This set of functions implements an
pdMat class to allow tensor product smooths to be estimated by
lme as called by
gamm. Tensor product smooths have a penalty matrix made up of a weighted sum of penalty matrices, where the weights are the smoothing parameters. In the mixed model formulation the penalty matrix is the inverse of the covariance matrix for the random effects of a term, and the smoothing parameters (times a half) are variance parameters to be estimated. It's not possible to transform the problem to make the required random effects covariance matrix look like one of the standard
pdMat classes: hence the need for the
pdTens class. A
notLog2 parameterization ensures that the parameters are positive.
These functions (
summary.pdTens) would not normally be called directly.
pdTens(value = numeric(0), form = NULL, nam = NULL, data = sys.frame(sys.parent()))
- Initialization values for parameters. Not normally used.
- A one sided formula specifying the random effects structure. The formula should have an attribute
Swhich is a list of the penalty matrices the weighted sum of which gives the inverse of the covariance matrix for these random effects.
- a names argument, not normally used with this class.
- data frame in which to evaluate formula.
If using this class directly note that it is worthwhile scaling the
S matrices to be of `moderate size', for example by dividing each matrix by its largest singular value: this avoids problems with
lme defaults (
smooth.construct.tensor.smooth.spec does this automatically).
This appears to be the minimum set of functions required to implement a new
Note that while the
pdMatrix functions return the inverse of the scaled random effect covariance matrix or its factor, the
pdConstruct function is sometimes initialised with estimates of the scaled covariance matrix, and sometimes intialized with its inverse.
Pinheiro J.C. and Bates, D.M. (2000) Mixed effects Models in S and S-PLUS. Springer
nlme source code.
# see gamm
Documentation reproduced from package mgcv, version 1.7-22. License: GPL (>= 2)