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

[Haifeng (Kevin) Xie]

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