11:35 a.m.
Professor Cottrell:
During my testing of gretl using the StRD linear regressions test
suit, I found that QR decomposition performs better than the Cholesky
decomposition and sent you a pdf file containing a table comparing the
two methods. QR method mostly creates higher number of accurate digits
and is able to produce a solution for the Flip data set, where
Cholesky fails.
In the light of this evidence I wrote my paper and prepared the
summary tables assuming the new default for linear regressions would
be the QR decomposition. I see that the new snapshots still have
Cholesky as the default. If Cholesky will stay as the default in the
new version, please let me know so that I can update my tables.
I am attaching the pdf file containing the comparisons.
Sincerely,
Talha
--
A positive attitude may not solve all your problems, but it will annoy
enough people to make it worth the effort. - Herm Allbright
(1876-1944)
--
12:23 p.m.
On Thu, July 20, 2006 17:35, Talha Yalta wrote:
Professor Cottrell:
During my testing of gretl using the StRD linear regressions test
suit, I found that QR decomposition performs better than the Cholesky
decomposition and sent you a pdf file containing a table comparing the
two methods. QR method mostly creates higher number of accurate digits
and is able to produce a solution for the Flip data set, where
Cholesky fails.
In the light of this evidence I wrote my paper and prepared the
summary tables assuming the new default for linear regressions would
be the QR decomposition. I see that the new snapshots still have
Cholesky as the default. If Cholesky will stay as the default in the
new version, please let me know so that I can update my tables.
I am attaching the pdf file containing the comparisons.
IIRC, Sven brought this up some time ago. I did a little testing, and QR is
about 10-15% slower than Cholesky. This is the price you have to pay for
greater accuracy. So, it all boils down to choosing speed over precision. I
would go for QR myself, but in 99.99% of the cases the difference in precision
is not even noticeable: the test cases you give are artificial datasets
especially designed to be very ill-conditioned (but, to be honest, I did
stumble once into a real-life dataset where Cholesky couldn't cut it and QR
would). Besides, with the CPUs we have today, a few microseconds are nothing.
What's other people's opinion?
Riccardo "Jack" Lucchetti
Dipartimento di Economia
Facoltà di Economia "G. Fuà"
Ancona
3:45 p.m.
I want to draw attention to gretl's results in calculating the R^2 for
the noint1 a noint2 data sets. Results are very poor with both QR and
Cholesky methods. Can there be a bug that affects calculating the R^2
in regressions without the constant term?
IIRC, Sven brought this up some time ago. I did a little testing, and
QR is
about 10-15% slower than Cholesky. This is the price you have to pay for
greater accuracy. So, it all boils down to choosing speed over precision. I
would go for QR myself, but in 99.99% of the cases the difference in precision
is not even noticeable: the test cases you give are artificial datasets
especially designed to be very ill-conditioned (but, to be honest, I did
stumble once into a real-life dataset where Cholesky couldn't cut it and QR
would). Besides, with the CPUs we have today, a few microseconds are nothing.
I also support using QR. Memory or microseconds of speed differences
are not enough reason today to support an inferior algorithm
(http://www.ee.ucla.edu/~vandenbe/103/qr.pdf provides a simple example
why this is so). One can easily switch back to Cholesky if speed or
memory is a concern.
On 7/20/06, Riccardo Jack Lucchetti <r.lucchetti(a)univpm.it> wrote:
>
> On Thu, July 20, 2006 17:35, Talha Yalta wrote:
> > Professor Cottrell:
> > During my testing of gretl using the StRD linear regressions test
> > suit, I found that QR decomposition performs better than the Cholesky
> > decomposition and sent you a pdf file containing a table comparing the
> > two methods. QR method mostly creates higher number of accurate digits
> > and is able to produce a solution for the Flip data set, where
> > Cholesky fails.
> >
> > In the light of this evidence I wrote my paper and prepared the
> > summary tables assuming the new default for linear regressions would
> > be the QR decomposition. I see that the new snapshots still have
> > Cholesky as the default. If Cholesky will stay as the default in the
> > new version, please let me know so that I can update my tables.
> >
> > I am attaching the pdf file containing the comparisons.
>
IIRC, Sven brought this up some time ago. I did a little testing, and
QR is
about 10-15% slower than Cholesky. This is the price you have to pay for
greater accuracy. So, it all boils down to choosing speed over precision. I
would go for QR myself, but in 99.99% of the cases the difference in precision
is not even noticeable: the test cases you give are artificial datasets
especially designed to be very ill-conditioned (but, to be honest, I did
stumble once into a real-life dataset where Cholesky couldn't cut it and QR
would). Besides, with the CPUs we have today, a few microseconds are nothing.
>
> What's other people's opinion?
>
> Riccardo "Jack" Lucchetti
> Dipartimento di Economia
> Facoltà di Economia "G. Fuà"
> Ancona
>
> _______________________________________________
> Gretl-users mailing list
> Gretl-users(a)ricardo.ecn.wfu.edu
> http://ricardo.ecn.wfu.edu/mailman/listinfo/gretl-users
>
--
A positive attitude may not solve all your problems, but it will annoy
enough people to make it worth the effort. - Herm Allbright
(1876-1944)
--
4:15 p.m.
On Thu, 20 Jul 2006, Talha Yalta wrote:
I want to draw attention to gretl's results in calculating the
R^2 for the noint1 a noint2 data sets. Results are very poor
with both QR and Cholesky methods. Can there be a bug that
affects calculating the R^2 in regressions without the
constant term?
Have you read the section dealing with this at
http://gretl.sourceforge.net/nist/index.html
<quote>
In the NoInt1 and NoInt2 datasets there is a methodological
disagreement over the calculation of the coefficient of
determination, R^2, where the regression does not have an
intercept. gretl reports the square of the correlation
coefficient between the fitted and actual values of the
dependent variable in this case, while the NIST figure is
R^2 = 1 - ESS / sum(y^2)
There is no universal agreement among statisticians on the
"correct" formula (see for instance the discussion in
Ramanathan, 2002, pp. 163-4). Eviews 3.1 produces a different
figure again (which has a negative value for the NoInt test
files). The figure chosen by NIST was obtained for these
regressions using the command
genr r2alt = 1 - $ess/sum(y * y)
and the numbers thus obtained were in agreement with the
certified values, up to gretl's precision.
</quote>
Allin Cottrell
4:21 p.m.
Ahh, I remember this now. You are right. Sorry for the bother.
On 7/20/06, Allin Cottrell <cottrell(a)wfu.edu> wrote:
On Thu, 20 Jul 2006, Talha Yalta wrote:
> I want to draw attention to gretl's results in calculating the
> R^2 for the noint1 a noint2 data sets. Results are very poor
> with both QR and Cholesky methods. Can there be a bug that
> affects calculating the R^2 in regressions without the
> constant term?
Have you read the section dealing with this at
http://gretl.sourceforge.net/nist/index.html
<quote>
In the NoInt1 and NoInt2 datasets there is a methodological
disagreement over the calculation of the coefficient of
determination, R^2, where the regression does not have an
intercept. gretl reports the square of the correlation
coefficient between the fitted and actual values of the
dependent variable in this case, while the NIST figure is
R^2 = 1 - ESS / sum(y^2)
There is no universal agreement among statisticians on the
"correct" formula (see for instance the discussion in
Ramanathan, 2002, pp. 163-4). Eviews 3.1 produces a different
figure again (which has a negative value for the NoInt test
files). The figure chosen by NIST was obtained for these
regressions using the command
genr r2alt = 1 - $ess/sum(y * y)
and the numbers thus obtained were in agreement with the
certified values, up to gretl's precision.
</quote>
Allin Cottrell
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Gretl-users(a)ricardo.ecn.wfu.edu
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--
A positive attitude may not solve all your problems, but it will annoy
enough people to make it worth the effort. - Herm Allbright
(1876-1944)
--
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4 comments
3 participants
participants (3)
-
Allin Cottrell -
Riccardo Jack Lucchetti -
Talha Yalta