st: Adjusted R-squared comparison

[Panagiotis Manganaris <mangan@econ.auth.gr>]

Unfortunately Nick and John, I must use adj r-squared because it  
represents a specific metric in the field of accounting. More  
specifically, I use a model where returns are the dependent variable  
and earnings, along with the change in earnings, are the independent  
variables. In this model the adjusted r-squared represents the value  
relevance of the earnings (this is what I am trying to gauge).  
Therefore, I am obliged to use r2.
Thank you for the procedure you mention John, but I had already tried  
it in the past. It is helpful, but only in a vague way. It does not  
provide the mean and the variance of r2, so I could use them to test  
the significance. For instance, the intervals almost always overlap  
when I use this method. That does not provide concrete evidence of  
statistical significance or non-significance. If I don't prove that  
there is (or there is not) a statistically significant difference, I  
cannot show whether my metric (value relevance) has been altered  
between the two periods.



2013/2/6 John Antonakis <John.Antonakis@unil.ch>
Can't agree more with you Nick.  We should care more about having  
consistent estimators than high r-squares (i.e., Panagiotis, what I  
mean here is that we can still estimate the slope consistently even if  
we don't have a tight fitting regression line).  So, I don't know why  
you are interested in this comparison, Panagiotis. I would think you  
would be more interested in comparing estimates, as in a Chow test  
(Chow, G. C. (1960). Tests of equality between sets of coefficients in  
two linear regressions. Econometrica, 28(3), 591-605). If you are  
using fixed-effects models, you can model the fixed-effects with  
dummies and then do a Chow test via suest....see -help suest-.


Best,
J.

__________________________________________

John Antonakis
Professor of Organizational Behavior
Director, Ph.D. Program in Management

Faculty of Business and Economics
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The Leadership Quarterly
__________________________________________

On 06.02.2013 11:40, Nick Cox wrote:
That's positive advice.

My own other idea is that adjusted R-squares are a lousy basis to
compare two models, even of the same kind. They leave out too much
information.

Nick

On Wed, Feb 6, 2013 at 10:37 AM, John Antonakis  
<John.Antonakis@unil.ch> wrote:
I think that the only think you can do is to bootstrap the r-squares and see
if their confidence intervals overlap.

To bootstrap you just do:

E.g.,

sysuse auto
bootstrap e(r2), seed(123) reps(1000) : reg price mpg weight

You will be interested in either:

       e(r2_w)             R-squared within model
       e(r2_o)             R-squared overall model
       e(r2_b)             R-squared between model

See help xtreg with respect to saved results.

Let's see if others have other ideas.
On 06.02.2013 10:22, Panagiotis Manganaris wrote:

I need to compare two adjusted r-squared of the same model for two
different periods of time (each one spans for a period of years). So far, I
have split my data in two groups, those that belong to the period 1998-2004
and those that belong to the period 2005-2011. Then I used xtreg on the same
model for each group of data. I've derived their adjusted r-squared and I
want to know if those two adjusted r-squared are significantly different
from each other.
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