Generates the basis matrix of the regression spline called M-spline or the corresponding derivatives of given order. For monotone regression, iSpline should be used instead of M-splines.

  df = NULL,
  knots = NULL,
  degree = 3L,
  intercept = FALSE,
  Boundary.knots = NULL,
  derivs = 0L,



The predictor variable. Missing values are allowed and will be returned as they are.


Degree of freedom that equals to the column number of returned matrix. One can specify df rather than knots, then the function chooses df - degree - as.integer(intercept) internal knots at suitable quantiles of x ignoring missing values and those x outside of the boundary. If internal knots are specified via knots, the specified df will be ignored.


The internal breakpoints that define the spline. The default is NULL, which results in a basis for ordinary polynomial regression. Typical values are the mean or median for one knot, quantiles for more knots.


A non-negative integer specifying the degree of the piecewise polynomial. The default value is 3 for cubic splines. Zero degree is allowed for piece-wise constant bases.


If TRUE, the complete basis matrix will be returned. Otherwise, the first basis will be excluded from the output.


Boundary points at which to anchor the spline basis. By default, they are the range of the non-NA data. If both knots and Boundary.knots are supplied, the basis parameters do not depend on x. Data can extend beyond Boundary.knots.


A non-negative integer specifying the order of derivatives of M-splines. The default value is 0L for M-spline bases.


Optional arguments that are not used.


A numeric matrix with length(x) rows and df columns if df is specified or length(knots) + degree + as.integer(intercept) columns if knots are specified instead. Attributes that correspond to the arguments specified are returned for usage of other functions in this package.


It is an implementation of the close form M-spline basis based on the recursion formula given by Ramsay (1988).


Ramsay, J. O. (1988). Monotone regression splines in action. Statistical science, 3(4), 425--441.

See also

bSpline for B-splines; iSpline for I-splines; cSpline for C-splines.


library(splines2) ## Example given in the reference paper by Ramsay (1988) x <-, 1, 0.01) knots <- c(0.3, 0.5, 0.6) msMat <- mSpline(x, knots = knots, degree = 2, intercept = TRUE) par(mar = c(2.5, 2.5, 0.2, 0.1), mgp = c(1.5, 0.5, 0)) matplot(x, msMat, type = "l", ylab = "y")
abline(v = knots, lty = 2, col = "gray")
## derivatives of M-splines dmsMat <- mSpline(x, knots = knots, degree = 2, intercept = TRUE, derivs = 1) ## or using the deriv method dmsMat1 <- deriv(msMat) stopifnot(all.equal(dmsMat, dmsMat1, check.attributes = FALSE))