Deepayan, Yes, thanks for confirming my suspicions. I know mixed models are "different" but, I did not think they were so different as to preclude estimating the var-cov matrix (via the Hessian in Maximum likelihood, as you point out).
Thanks for prompting me to think about MCMC. Your suggestion to consider MCMC makes me realize that using BUGS, I could directly sample from the posterior of the linear combination of parameters - to get its variance and eliminate the extra step using the var-cov matrix. As you say, with results better than the asymptotic approximation. (Maybe I can do the same thing with mcmcsamp?, but I'm not familiar with this and will have to take a look at it.) -----Original Message----- From: Deepayan Sarkar [mailto:[EMAIL PROTECTED] Sent: Thursday, November 17, 2005 2:22 PM To: Doran, Harold Cc: Wassell, James T., Ph.D.; [email protected] Subject: Re: nlme question On 11/17/05, Doran, Harold <[EMAIL PROTECTED]> wrote: > I think the authors are mistaken. Sigma is random error, and due to its > randomness it cannot be systematically related to anything. It is this > ind. assumption that allows for the likelihood to be expressed as > described in Pinhiero and Bates p.62. I think not. The issue is dependence between the _estimates_ of sigma, tao, etc, and that may well be present. Presumably, if one can compute the likelihood surface as a function of the 3 parameters, the hessian at the MLE's would give the estimated covariance. However, I don't think nlme does this. A different approach you might want to consider is using mcmcsamp in the lme4 package (or more precisely, the Matrix package) to get samples from the joint posterior distribution. This is likely to be better than the asymptotic normal approximation in any case. Deepayan ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
