

Returns

Coefficients (intercept and slope) for the ATS line are printed, along with Kendall's tau correlation coefficient, test statistic S, and the (single) p-value for the test that tau and slope both equal zero. A scatterplot with the fitted trend-line superimposed is also drawn.

Examples

# Both y and x are censored
data(PbHeron)
with(PbHeron, ATS(Blood, BloodCen, Kidney, KidneyCen))

# x is not censored
data(Brumbaugh)
with(Brumbaugh,ATS(Hg, HgCen, PctWetland))

References

Akritas, M.G., Murphy, S.A., LaValley, M.P., 1995. The Theil-Sen Estimator With Doubly Censored Data and Applications to Astronomy. Journal of the American Statistical Association 90, 170–177. https://doi.org/10.2307/2291140

Helsel, D.R., 2011. Statistics for Censored Environmental Data using Minitab and R, 2nd ed. John Wiley & Sons, USA, N.J.