[R] use of predict() with confidence/prediction bands

From: Alan Arnholt <arnholt_at_cs.cs.appstate.edu>
Date: Fri 30 Dec 2005 - 05:41:10 EST

To my understanding, a confidence interval typically covers a single valued parameter. In contrast, a confidence band covers an entire line with a band. In regression, it is quite common to construct confidence and prediction bands. I have found that many people are connecting individual confidence/prediction interval values produced with predict(object,sd.fit=T,type="conf/pred") and calling the result a confidence/prediction band. Since there is no specific probability statement that can be attached to these connected confidence/prediction intervals, this does not seem reasonable to me. This is done, for example, in ISWR pg. 105, UsingR for Introductory Statistics pg 296, and Linear Models with R pg. 39 (Although in this instance the intervals are called 95% "pointwise" confidence bands versus simply 95% confidence bands.) To make a confidence/prediction band, one should construct simultaneous confidence/prediction intervals with say a Scheffe approach as mentioned in the S-PLUS Guide to statistics pg 274. If these connected intervals were called pointwise confidence/prediction intervals with the understanding that have no particular probability interpretation, then they are useful in understanding where the line should fall. However, they are not confidence/prediction bands as such, and I think it is misleading to name them so. Should the intervals the authors in the three mentioned references construct not be called something similar to connected 95% pointwise confidence/prediction intervals versus 95% confidence/prediction bands? Or, have I missed the boat? Fire away...

Alan T. Arnholt
Associate Professor
Dept. of Mathematical Sciences
Appalachian State University

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