Angelo and Folks: Beware! It is not at all clear what you mean by "robust" regression. The sandwich estimator is often said to be "robust" to model misspecification in the sense that it converges to the correct covariance matrix whether or not the correlation structure in the GEE has been correctly specified (as Dmitris implied). Is this what you mean? Mixed effect models are often said to be "robust" in the sense that individual group "estimators" (blups) are shrunk toward the overall fixed effect estimates. Is this what you mean?
In other applications, "robustness" can mean insensitivity to distributional assumptions. Mixed effects models for continupus responses commonly assume normality (as the estimates solve likelihood equations), as do GLMM's for the random effects. I know of no definitive work that has examined sensitivity of estimates (or inferences, which are, at best, asymptotic anyway) to those assumptions. (in the simple independent errors case, it is usually the case that estimates are not at all sensitive). However, I am a novice here, so others may be able to illuminate the issue more. Finally, "robustness" is often used to mean "outlier resistance." Here the situation is yet murkier. Do you mean resistance to individual "outlying" observations within a subject or resistance to outlying subjects? Shrinkage should help with both, but, again, I know of no definitive work, especially regarding resistance to individual extreme values. Given the sensitivity of covariance estimates to heavy tails and the consequent inferential inefficiency, this presumably could be a problem. Finding methods that could deal with this may be nearly impossible, as you are adding yet another layer of nonlinear estimation (that of determining optimal case weights/parameters for mixture contamination models/or whatever...) to the problem; it is easy to come up with examples where the data are inherently ambiguous and parameter estimates for resistant case weights and the model would trade off with each other depending on starting values. That is, too many nonlinear parameters are being estimated and the model estimates are therefore unstable. Again, I am happy to leave more definitive resolution and correction of any errors in my comments to the experts, but, at the least, I think you need to think more and communicate more clearly about what you mean by "robust." Cheers, -- Bert Gunter Genentech Non-Clinical Statistics South San Francisco, CA "The business of the statistician is to catalyze the scientific learning process." - George E. P. Box > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of > Dimitris Rizopoulos > Sent: Wednesday, October 20, 2004 7:08 AM > To: Angelo Secchi > Cc: [EMAIL PROTECTED] > Subject: Re: [R] Robust regression with groups > > Hi Angelo, > > There are two possible options (at least to my knowledge): > > 1. to use a random-effects model, either using `lme' (packages: nlme, > lme4) if you have normal data or `glmmPQL' (package: MASS) or `GLMM' > (package: lme4) or `glmmML' (package:glmmML) if you cannot use the > normal distribution. > > 2. to use a gee model with a robust (sandwich) std.error estimation. > See at `gee' (package: gee) and `geese' (package: geepack). > > I hope this helps. > > Best, > Dimitris > > ---- > Dimitris Rizopoulos > Ph.D. Student > Biostatistical Centre > School of Public Health > Catholic University of Leuven > > Address: Kapucijnenvoer 35, Leuven, Belgium > Tel: +32/16/396887 > Fax: +32/16/337015 > Web: http://www.med.kuleuven.ac.be/biostat/ > http://www.student.kuleuven.ac.be/~m0390867/dimitris.htm > > > > > ----- Original Message ----- > From: "Angelo Secchi" <[EMAIL PROTECTED]> > To: <[EMAIL PROTECTED]> > Sent: Wednesday, October 20, 2004 3:22 PM > Subject: [R] Robust regression with groups > > > > > > > > Hi, > > I have data on a group of subjects in different years. I should > > assume > > that observations regarding different individuals are independent > > but > > observations for the same individual in different years are not and > > I > > would like to have an estimated standard error (and > > variance-covariance > > matrix) taking into account this problem. > > > > More in general is there a way in R to run a (robust)regression > > having > > different groups in the observations and specifying that the > > observation > > are independent across groups but not necessarily independent within > > groups? > > > > Thanks > > a. > > > > ______________________________________________ > > [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 > > > > ______________________________________________ > [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 > ______________________________________________ [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
