[R] Robust regression with groups

Thu Oct 21 12:11:22 CEST 2004

Hi Bert,

Regarding the sensitivity in the choice of the random-effects 
distribution, I know that usually estimates of the fixed-effects (and 
their std.errors) do not have serious problems, even if you assume 
normality where in fact you have log-normality. However, you do have a 
problem in the EB estimates of the random-effects.

More info could be found in:

G. Verbeke and E. Lesaffre (1996). A linear mixed-effects model with 
heterogeneity in the random-effects population, JASA, 91, 217-221.

W. Ghidey, E. Lesaffre and P. Eilers (2004). Smooth random-effects 
distribution in linear mixed model, Biometrics, 60, 945-953.
(to appear in December)

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: "Berton Gunter" <gunter.berton at gene.com>
To: "'Dimitris Rizopoulos'" <dimitris.rizopoulos at med.kuleuven.ac.be>; 
"'Angelo Secchi'" <secchi at sssup.it>
Cc: <r-help at stat.math.ethz.ch>
Sent: Wednesday, October 20, 2004 5:42 PM
Subject: RE: [R] Robust regression with groups

> 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: r-help-bounces at stat.math.ethz.ch
>> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of
>> Dimitris Rizopoulos
>> Sent: Wednesday, October 20, 2004 7:08 AM
>> To: Angelo Secchi
>> Cc: r-help at stat.math.ethz.ch
>> 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" <secchi at sssup.it>
>> To: <r-help at stat.math.ethz.ch>
>> 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.
>> >
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>>
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