nsDS {dsBase} R Documentation

## Generate a Basis Matrix for Natural Cubic Splines

### Description

This function is based on the native R function `ns` from the `splines` package. This function generate the B-spline basis matrix for a natural cubic spline.

### Usage

```nsDS(x, df, knots, intercept, Boundary.knots)
```

### Arguments

 `x` the predictor variable. Missing values are allowed. `df` degrees of freedom. One can supply df rather than knots; ns() then chooses df - 1 - intercept knots at suitably chosen quantiles of x (which will ignore missing values). The default, df = NULL, sets the number of inner knots as length(knots). `knots` breakpoints that define the spline. The default is no knots; together with the natural boundary conditions this results in a basis for linear regression on x. Typical values are the mean or median for one knot, quantiles for more knots. See also Boundary.knots. `intercept` if TRUE, an intercept is included in the basis; default is FALSE. `Boundary.knots` boundary points at which to impose the natural boundary conditions and anchor the B-spline basis (default the range of the data). If both knots and Boundary.knots are supplied, the basis parameters do not depend on x. Data can extend beyond Boundary.knots

### Details

`ns` is native R is based on the function `splineDesign`. It generates a basis matrix for representing the family of piecewise-cubic splines with the specified sequence of interior knots, and the natural boundary conditions. These enforce the constraint that the function is linear beyond the boundary knots, which can either be supplied or default to the extremes of the data. A primary use is in modeling formula to directly specify a natural spline term in a model.

### Value

A matrix of dimension length(x) * df where either df was supplied or if knots were supplied, df = length(knots) + 1 + intercept. Attributes are returned that correspond to the arguments to ns, and explicitly give the knots, Boundary.knots etc for use by predict.ns(). The object is assigned at each serverside.

### Author(s)

Demetris Avraam for DataSHIELD Development Team

[Package dsBase version 6.2.0 ]