Re: Negative objective functions
From: James <J.G.Wright@ncl.ac.uk>
Subject: Re: Negative objective functions
Date: Sun, 01 Nov 1998 14:18:33 +0000
I am inclined to agree that this isn't important, although as your sample size tends to infinity your objective function will tend to minus infinity, this is only a technical nuisance. My query is essentially about, why is this constant there? If you let your likelihood have the property of being the probability of the data given the model (ie drop the constant) it then provides some indication of how likely the data is to have arisen for your model (and makes it possible to calculate "individual likelihoods" more easily and compare subsets of the population for compatibility with the model). It had occurred to me that this number may be some kind of compensatory factor for the oddity that adding an observation always makes the data less likely to have arisen from your model, however none of the replies to the list have indicated that this is the case.
James
At 11:54 AM 10/31/98 -0800, you wrote:
>There is nothing about a likelihood having an
>arbitrary porportionality constant that affects consistency or
>any of the other properties of ML estimates that can be
>proved.
>
>LBS.