pdIdnot Overflow proof pdMat class for multiples of the identity matrix

Description

This set of functions is a modification of the pdMat class pdIdent from library nlme. The modification is to replace the log parameterization used in pdMat with a notLog2 parameterization, since the latter avoids indefiniteness in the likelihood and associated convergence problems: the parameters also relate to variances rather than standard deviations, for consistency with the pdTens class. The functions are particularly useful for working with Generalized Additive Mixed Models where variance parameters/smoothing parameters can be very large or very small, so that overflow or underflow can be a problem.

These functions would not normally be called directly, although unlike the pdTens class it is easy to do so.

Usage

pdIdnot(value = numeric(0), form = NULL, 
       nam = NULL, data = sys.frame(sys.parent()))

Arguments

value	Initialization values for parameters. Not normally used.
form	A one sided formula specifying the random effects structure.
nam	a names argument, not normally used with this class.
data	data frame in which to evaluate formula.

Details

The following functions are provided: Dim.pdIndot, coef.pdIdnot, corMatrix.pdIdnot, logDet.pdIdnot, pdConstruct.pdIdnot, pdFactor.pdIdnot, pdMatrix.pdIdnot, solve.pdIdnot, summary.pdIdnot. (e.g. mgcv:::coef.pdIdnot to access.)

Note that while the pdFactor and pdMatrix functions return the inverse of the scaled random effect covariance matrix or its factor, the pdConstruct function is initialised with estimates of the scaled covariance matrix itself.

Value

A class pdIdnot object, or related quantities. See the nlme documentation for further details.

Author(s)

Simon N. Wood [email protected]

References

Pinheiro J.C. and Bates, D.M. (2000) Mixed effects Models in S and S-PLUS. Springer

The nlme source code.

https://www.maths.ed.ac.uk/~swood34/

See Also

te, pdTens, notLog2, gamm

Examples

# see gamm