Re: negative objective value

From: SMITH_BRIAN_P@Lilly.com Subject: Re: negative objective value Date: Mon, 23 Apr 2001 10:02:10 -0500 A negative objective function is not a problem. Remember that the objective function is -2*ln(Likelihood). This is negative if the ln(Likelihood) is positive or when the Likelihood is greater than 1. There is no restriction in the likelihood that would restrict it to be less than 1. In fact, a negative objection function could be expected if your fit is very good. Example 1: Assume a normal distribution with unknown mean and variance. You have 3 observations 0.9, 1, and 1.1. The maximum likelihood estimates of the mean and varaiance are 1 and 0.006667 respectively. The objective function is -21.5. Example 2: Same assumptions. You have 3 observations 0, 1, and 2. The maximum likelihood estimates of the mean and variance are 1 and 0.6667 respectively. The objective function is 6.1. (Note: there is a constant sqrt(2*pi) that sometimes is and sometimes is not used in the objective function calculation. I assumed that it was included, but either way the first example has a negative objective function and the second has a positive objective function.) Conclusion: A negative objection function indicates a good fit, not that there is a problem. Sincerely, Brian Smith