extract.lme.cov: Extract the data covariance matrix from an lme object

In mgcv: Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

Extract the data covariance matrix from an lme object

Description

This is a service routine for gamm. Extracts the estimated covariance matrix of the data from an lme object, allowing the user control about which levels of random effects to include in this calculation. extract.lme.cov forms the full matrix explicitly: extract.lme.cov2 tries to be more economical than this.

Usage

extract.lme.cov(b,data=NULL,start.level=1)
extract.lme.cov2(b,data=NULL,start.level=1)

Arguments

b	A fitted model object returned by a call to lme

.

data	The data frame/ model frame that was supplied to lme, but with any rows removed by the na action dropped. Uses the data stored in the model object if not supplied.
start.level	The level of nesting at which to start including random effects in the calculation. This is used to allow smooth terms to be estimated as random effects, but treated like fixed effects for variance calculations.

Details

The random effects, correlation structure and variance structure used for a linear mixed model combine to imply a covariance matrix for the response data being modelled. These routines extracts that covariance matrix. The process is slightly complicated, because different components of the fitted model object are stored in different orders (see function code for details!).

The extract.lme.cov calculation is not optimally efficient, since it forms the full matrix, which may in fact be sparse. extract.lme.cov2 is more efficient. If the covariance matrix is diagonal, then only the leading diagonal is returned; if it can be written as a block diagonal matrix (under some permutation of the original data) then a list of matrices defining the non-zero blocks is returned along with an index indicating which row of the original data each row/column of the block diagonal matrix relates to. The block sizes are defined by the coarsest level of grouping in the random effect structure.

gamm uses extract.lme.cov2.

extract.lme.cov does not currently deal with the situation in which the grouping factors for a correlation structure are finer than those for the random effects. extract.lme.cov2 does deal with this situation.

Value

For extract.lme.cov an estimated covariance matrix.

For extract.lme.cov2 a list containing the estimated covariance matrix and an indexing array. The covariance matrix is stored as the elements on the leading diagonal, a list of the matrices defining a block diagonal matrix, or a full matrix if the previous two options are not possible.

Author(s)

Simon N. Wood [e-mail]

References

For lme see:

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

For details of how GAMMs are set up here for estimation using lme see:

Wood, S.N. (2006) Low rank scale invariant tensor product smooths for Generalized Additive Mixed Models. Biometrics 62(4):1025-1036

or

Wood S.N. (2017) Generalized Additive Models: An Introduction with R (2nd edition). Chapman and Hall/CRC Press.

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

See Also

gamm, formXtViX

Examples

## see also ?formXtViX for use of extract.lme.cov2
require(mgcv)
library(nlme)
data(Rail)
b <- lme(travel~1,Rail,~1|Rail)
extract.lme.cov(b)
extract.lme.cov2(b)

mgcv documentation built on May 29, 2024, 4:34 a.m.