R help - Oct 2003 - Variance-covariance matrix for beta hat and b hat from lme

Dear all,

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?

The reason for needing this is because I want to have interval prediction on
the predicted values (at level = 0:1). The "predict.lme" seems to
provide
point estimates only. The predicted value for new observation of the i_th
subject, with E_i and F_i as regressor matrices for fixed- and
random-effects respectively, is
y_i hat = E_i * beta hat + F_i * b_i hat

which can also be written as
y_i hat = [ E_i, F_i ] * [ beta hat ', b_i hat' ]' , where prime
denotes
transpose.

Therefore, the variance of y_i hat is
Var(y_i hat) = [ E_i, F_i ] * var( [ beta hat ', b_i hat' ]' ) * [
E_i,
F_i ]' ,

I'm not entire sure if this is the correct way to do, any suggestions will
be particularly welcome.

Many thanks.

Kevin Xie
Research Student
University of Westminster
London, UK

"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/