`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

```
gsl.bs(…)
# S3 method for default
gsl.bs(x,
degree = 3,
nbreak = 2,
deriv = 0,
x.min = NULL,
x.max = NULL,
intercept = FALSE,
knots = NULL,
…)
```

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

`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.

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)

Li, Q. and J.S. Racine (2007), *Nonparametric Econometrics:
Theory and Practice,* Princeton University Press.

Ma, S. and J.S. Racine and L. Yang (2015), “Spline Regression in the Presence of Categorical Predictors,” Journal of Applied Econometrics, Volume 30, 705-717.

Ma, S. and J.S. Racine (2013), “Additive Regression Splines with Irrelevant Categorical and Continuous Regressors,” Statistica Sinica, Volume 23, 515-541.

# NOT RUN { ## 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))) # }