Zncsspline {dae} | R Documentation |

## Calculates the design matrix for fitting the random component of a natural cubic smoothing spline

### Description

Calculates the design matrix, **Z**, of the random effects for a
natural cubic smoothing spline as described by Verbyla et al., (1999).
An initial design matrix,
`\bold{\Delta} \bold{\Delta}^{-1} \bold{\Delta}`

,
based on the knot points is computed. It can
then be post multiplied by the power of the tri-diagonal matrix
`\bold{G}_s`

that is proportional to the variance matrix of the
random spline effects. If the power is set to 0.5 then the random
spline effects based on the resulting Z matrix will be independent
with variance `\sigma_s^2`

.

### Usage

`Zncsspline(knot.points, Gpower = 0, print = FALSE)`

### Arguments

`knot.points` |
A |

`Gpower` |
A |

`print` |
A |

### Value

A `matrix`

containing the design matrix.

### Author(s)

Chris Brien

### References

Verbyla, A. P., Cullis, B. R., Kenward, M. G., and Welham, S. J. (1999).
The analysis of designed experiments and longitudinal data by using
smoothing splines (with discussion). *Journal of the Royal
Statistical Society, Series C (Applied Statistics)*, **48**, 269-311.

### See Also

### Examples

```
Z <- Zncsspline(knot.points = 1:10, Gpower = 0.5)
```

*dae*version 3.2.28 Index]