Leecht - By definition, the likelihood function is just the joint density of
the observations evaluated at their observed values. The log likelihhod is
the log of the likelihood function. For a set of independent observations of
a N(xbeta,sigma) random variable, the log likelihood is No. 1 in your
posting. That's because 1/sigma appears as a multiplier in the
normal(xbeta,sigma) density function. Look in any beginning mathematical
statistics book for a discussion on the normal density function. Without
1/sigma, it won't integrate to 1.
Al Feiveson
-----Original Message-----
From: leechtcn [mailto:[email protected]]
Sent: Thursday, October 30, 2003 8:31 AM
To: [email protected]
Subject: Re: st: RE: Log Likelihood for Linear Regression Models
Dear Al FEiveson,
Thanks for your conments, but i am still lost. Can
you give me some references? I can just find No. 2 in
some textbooks!
thanks again
Leecht
--- "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)"
<[email protected]> wrote:
> Leecht -
>
> NO. 1 is the true log likelihood. The second is ok
> to use for a "log
> likelihood" for purposes of maximimization with
> respect to beta since
> log(sigma) is just an additive constant. But when
> estimating beta AND
> sigma,you need the other term.
>
> Al FEiveson
>
> -----Original Message-----
> From: leechtcn [mailto:[email protected]]
> Sent: Thursday, October 30, 2003 5:43 AM
> To: [email protected]
> Subject: st: Log Likelihood for Linear Regression
> Models
>
>
> Dear Listers,
>
> I have asked this question before. I am posting it a
> second time in case you guys have not received it.
>
> I am sorry for the all convinence caused!
>
> I have a question concerning William Gould and
> William
> Sribney's "MAximium Likelihood Estimation" (1st
> edition):
>
>
> In its 29th page, the author write the the following
> lines:
>
> For instance, most people would write the log
> likelihood for the linear regression model as:
>
> LnL =
> SUM(Ln(Normden((yi-xi*beta)/sigma)))-ln(sigma)
> (1)
>
> But in most econometrics textbooks, such as William
> Green, the log likelihood for a linear regression is
> only:
>
> LnL = SUM(Ln(Normden((yi-xi*beta)/sigma)))
>
> (2)
>
>
> that is, the last item is dropped
>
> I have also tried to use (2) in stata, it will give
> "no concave" error message. In my Monte Carlo
> experiments, (1) always gives reasonable results.
>
> Can somebody tell me why there is a difference
> between
> stata's log likelihood and those of the other
> textbooks?
>
> thanks a lot
>
> Leecht
>
>
>
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