Like various other people, I am most reluctant
to consider this as reducible to a single test,
not perhaps that anyone is suggesting that.
Yet another cautionary note about R-square in
this context is that
square of correlation of log response and
fitted log response
square of correlation of response and
fitted response
are different beasts.
Generalised linear models offer a framework
for this question, with at least one key advantage,
that predicted and residuals are returned
on the scale of the response and can be so compared
for different models.
In addition to consistency of limiting behaviour
of any model fitted with scientific knowledge,
I'd always want to check for lack of structure in
the residuals. I am not clear whether Christer,
who started this thread, has one or several covariates,
but even in the latter case, a residual vs. fitted
plot is always worth a quick look. That is -rvfplot-
after -regress- and -rvfplot2- more generally.
No single test statistic can adequately capture
the information in a complete set of residuals.
With one covariate, a direct scatter plot with
fitted line or curve is naturally of great interest.
Nick
[email protected]
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