# bsx: Polynomial B-splines with eXtensions In cuRe: Parametric Cure Model Estimation

 bsx R Documentation

## Polynomial B-splines with eXtensions

### Description

Generate the B-spline basis matrix for a polynomial spline with derivative restrictions at the boundary knots.

### Usage

```bsx(
x,
df = NULL,
knots = NULL,
degree = 3,
intercept = FALSE,
Boundary.knots = range(x),
deriv = NULL
)
```

### Arguments

 `x` the predictor variable. Missing values are allowed. `df` degrees of freedom; one can specify `df` rather than knots; `bs()` then chooses `df`-`degree` (minus one if there is an intercept) knots at suitable quantiles of `x` (which will ignore missing values). The default, `NULL`, corresponds to no inner knots, i.e., `degree`-`intercept`. `knots` 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. See also `Boundary.knots`. `degree` degree of the piecewise polynomial—default is `3` for cubic splines. `intercept` if `TRUE`, an intercept is included in the basis; default is `FALSE`. `Boundary.knots` boundary points at which to anchor the B-spline basis (default 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`. `deriv` an integer vector of length 2 with values between 0 and `degree + 1` giving the derivative constraint order at the left and right boundary knots; an order of 2 constrains the second derivative to zero (f”(x)=0); an order of 1 constrains the first and second derivatives to zero (f'(x)=f”(x)=0); an order of 0 constrains the zero, first and second derivatives to zero (f(x)=f'(x)=f”(x)=0) An order of `degree + 1` computes the basis matrix similarly to `bs`.

### Value

A matrix with containing the basis functions evaluated in `x`.

cuRe documentation built on May 17, 2022, 1:05 a.m.