4:52 p.m.
Greetings, everyone
While working in gretl I noticed that there's no adjustment for the Akaike Information
Criterion for small samples nor corrected for bias (I think this one is not that
important). Although it´s fairly easy to do it, couldn't help but wonder if it would
be possible to create the function for both and maybe include the AIC for small samples in
the Model information alongside the other Information Criteria.
Here's a little script for both adjustments of the AIC (after esmimating a model):
#Akaike information criterion corrected for bias
AICbias=-2*$lnl + (2*($ncoeff)*$T/($T-$ncoeff-1))
#AIC for small samples
AICc=$aic+(2*($ncoeff)*($ncoeff+1)/($T-$ncoeff-1))
5:54 a.m.
Am 23.05.2018 um 18:52 schrieb Olivier Montes Ferrer:
Greetings, everyone
While working in gretl I noticed that there's no adjustment for the
Akaike Information Criterion for small samples nor corrected for bias
(I think this one is not that important). Although it´s fairly easy to
do it, couldn't help but wonder if it would be possible to create the
function for both and maybe include the AIC for small samples in the
Model information alongside the other Information Criteria.
Here's a little script for both adjustments of the AIC (after
esmimating a model):
#Akaike information criterion corrected for bias
AICbias=-2*$lnl + (2*($ncoeff)*$T/($T-$ncoeff-1))
#AIC for small samples
AICc=$aic+(2*($ncoeff)*($ncoeff+1)/($T-$ncoeff-1))
Hi, I guess the argument against showing it is that there's not enough
space for everything. In principle having this additional measure would
be nice. I don't think replacing the original AIC would be a good idea,
though, because it's a standard thing and so it would be confusing.
thanks,
sven
8:19 a.m.
Am 24.05.2018 um 07:54 schrieb Sven Schreiber:
Am 23.05.2018 um 18:52 schrieb Olivier Montes Ferrer:
> Greetings, everyone
>
> While working in gretl I noticed that there's no adjustment for the
> Akaike Information Criterion for small samples nor corrected for bias
> (I think this one is not that important). Although it´s fairly easy
> to do it, couldn't help but wonder if it would be possible to create
> the function for both and maybe include the AIC for small samples in
> the Model information alongside the other Information Criteria.
>
> Here's a little script for both adjustments of the AIC (after
> esmimating a model):
>
> #Akaike information criterion corrected for bias
> AICbias=-2*$lnl + (2*($ncoeff)*$T/($T-$ncoeff-1))
> #AIC for small samples
> AICc=$aic+(2*($ncoeff)*($ncoeff+1)/($T-$ncoeff-1))
>
Hi, I guess the argument against showing it is that there's not enough
space for everything. In principle having this additional measure
would be nice. I don't think replacing the original AIC would be a
good idea, though, because it's a standard thing and so it would be
confusing.
Hi,
of course these alternative information criteria could easily be added
to Allin's user-contributed "criteria" package. As such they would not
be accessible through the standard $aic accessor but via the package
instead.
@Oliver: You could ask Allin for a collaboration and add these criteria.
Best,
Artur
10:02 a.m.
Am 24.05.2018 um 10:19 schrieb Artur T.:
> Am 23.05.2018 um 18:52 schrieb Olivier Montes Ferrer:
>>
>> #Akaike information criterion corrected for bias
>> AICbias=-2*$lnl + (2*($ncoeff)*$T/($T-$ncoeff-1))
>> #AIC for small samples
>> AICc=$aic+(2*($ncoeff)*($ncoeff+1)/($T-$ncoeff-1))
>>
>
of course these alternative information criteria could easily be added
to Allin's user-contributed "criteria" package. As such they would not
be accessible through the standard $aic accessor but via the package
instead.
@Oliver: You could ask Allin for a collaboration and add these criteria.
Excellent idea! I had forgotten about the criteria package.
thanks,
sven
4:57 p.m.
@Allin Cottrell<mailto:cottrell@wfu.edu>
What's your take on this, Allin?
________________________________
De: gretl-users-bounces(a)lists.wfu.edu <gretl-users-bounces(a)lists.wfu.edu> en nombre
de Sven Schreiber <svetosch(a)gmx.net>
Enviado: jueves, 24 de mayo de 2018 05:02 a. m.
Para: gretl-users(a)lists.wfu.edu
Asunto: Re: [Gretl-users] AIC with correction for small samples and for bias
Am 24.05.2018 um 10:19 schrieb Artur T.:
Am 23.05.2018 um 18:52 schrieb Olivier Montes Ferrer:
#Akaike information criterion corrected for bias
AICbias=-2*$lnl + (2*($ncoeff)*$T/($T-$ncoeff-1))
#AIC for small samples
AICc=$aic+(2*($ncoeff)*($ncoeff+1)/($T-$ncoeff-1))
of course these alternative information criteria could easily be added to Allin's
user-contributed "criteria" package. As such they would not be accessible
through the standard $aic accessor but via the package instead.
@Oliver: You could ask Allin for a collaboration and add these criteria.
Excellent idea! I had forgotten about the criteria package.
thanks,
sven
6:06 p.m.
On Thu, 24 May 2018, Olivier Montes Ferrer wrote:
@Allin Cottrell<mailto:cottrell@wfu.edu>
What's your take on this, Allin?
Yes, let's do it; this will add value to the little "criteria"
package. I'll produce a modified version and send it to you for
approval.
One point though: the two formulae you gave, for AICbias and AICc, are
actually mathematically equivalent: there's only one "corrected AIC"
value.
AIC = -2L + 2k
AICbias = -2L + 2k * n/(n-k-1)
AICc = AIC + 2k * (k+1)/(n-k-1)
= -2L + 2k * (1 + (k+1)/(n-k-1))
= -2L + 2k * ((n-k-1+k+1)/(n-k-1))
= -2L + 2k * n/(n-k-1) = AICbias
#Akaike information criterion corrected for bias
AICbias=-2*$lnl + (2*($ncoeff)*$T/($T-$ncoeff-1))
#AIC for small samples
AICc=$aic+(2*($ncoeff)*($ncoeff+1)/($T-$ncoeff-1))
Allin
6:10 p.m.
Awesome!
Sorry about that, a careless mistake.
Olivier
________________________________
De: Allin Cottrell <cottrell(a)wfu.edu>
Enviado: jueves, 24 de mayo de 2018 01:06:23 p. m.
Para: Olivier Montes Ferrer
CC: gretl-users(a)lists.wfu.edu
Asunto: Re: [Gretl-users] AIC with correction for small samples and for bias
On Thu, 24 May 2018, Olivier Montes Ferrer wrote:
@Allin Cottrell<mailto:cottrell@wfu.edu>
What's your take on this, Allin?
Yes, let's do it; this will add value to the little "criteria"
package. I'll produce a modified version and send it to you for
approval.
One point though: the two formulae you gave, for AICbias and AICc, are
actually mathematically equivalent: there's only one "corrected AIC"
value.
AIC = -2L + 2k
AICbias = -2L + 2k * n/(n-k-1)
AICc = AIC + 2k * (k+1)/(n-k-1)
= -2L + 2k * (1 + (k+1)/(n-k-1))
= -2L + 2k * ((n-k-1+k+1)/(n-k-1))
= -2L + 2k * n/(n-k-1) = AICbias
#Akaike information criterion corrected for bias
AICbias=-2*$lnl + (2*($ncoeff)*$T/($T-$ncoeff-1))
#AIC for small samples
AICc=$aic+(2*($ncoeff)*($ncoeff+1)/($T-$ncoeff-1))
Allin
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6 comments
4 participants
participants (4)
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Allin Cottrell -
Artur T. -
Olivier Montes Ferrer -
Sven Schreiber