Description Arguments Details Value Author(s) References Examples

Given an `sme`

object, returns the roughness matrix which can be used to quickly
calculate the integrated squared second derivative of the mean and individual level curves

`object` |
a fitted SME model object returned from the |

The parameters of the SME model are estimated using maximum *penalized* likelihood, where the
penalized likelihood is the standard likelihood with the addition of penalty terms corresponding to
the roughness of the mean and individual level curves. Typically the roughness of a curve is
quantified as its integrated squared second derivative. Green and Silverman (1994) show that, for a
natural cubic spline interpolating the vector of points $f$, there exists a *roughness matrix*
$G$ such that the integrated squared second derivate is $f'Gf$ where $f'$ denotes $f$ transposed.
For details on constructing the matrix $G$, either refer to the original source of
Green and Silverman (1994) or it may prove easier to access Berk and Montana (2009) where they can
be found in the appendix.

The roughness matrix corresponding to the SME model fit

Maurice Berk [email protected]

Berk, M. (2012). *Smoothing-splines Mixed-effects Models in R*. Preprint

Berk, M. & Montana, G. (2009). *Functional modelling of microarray time series with covariate curves*. Statistica, 2-3, 158-187

Green, P. J. & Silverman, B. W. (1994). *Nonparametric Regression and Generalized Linear Models*. Chapman and Hall

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