- I want to touch on one point here -

On 13 Jun 2003 20:22:14 -0700, [EMAIL PROTECTED] (dave martin)
wrote:

> Rich�Ulrich�<[EMAIL PROTECTED]>�wrote�on�6/13/03�4:14:55�PM:
[ snip, various, down to my comment --   ]
> >
> >AIC��and�BIC��are�keywords�for�looking�up�comparisons
> >of�non-nested�models.
> >
dm >
> I�will�follow�up�on�AIC�and�BIC.�Thanks.
>  
> A�simple�decrease�in�residuals�can�be�purely�by�chance.�
> 
> It�is�not�necessary�to�use�nested�model�logic for the F-test to be
> applicable.

 - Strictly speaking,  Is an F-test is "applicable" here?   No.
Nested-model logic  *is*   necessary to have a result that 
honestly is "distributed as F".   You might call this result an F, 
and it might not be horribly off.  But that is not as satisfactory
as it might be, I think, as an application of statistical theory.
More, below.

 [ snip, some ]
> It�is�true�that�the�F-test�is�often�used�to�tell�if�the�change�in
> residual�due�to�an�additional�parameter�is�significant.�
> 
> However,�by�its�defiinition,�the�F-test�can�be�applied�to�test�the
> ratio�of�residuals�with�the�same�or�different�degrees�of�freedom.�
> There�is�no�reason�these�residuals�must�come�from
> functionally�nested�or�even�related models.
[ snip, rest]

Yes, there is a reason that the residuals come from 
nested models;  and that is so that the difference will be, 
as we say, "distributed as F."   

The AIC  and BIC  are for non-nested models.  They make use
of the F-test, but they admit that the F is used in a "loose" way.

For the two models that differ by 1/T,  you don't even know
which one to subtract from which:  What results is definitely 
not an F, since it could be negative.  

 - I can suggest an ordinary way to convert the model to a 
nested model:  Replace the [1/T]  with [T raised to power p].
The fitted value for the exponent p  is near zero for one model,
near  -1 for the other.  The CI  for p  might contain neither value, 
or both; the model can give you a p-value to compare either
one (a model with or without 1/T) as a starting point.

-- 
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
"Taxes are the price we pay for civilization."  Justice Holmes.
.
.
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