CMLS (version 1.0-1)

MsplineBasis: M-Spline Basis for Polynomial Splines

Description

Generate the M-spline basis matrix for a polynomial spline.

Usage

MsplineBasis(x, df = NULL, knots = NULL, degree = 3, intercept = FALSE,
             Boundary.knots = range(x), periodic = FALSE)

Value

A matrix of dimension c(length(x), df) where either df was supplied or df = length(knots) + degree + ifelse(intercept, 1, 0)

Arguments

x

the predictor variable. Missing values are not allowed.

df

degrees of freedom; if specified the number of knots is defined as df - degree - ifelse(intercept, 1, 0); the knots are placed at the quantiles of x

knots

the internal breakpoints that define the spline (typically the quantiles of x)

degree

degree of the piecewise polynomial---default is 3 for cubic splines

intercept

if TRUE, the basis includes an intercept column

Boundary.knots

boundary points for M-spline basis; defaults to min and max of x

periodic

if TRUE, the M-spline basis is constrained to be periodic

Author

Nathaniel E. Helwig <[e-mail]>

Details

Syntax is adapted from the bs function in the splines package (R Core Team, 2021).

Used for implementing various types of smoothness constraints in the cmls fucntion.

References

R Core Team (2023). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/

Ramsay, J. O. (1988). Monotone regression splines in action. Statistical Science, 3, 425-441. tools:::Rd_expr_doi("10.1214/ss/1177012761")

See Also

IsplineBasis

Examples

x <- seq(0, 1, length.out = 101)
M <- MsplineBasis(x, df = 8, intercept = TRUE)
M <- scale(M, center = FALSE)
plot(x, M[,1], ylim = range(M), t = "l")
for(j in 2:8) lines(x, M[,j], col = j)