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" <[EMAIL PROTECTED]> To: "Haifeng (Kevin) Xie" <[EMAIL PROTECTED]> Cc: "R-help mailing list" <[EMAIL PROTECTED]> 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" <[EMAIL PROTECTED]> 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 [EMAIL PROTECTED] > Statistics Department 608/262-2598 > University of Wisconsin - Madison http://www.stat.wisc.edu/~bates/ > ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
