Odd diagnostic plots in mixed-effects models

Is the fixed effect estimated at the innermost level?  If not,
plots of residuals at that level are surely of limited interest.
qqplots, to be relevant, surely need to assess normality of
effects (rather than residuals) at the level that matters for
the intended inferences.

If the fixed effect is estimated at the level of the random
effect, then of course there are just 12 effects that should
appear in any qq or suchlike plot.

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Bioinformation Science, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.

On 19 Apr 2005, at 8:03 PM, r-help-request at stat.math.ethz.ch wrote:

From: Andrew Robinson <andrewr at uidaho.edu>
Date: 19 April 2005 12:41:24 PM
To: r-help at stat.math.ethz.ch
Subject: [R] Odd diagnostic plots in mixed-effects models

Dear R community,

In the excellent nlme package the default diagnostic plot graphs 

the 

innermost residuals against innermost fitted values.  I recently 

fit a 

mixed-effects model in which there was a very clear positive 

linear 

trend in this plot.

I inferred that this trend occurred because my fixed effect was 

a 

two-level factor, and my random effect was a 12-level factor. 

The 

negative residuals were associated with negative random effects 
(because of shrinkage, I assume), and the positive with 

positive.  The 

fixed effects explained little varaition. Therefore plotting the 
innermost residuals against the innermost fitted values had the 
negative residuals to the left and the positive residuals to the 
right, occasioning a trend.

My questions are: is it (as I suspect) harmless, or does it 

suggest 

that the model is lacking?  And, is this effect likely to 

compromise 

the interpretation of any of the other standard diagnostic plots 

(eg 

qqnorm)?

Thanks much for any thoughts,

Andrew
--
Andrew Robinson                      Ph: 208 885 7115
Department of Forest Resources       Fa: 208 885 6226
University of Idaho                  E : andrewr at uidaho.edu
PO Box 441133                        W : 

http://www.uidaho.edu/~andrewr> Moscow ID 83843                    
 Or: 

http://www.biometrics.uidaho.edu