[R] Variance-covariance matrix for beta hat and b hat from lme

[Haifeng (Kevin) Xie]

Dear Prof. Bates,

Many thanks for your reply. I think I will resolve to manually reading off
the necessary information from the summary report produced by summary.lme
and calculate the variance-covariance matrix based on expressions given in
Laird & Ware (1982) and Henderson (1975). In particular I will make use of
the result that the covariance between beta hat and b_i hat's are zero, and
covariance between b_i hat's themselves are zero as well, i.e. the matrix
cov(beta hat, b hat) is block diagonal, where b hat = [b_1 hat; b_2 hat;
...; b_m hat]' , m is the number of groups.

Reference
Laird, N. M. and J. H. Ware (1982).  Random-effects models for longitudinal
data.  Biometrics 38, 963-974.
Henderson, C. R. (1975).  Best linear unbiased estimation and prediction
under a selection model.  Biometrics 31, 423-447.


Many thanks again.

Haifeng Xie
Research Student
University of Westminster
London, UK


----- Original Message ----- 
From: "Douglas Bates" <bates at stat.wisc.edu>
To: "Haifeng (Kevin) Xie" <H.F.Xie at westminster.ac.uk>
Cc: "R-help mailing list" <r-help at stat.math.ethz.ch>
Sent: Thursday, October 23, 2003 5:50 PM
Subject: Re: [R] Variance-covariance matrix for beta hat and b hat from lme


> "Haifeng \(Kevin\) Xie" <H.F.Xie at westminster.ac.uk> writes:
>
> > Given a LME model (following the notation of Pinheiro and Bates 2000)
y_i
> > = X_i*beta + Z_i*b_i + e_i, is it possible to extract the
> > variance-covariance matrix for the estimated beta_i hat and b_i hat from
the
> > lme fitted object?
>
> Not easily.  The pieces that you need are in the condensed linear
> model structure and you may be able to extract them in R code but I
> have not written any code to do that.
>
> I am revising the internal representation of lme objects using S4
> classes.  Saikat DebRoy and I have one representation in the lme4
> package but will probably revise that.  Some recent work on
> computational methods
>         http://www.stat.wisc.edu/~bates/reports/MixedComp.pdf
> has me convinced that even this representation should be reorganized
> and simplified.
>
> If you really want to delve into the old structures I can give you
> some pointers (pun unintended) on where to look but beware that it's a
> quagmire.  (Oops - not supposed to use that word in e-mail originating
> in the U.S.A.  My regards to the NSA.)
>
>
> -- 
> Douglas Bates                            bates at stat.wisc.edu
> Statistics Department                    608/262-2598
> University of Wisconsin - Madison        http://www.stat.wisc.edu/~bates/
>