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From |
"FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" <[email protected]> |

To |
"'[email protected]'" <[email protected]> |

Subject |
RE: st: RE: Log Likelihood for Linear Regression Models |

Date |
Thu, 30 Oct 2003 08:38:47 -0600 |

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 > > > > __________________________________ > Do you Yahoo!? > Yahoo! SiteBuilder - Free, easy-to-use web site > design software > http://sitebuilder.yahoo.com > * > * For searches and help try: > * > http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * > * For searches and help try: > * > http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ __________________________________ Do you Yahoo!? The New Yahoo! Shopping - with improved product search http://shopping.yahoo.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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