# plf: Basis of a Piecewise Linear Function In qrcm: Quantile Regression Coefficients Modeling

## Description

Generates b1(p), b2(p), … such that, for 0 < p < 1,

θ1*b1(p) + θ2*b2(p) + …

is a piecewise linear function with slopes θ1, θ2, ….

## Usage

 `1` ```plf(p, knots) ```

## Arguments

 `p` a numeric vector of values between 0 and 1. `knots` a set of internal knots between 0 and 1. It can be NULL for no internal knots.

## Details

This function permits computing a piecewise linear function on the unit interval. A different slope holds between each pair of knots, and the function is continuous at the knots.

## Value

A matrix with one row for each element of p, and `length(knots) + 1` columns. The knots are returned as `attr(, "knots")`. Any linear combination of the basis matrix is a piecewise linear function where each coefficient represents the slope in the corresponding sub-interval (see ‘Examples’).

## Note

This function is typically used within a call to `iqr`. A piecewise linear function can be used to describe how quantile regression coefficients depend on the order of the quantile.

## Author(s)

Paolo Frumento [email protected]

`slp`, for shifted Legendre polynomials.

## Examples

 ```1 2 3 4 5 6 7``` ``` p <- seq(0,1, 0.1) a1 <- plf(p, knots = NULL) # returns p a2 <- plf(p, knots = c(0.2,0.7)) plot(p, 3 + 1*a2[,1] - 1*a2[,2] + 2*a2[,3], type = "l") # intercept = 3; slopes = (1,-1,2) ```

### Example output

```Loading required package: survival