mono.con {mgcv} R Documentation

## Monotonicity constraints for a cubic regression spline

### Description

Finds linear constraints sufficient for monotonicity (and optionally upper and/or lower boundedness) of a cubic regression spline. The basis representation assumed is that given by the `gam`, `"cr"` basis: that is the spline has a set of knots, which have fixed x values, but the y values of which constitute the parameters of the spline.

### Usage

```mono.con(x,up=TRUE,lower=NA,upper=NA)
```

### Arguments

 `x` The array of knot locations. `up` If `TRUE` then the constraints imply increase, if `FALSE` then decrease. `lower` This specifies the lower bound on the spline unless it is `NA` in which case no lower bound is imposed. `upper` This specifies the upper bound on the spline unless it is `NA` in which case no upper bound is imposed.

### Details

Consider the natural cubic spline passing through the points: (x_i,p_i), i=1..n. Then it is possible to find a relatively small set of linear constraints on p sufficient to ensure monotonicity (and bounds if required): Ap>=b. Details are given in Wood (1994). This function returns a list containing `A` and `b`.

### Value

The function returns a list containing constraint matrix `A` and constraint vector `b`.

### Author(s)

Simon N. Wood simon.wood@r-project.org

### References

Gill, P.E., Murray, W. and Wright, M.H. (1981) Practical Optimization. Academic Press, London.

Wood, S.N. (1994) Monotonic smoothing splines fitted by cross validation SIAM Journal on Scientific Computing 15(5):1126-1133

`mgcv ` `pcls`
```## see ?pcls