Thank you very much for the reply (and hopefully I am replying back in the proper way). Do you think the delta method would be an acceptable way to estimate approximate confidence intervals for the resulting group specific coefficients (combining fixed effects and BLUPS)? Regarding the MCMC related approach, how is it possible to save the fixed and the random effects from the MCMC chain? Can this be implemented through nlme library or is there some more clear cut way (I wish I had a strong statistical background and abilities but... :)) to evaluate the empirical distribution of a parameter that is linear combination of these quantities?
All the best, Irene ________________________________ Από: [EMAIL PROTECTED] εκ μέρους Douglas Bates Αποστολή: Τετ 17/10/2007 10:04 μμ Προς: Doran, Harold Κοιν.: Irene Mantzouni; [EMAIL PROTECTED]; R-SIG-Mixed-Models Θέμα: Re: [R] coef se in lme On 10/15/07, Doran, Harold <[EMAIL PROTECTED]> wrote: > ?vcov The vcov method returns the estimated variance-covariance matrix of the fixed-effects only. I think Irene's question is about the combination of the fixed-effects parameters and the BLUPs of the random effects that is returned by the coef method applied to an lmer object. (You may recall that you were the person who requested such a method in lme4 like the coef method in nlme :-) On the face of it this quantity should be easy to define and evaluate but in fact it is not easy to do so because these are combinations of model parameters (the fixed effects) and unobserved random variables (the random effects). It gets a bit tricky trying to decide what the variance of this combination would be. I think there is a sensible definition, or at least a computationally reasonable definition, but there are still a few slippery points in the argument. Lately I have taken to referring to the "estimates" of the random effects, what are sometimes called the BLUPs or Best Linear Unbiased Predictors, as the "conditional modes" of the random effects. That is, they are the values that maximize the density of the random effects given the observed data and the values of the model parameters. For a linear mixed model the conditional distribution of the random effects is multivariate normal so the conditional modes are also the conditional means. Also, we can evaluate the conditional variance-covariance matrix of the random effects up to a scale factor. The next part is where things get a bit hazy for me but I think it makes sense to consider the joint distribution of the estimator of the fixed-effects parameters and the random effects conditional on the data and, possibly, on the variance components. Conditional on the relative variance-covariance of the random effects (i.e. the matrix that occurs as the penalty term in the penalized least squares representation of the model) the joint distribution of the fixed-effects estimators and the random effects is multivariate normal with mean and variance-covariance matrix determined from the mixed-model equations. This big (p+q by p+q, where p is the dimension of the fixed effects and q is the dimension of the random effects) variance-covariance matrix could be evaluated and, from that, the variance of any linear combination of components. However, I have my doubts about whether it is the most sensible answer to evaluate. Conditioning on the relative variance-covariance matrix of the random effects is cheating, in a way. It would be like saying we have a known variance, $\sigma^2$ when, in fact, we are using an estimate. The fact that we don't know $\sigma^2$ is what gives rise to the t distributions and F distributions in linear models and we are all trained to pay careful attention to the number of degrees of freedom in that estimate and how it affects our ideas of the precision of the estimates of other model parameters. For mixed models, though, many practioners are quite comfortable conditioning on the value of some of the variance components but not others. It could turn out that conditioning on the relative variance-covariance of the random effects is not a big deal but I don't know. I haven't examined it in detail and I don't know of others who have. Another approach entirely is to use Markov chain Monte Carlo to examine the joint distribution of the parameters (in the Bayesian sense) and the random effects. If you save the fixed effects and the random effects from the MCMC chain then you can evaluate the linear combination of interest throughout the chain and get an empirical distribution of the quantities returned by coef. This is probably an unsatisfactory answer for Irene who may have wanted something quick and simple. Unfortunately, I don't think there is a quick, simple answer here. I suggest we move this discussion to the R-SIG-Mixed-Models list which I am cc:ing on this reply. > -----Original Message----- > From: [EMAIL PROTECTED] on behalf of Irene Mantzouni > Sent: Mon 10/15/2007 3:20 PM > To: [EMAIL PROTECTED] > Subject: [R] coef se in lme > > Hi all! > > How is it possible to estimate standard errors for coef obtained from lme? > Is there sth like se.coef() for lmer or what is the anaytical solution? > > Thank you! > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
