Well, I agree strongly and I don't. Assessing parsimony and goodness of
fit -- which often but not always is a trade-off problem -- are I
imagine major issues for many if not most people in this list. Wanting
to regard the trade-off as a testing problem is not however universal. I
am fortunate enough to find myself in fields where the choice of model
depends finally almost always on physical or biological criteria rather
than some P-value. (Substitute "economic" or whatever for your own
analogue.)
One of the most intriguing divides in statistical science is between
those whose ideal is evidently a formal set of rules which will guide
one ineluctably towards the correct model or decision for any dataset --
and those who doubt very much whether that is desirable, let alone
possible. (A pretty large class of questions on this list ends with the
question "Is this correct?". Most of those seem to be "econometrically
correct".)
Those who agree with the first position then commit themselves to a
career-long argument with each other about quite what those rules are
going to be.
Nick Cox
John LeBlanc
Thanks for the reply. I take your point about the limitations of sw
regression and I will be more hesitant in using them. However, whether
one uses sw or whether a more appropriate theory-driven approach with
thoughtful removal of variables, there is still a problem of testing
whether a more parsimonious model differs in the fit of the data from
its more saturated model.
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