Have you plotted the data in creative ways, e.g., normal probability plots and plots vs. time with a separate line for each subject and with separate line types colors and plotting symbols for the different experimental / treatment groups? [If the response variable(s) are all positive, I would also try the same thing using log="y". If the responses were percentages, I'd transform to empirical logits log(y/(1-y)) with some adjustment to "y" to shrink it away from 0 and 1.] I always want to do the simple things first. Plots like this too often show me that my favorite model is not appropriate. I've sometimes skipped this step only to be forced back to it after getting nonsense fits. The Gods may have smiled upon Pygmalion, turning his beloved creation into a flesh and blood woman. I more often encounter the "great tragedy of science: a beautiful theory slain by an ugly fact."
If these plot do NOT show wild outliers, then I would think that "lme" would be precisely what you want, as Bert suggested. Years ago George Box said he thought that unmodelled autocorrelation was harder to detect and potentially more damaging than nonnormality. He said something to the effect, "Why worry about mice when there are tigers about?"
hope this helps. spencer graves
Berton Gunter wrote:
Angelo:
If I understand you correctly, what you want is exactly the mixed effects model that Dmitris has already suggested. As you appear to be confused about the underlying statistical concepts, I suggest that you read at least the first and fourth chapters of MIXED-EFFECTS MODELS IN S AND S-PLUS by Bates and Pinheiro. Chapter 10 of MASS (4th Edition) by Venables and Ripley (which I would unequivocally say should be on every S language user's shelf) contains a much terser overview, but consequently requires a stronger statistical background to understand.
My apologies if I have misunderstood, but the references are good ones anyway.
Cheers, Bert
-- 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 Angelo Secchi
Sent: Thursday, October 21, 2004 7:58 AM
To: [EMAIL PROTECTED]
Subject: Re: [R] Robust regression with groups
Hi, Bert you are definitely right I've been confuse and unclear on the nature of my problem (sorry about that).
In my message "robust regression" was referred to techniques able to
deal (when you estimate the variance of your coefficients) with
departures from the set of assumptions in a standard linear regression,
like for example the presence of heteroskedaciticy. In this case the
robust estimator of the variance of \beta (i.e. the coefficients) is
obtained considering a correction that take into account the
contribution from each observation to the score(d(ln L)/d\beta). Now I
would like to consider also the possibility that observations are not
independent as they are but they can be divided into groups that are
independent. In this case to obtain an estimator for the variance
that take into account this departure from the standard assumptions I
need a correction that take into account the contribution of each group
(and not of each observation) to the score(d(ln L)/d\beta). In summary,
I do not need more sophisticated way to estimate my coefficients but
only a routine to obtain a meaningful estimate for the variance of them.
Does this routine already exist in R?
Thanks, a.
PS Thanks Dimitris but it seems that I cannot use a random effects model
since the Hausmann specification test casts doubt on the assumptions
justifying the use of a GLS estimator.
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