sme (version 0.8)

getRoughnessMatrix: Extract the roughness matrix used in an SME model fit

Description

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

Arguments

object

a fitted SME model object returned from the sme function

Value

The roughness matrix corresponding to the SME model fit

Details

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.

References

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

Examples

  data(MTB)
  fit <- sme(MTB[MTB$variable==6031,c("y","tme","ind")])
  getRoughnessMatrix(fit)