Computes the Theil-Sen median slope, Siegel's repeated median slope or te equivariant Passing-Bablok slope. The algorithms run in an expected linearithmic time while requiring \(O(n)\) storage. They are based on Dillencourt et. al (1992), Matousek et. al (1998) and Raymaekers and Dufey (2022).
robslope(formula, data, subset, weights, na.action,
type = c("TheilSen", "RepeatedMedian","PassingBablok"),
alpha = NULL, beta = NULL, verbose = TRUE)robslope returns an object of class
"lm".
The generic accessor functions coefficients,
fitted.values and residuals extract
various useful features of the value returned by lm.
an object of class "formula" (or one that
can be coerced to that class): a symbolic description of the
model to be fitted. The details of model specification are given
under ‘Details’.
an optional data frame, list or environment (or object
coercible by as.data.frame to a data frame) containing
the variables in the model. If not found in data, the
variables are taken from environment(formula),
typically the environment from which robslope is called.
an optional vector specifying a subset of observations to be used in the fitting process.
an optional vector of weights to be used in the fitting process. Currently not supported.
a function which indicates what should happen
when the data contain NAs. The default na.exclude is applied and an informative message is given in case NAs were removed.
the type of robust slope estimator. Should be one of "TheilSen" (default), "RepeatedMedian" or "PassingBablok".
Determines the order statistic of the target slope. Defaults to the upper median. See below for details.
Determines the inner order statistic. Only used when type = "RepeatedMedian". See below for details.
Whether or not to print out the progress of the algorithm. Defaults to TRUE.
Jakob Raymaekers
This function provides a wrapper around robslope.fit, which in turn calls the individual functions TheilSen, RepeatedMedian or PassingBablok. The details on changing the parameters alpha and beta can be found in the documentation of those respective functions.
Theil, H. (1950), A rank-invariant method of linear and polynomial regression analysis (Parts 1-3), Ned. Akad. Wetensch. Proc. Ser. A, 53, 386-392, 521-525, 1397-1412.
Sen, P. K. (1968). Estimates of the regression coefficient based on Kendall's tau. Journal of the American statistical association, 63(324), 1379-1389.
Dillencourt, M. B., Mount, D. M., & Netanyahu, N. S. (1992). A randomized algorithm for slope selection. International Journal of Computational Geometry & Applications, 2(01), 1-27.
Siegel, A. F. (1982). Robust regression using repeated medians. Biometrika, 69(1), 242-244.
Matousek, J., Mount, D. M., & Netanyahu, N. S. (1998). Efficient randomized algorithms for the repeated median line estimator. Algorithmica, 20(2), 136-150.
Passing, H., Bablok, W. (1983). A new biometrical procedure for testing the equality of measurements from two different analytical methods. Application of linear regression procedures for method comparison studies in clinical chemistry, Part I, Journal of clinical chemistry and clinical biochemistry, 21,709-720.
Bablok, W., Passing, H., Bender, R., Schneider, B. (1988). A general regression procedure for method transformation. Application of linear regression procedures for method comparison studies in clinical chemistry, Part III. Journal of clinical chemistry and clinical biochemistry, 26,783-790.
Raymaekers J., Dufey F. (2022). Equivariant Passing-Bablok regression in quasilinear time. (link to open access pdf)
Raymaekers (2023). "The R Journal: robslopes: Efficient Computation of the (Repeated) Median Slope", The R Journal. (link to open access pdf)
robslope.fit
TheilSen
RepeatedMedian
PassingBablok
set.seed(123)
df <- data.frame(cbind(rnorm(20), rnorm(20)))
colnames(df) <- c("x", "y")
robslope.out <- robslope(y~x, data = df,
type = "RepeatedMedian", verbose = TRUE)
coef(robslope.out)
plot(fitted.values(robslope.out))
robslope.out <- robslope(y~x, data = df,
type = "TheilSen", verbose = TRUE)
plot(residuals(robslope.out))
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