I agree with all of what you say about sums of squares, hypothesis tests,
and linear modelling. However, I find type I sums of squares at least
as objectionable as type III, because (at least in my sorts of problems)
they also create many tests involving model comparisons that one is
not really interested in. Type III SSq (selected judiciously) have
some real usefulness as a component of model selection. I don't think
I've personally made the sorts of errors in using them that you
mention, but I find myself regularly criticizing others for those
errors, so you are basically correct.
There are three underlying problems here: distinguishing model selection
from estimation (when, in many cases, they are closely related);
establishing a broad, common-sense strategy for model selection,
in which sums of squares play only a limited role; and making clear
that EVERY sum of squares is a comparison of 2 models, and should
be attended to ONLY if the comparison of those two models is interesting.
The former two problems may be difficult to address purely from a
packaged software standpoint, though someone doing AI and statistics
might give it a try. The latter problem can be dealt with in software,
by insisting on explicit specification of a pair of models to generate
any sum of squares, and by labelling that SSq by a pair of model
names or specifications. I believe this should be the standard,
and the current hodgepodge of shortcuts should be eliminated from
good software.
Dave Krantz
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