gsl-bs: GSL (GNU Scientific Library) B-spline/B-spline Derivatives

In JeffreyRacine/npiv: Nonparametric Instrumental Variables Estimation and Inference

GSL (GNU Scientific Library) B-spline/B-spline Derivatives

Description

gsl.bs generates the B-spline basis matrix for a polynomial spline and (optionally) the B-spline basis matrix derivative of a specified order with respect to each predictor

Usage

gsl.bs(...)
## Default S3 method:
gsl.bs(x,
       degree = 3,
       nbreak = 2,
       deriv = 0,
       x.min = NULL,
       x.max = NULL,
       intercept = FALSE,
       knots = NULL,
       ...)

Arguments

x	the predictor variable. Missing values are not allowed
degree	degree of the piecewise polynomial - default is ‘3’ (cubic spline)
nbreak	number of breaks in each interval - default is ‘2’
deriv	the order of the derivative to be computed-default if 0
x.min	the lower bound on which to construct the spline - defaults to min(x)
x.max	the upper bound on which to construct the spline - defaults to max(x)
intercept	if ‘TRUE’, an intercept is included in the basis; default is ‘FALSE’
knots	a vector (default knots="NULL") specifying knots for the spline basis (default enables uniform knots, otherwise those provided are used)
...	optional arguments

Details

Typical usages are (see below for a list of options and also the examples at the end of this help file)

    B <- gsl.bs(x,degree=10)
    B.predict <- predict(gsl.bs(x,degree=10),newx=xeval)
  

Value

gsl.bs returns a gsl.bs object. A matrix of dimension ‘c(length(x), degree+nbreak-1)’. The generic function predict extracts (or generates) predictions from the returned object.

A primary use is in modelling formulas to directly specify a piecewise polynomial term in a model. See https://www.gnu.org/software/gsl/ for further details.

Author(s)

Jeffrey S. Racine [e-mail]

References

Chen, X., T. Christensen and S. Kankanala (2024). “Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities.” Review of Economic Studies, forthcoming. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/restud/rdae025")}

See Also

bs

Examples

## Plot the spline bases and their first order derivatives
x <- seq(0,1,length=100)
matplot(x,gsl.bs(x,degree=5),type="l")
matplot(x,gsl.bs(x,degree=5,deriv=1),type="l")

## Regression example
n <- 1000
x <- sort(runif(n))
y <- cos(2*pi*x) + rnorm(n,sd=.25)
B <- gsl.bs(x,degree=5,intercept=FALSE)
plot(x,y,cex=.5,col="grey")
lines(x,fitted(lm(y~B)))

JeffreyRacine/npiv documentation built on Jan. 17, 2025, 8:29 p.m.