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

http://www.maths.bath.ac.uk/~sw283/

### See Also

`mgcv `

`pcls`

### Examples

## see ?pcls

[Package

*mgcv* version 1.3-23

Index]