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Re: st: Outreg2 beta versus OLS beta


From   "roy wada" <roywada@hotmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Outreg2 beta versus OLS beta
Date   Fri, 08 Sep 2006 12:34:09 -0400

James wants to know about the possible differences in beta coefficients
as reported by -regress- and by -outreg2-.

Run the following codes and get the beta output.

.. sysuse auto, clear
.. reg mpg rep78 headroom trunk, beta

------------------------------------------------------------------------------
mpg Coef. Std. Err. t P>|t| Beta
-------------+----------------------------------------------------------------
rep78 1.889614 .5602162 3.37 0.001 .3188646
headroom -.0291626 .8552278 -0.03 0.973 -.0042413
trunk -.7116801 .1682518 -4.23 0.000 -.526878
_cons 24.85365 3.075496 8.08 0.000 .
------------------------------------------------------------------------------

The beta values are these:

rep78 has the beta of .318
headroom has the beta of -0.0042
trunk has the beta of -0.526

Now you can run outreg2 to get the beta output.

.. outreg2 using myfile, beta see

COEFFICIENT mpg

rep78 1.890***
(0.32)
headroom -0.0292
(-0.0042)
trunk -0.712***
(-0.53)
Constant 24.85***
(4.24)
Observations 69
R-squared 0.44

The help file for outreg2 says the following for about the location of
beta coefficients reported in the outreg2 output file:
"report normalized beta coefficients instead of standard errors"

You need to look at the numbers within the parenthesis where
standard errors would normally be reported:

rep78 has the beta of (0.32)
headroom has the beta of (-0.0042)
trunk has the beta of (-0.53)

You have exact match between the beta coefficients as reported
by -regress- and -outreg2- to the two significant digits. If you want
more digits, type -less(0)- option. Note that -outreg2- does not
adjust the constant, while -regress- opts not to report it at all.

You will no longer obtain the exact match if analytical weight was
used. In retrospect, you may want to ask Stata Corp about their
beta calculation when analytical weights are used.

As an exercise, run the following codes and still get your beta:

foreach var of varlist mpg-trunk {
qui sum `var'
qui replace `var'=(`var'-`r(mean)')/`r(sd)'
}
reg mpg rep78 headroom trunk
outreg2 using myfile, see

Beta transformation is actually the z-transformation or the
standard normalization of data by its own means and standard
deviation - the stuffs that you see in introductory statistics
classes and never to see them again until now.

Why do we use (beta) standarized coefficients? One reason
(so I have been told) is the relative ease of calculation and
convert it back into the unstandarized form. I am not sure
if Stata does this or not. Second reason is that standardized
coefficients let you see the metric-free changes in the covariates
associated with the changes in the outcome: one standard
deviation in one covariate as opposed to one standard
deviation in another.

Roy

********************
James said:

I wanted to thank you for the response to my post. I have to confess I am still
a bit confused. After receiving your comments I removed the -aweights- and still
obtained different Beta coefficients from OLS and the Outreg2 command.

- ----- Original Message -----
From: roy wada <roywada@hotmail.com>
Date: Friday, August 25, 2006 11:11 am
Subject: st: Outreg2 beta versus OLS beta


This is a repost with a correct subject line. My apologies.

James wants to know about beta coefficients and outreg2.

Standardized beta coefficients can be obtained by first standardizing all
variables to a mean of 0 and a standard deviation of 1. Or you can
deflate each estiamted coefficient by its standard error of its variable after the estimation, which is what outreg2 does. James is using analytic weights(see http://www.stata.com/support/faqs/stat/crc36.html), which
alters that relationship. I am assuming that Stata is applying the beta transformation prior to applying the analytic weights, but the application of analytic weight would likely cause it to violate the beta condition of zero means and unitary standard deviation - which is probably responsiblefor the discrepancy. It would be more meaningful
if the analytic weights were first applied (by hand, if necessary) and then the beta transformation is conducted. In that case you would have true beta coefficients.
Roy


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