# Re: st: Log Likelihood for Linear Regression Models

 From leechtcn <[email protected]> To [email protected] Subject Re: st: Log Likelihood for Linear Regression Models Date Thu, 30 Oct 2003 23:02:24 -0800 (PST)

```Thanks a lot
it is very helpful for me

--- David Greenberg <[email protected]> wrote:
> Equation 1 is correct. The reason some writers drop
> the second term is this. For most purposes, the
> likelihood function or its log are not of interest
> in themselves. One might want to compare two of
> them, or one might want to find the values of
> parameters that will maximize the likelihood
> function. If one is comparing two likelihood
> functions by taking the difference, constant terms
> will drop out. If one is finding the values of
> parameters that will maximize the likelihood
> function or its log, one will take the first
> derivative and set it equal to zero. Constant terms
> will have first derivatives that are zero, no matter
> what the value of the constant. In your example,
> sigma represents the standard deviation in the
> population. It is simply a number, which is assumed
> to be known. For purposes of estimating the
> coefficients in a regression equation, it is
> irrelevant. It can be disregarded. One might as well
> drop it, at the potential cost of confusing some
> students. David Greenbe
> rg, Sociology Department, New York University
>
> ----- Original Message -----
> From: leechtcn <[email protected]>
> Date: Thursday, October 30, 2003 6:42 am
> 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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