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st: RE: linear vs log-linear regression: specification test

From   "Nick Cox" <[email protected]>
To   <[email protected]>
Subject   st: RE: linear vs log-linear regression: specification test
Date   Wed, 29 Oct 2003 11:40:59 -0000

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. 

[email protected] 

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