# [R] Constructing simulataneous confidence intervals for residuals

Han Lai hlai at whsun1.wh.whoi.edu
Fri Nov 30 18:40:11 CET 2001

```Hi,

I use package "lme" and I am trying to construct the simultaneous
confidence intervals for subject residuals inorder to rank the
subject-effects.  The approach is found in the Fig. 2.12, p.37, and the
equation (2.17), p.36, by the textbook of Goldstein (1995): "Multilevel
Statistical Models".

Here, I quote from the book:

"Consider the JSP data where we have 48 estimated residuals together
with their comparative standard errors. .....
First, we order the residuals from smallest to largest.  We construct an
interval about each residual so that the creiterion for judging
statistical significance at the (1-a)% level for any pair of residuals
is whether their confidence intervals overlap.  For example, if we
consider a pair of residuals with a common standard error (s.e.), and
assuming nrmality, the confidence interval width for judging a
difference significant at the 5% level is given by +- 1.39(s.e.).
The genral procedure defines a set of confidence intervals for each
residual i as
uhat_i += c(s.e.)_i                            (2.17)
For each possible pair of intervals (2.17), there is a significance
level associated with the overlap criterion, and the value c is
determined so that the average over all possible pairs is (1-a)%.  A
serach procedure can be devised to determine c.  When the ratio of the
standard errors do not vary appreciably, say by more than 2:1, the value
1.4 can be used for c.  As this ratio increases so does the value of c.
In present case, all but two of these ratios are greater than 2 and we
have used the cmmon value of 1.4"

My question is how to calculate c-value in that equation. Or, where can
I find the exact formula and procedures?  Also, is any other methods can
be used for this purpose (e.g., ranking the school-effects)?

Thank you very much for the help.

Cheers!
Han-Lin Lai, Ph.D
Northeast Fisheries Science Center
Woods Hole, MA 02543
Han-Lin.Lai at noaa.gov
Tel.  508 495 2312

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