[Gretl-users] Constant in the log-likelihood
Alecos Papadopoulos
papadopalex at aueb.gr
Thu Jul 11 13:42:03 EDT 2013
Christ, what a stupid mistake. I apologize to everybody that has been
following this conversation.
Τhe correct constant is ln(4/sqrt(2*$pi))= 0.467355827915218...
...and now the code runs smoothly if I include the constant as an
expression, ln(4/sqrt(2*$pi)), it gives a zero gradient and the correct
value for the log-l, and estimates virtually identical with the mle code
without the constant.
It still has problems if I include the constant as a numerical value
0.467355827915218... in which case I get
loglikelihood = -172.877055337 (steplength = 5.36871e-021)
Gradients: 0.98941 -16.941 65.400 61.632 -0.42174 0.31255
-0.078953 0.32094 -0.099944 -0.028678 1.6085 23.937
0.80591 6.6747e-005 0.045333 0.0018853 (norm 7.16e-001)
...which is obviously not at the maximum. Also, here one of the non-negative terms is estimated as
as close to zero as possible - meaning that the iteration method was led towards negative values but wasn't
permitted, and this is perhaps why the gradient is not zero.
Also if I truncate the constant to only 7 decimal digits (instead of 15) the code runs and gives estimates and a non-zero gradient as above, but it also gives the message "Matrix is not positive definite , Error executing script: halting". Perhaps this explains some things to those who know more...
Still, Allin thanks, My issue is essentially solved. And apologies again.
Alecos Papadopoulos
Athens University of Economics and Business, Greece
Department of Economics
cell:+30-6945-378680
fax: +30-210-8259763
skype:alecos.papadopoulos
On 11/7/2013 19:00, gretl-users-request at lists.wfu.edu wrote:
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> 1. Re: Constant in log-likelihood (Alecos Papadopoulos)
> 2. Re: Constant in log-likelihood (Allin Cottrell)
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> Message: 1
> Date: Wed, 10 Jul 2013 19:18:08 +0300
> From: Alecos Papadopoulos <papadopalex at aueb.gr>
> Subject: Re: [Gretl-users] Constant in log-likelihood
> To: gretl-users at lists.wfu.edu
> Message-ID: <51DD8940.4030204 at aueb.gr>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>
> In model 1 (without the constant in the log-l), the value of the
> maximized log-likelihood is -447.
> If one wants to arrive at the actual full value of the log-likelihood
> one should add to this nobs*ln(4/sqrt(2/$pi)) = 595*0.46.. = 274, and
> obtain -447 + 274 = -173.
>
> Now in model 2, parameter estimates are virtually identical with model
> 1, so one would expect that, since here the constant is already included
> in the logl eq., it would arrive at a comparable result with the
> corrected full value (i.e. -173), and not +511, which is the value for
> the logl given by the code in model 2.
>
> Alecos Papadopoulos
> Athens University of Economics and Business, Greece
> Department of Economics
> cell:+30-6945-378680
> fax: +30-210-8259763
> skype:alecos.papadopoulos
>
> On 10/7/2013 19:00, gretl-users-request at lists.wfu.edu wrote:
>
>> ------------------------------ Message: 2 Date: Wed, 10 Jul 2013
>> 09:05:57 +0200 (CEST)
>> From: "Riccardo (Jack) Lucchetti" <r.lucchetti at univpm.it>
>> Subject: Re: [Gretl-users] Graph two densities together and Constant
>> in Log Likelihood To: Gretl list <gretl-users at lists.wfu.edu>
>> Message-ID: <alpine.DEB.2.10.1307100904510.23263 at ec-4.econ.univpm.it>
>> Content-Type: text/plain; charset="iso-8859-15" On Wed, 10 Jul 2013,
>> Alecos Papadopoulos wrote:
>>> Just a note that
>>> in model 2 (that is virtually identical to model 1 as regards to
>>> estimates and final gradient values), the value of the logl appears
>>> positive.
>> Since you add a positive constant to each observation, why would that be
>> surprising?
>>
>> -------------------------------------------------------
>> Riccardo (Jack) Lucchetti
>> Dipartimento di Scienze Economiche e Sociali (DiSES)
>>
>> Universit? Politecnica delle Marche
>> (formerly known as Universit? di Ancona)
>>
>> r.lucchetti at univpm.it
>> http://www2.econ.univpm.it/servizi/hpp/lucchetti
>> -------------------------------------------------------
>>
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>
> ------------------------------
>
> Message: 2
> Date: Wed, 10 Jul 2013 12:43:09 -0400 (EDT)
> From: Allin Cottrell <cottrell at wfu.edu>
> Subject: Re: [Gretl-users] Constant in log-likelihood
> To: Gretl list <gretl-users at lists.wfu.edu>
> Message-ID: <alpine.LFD.2.10.1307101237360.16292 at myrtle>
> Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed
>
> On Wed, 10 Jul 2013, Alecos Papadopoulos wrote:
>
>> In model 1 (without the constant in the log-l), the value of the
>> maximized log-likelihood is -447.
>> If one wants to arrive at the actual full value of the log-likelihood
>> one should add to this nobs*ln(4/sqrt(2/$pi)) = 595*0.46.. = 274, and
>> obtain -447 + 274 = -173.
> ln(4/sqrt(2/$pi)) is not 0.46..., it's 1.612... And multiplication
> by 595 gives an add factor of 959. You're calculating using 2*$pi
> rather than 2/$pi?
>
> Allin Cottrell
>
>
>
>
>
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