# Can maximum log likelihood take a value of 0?

Can maximum log likelihood take a value of 0 ? I am using nlminb() in R to minimize a function that returns -sum(log(x)), and I am getting the $objective from nlminb() of my full model as 0 and null model as 0.47. • Why shouldn't it take such value..? – Tim Dec 2 '16 at 23:03 • @Tim Since a likelihood is often defined as a probability and all probabilities are$1\$ or less, the logarithm must not be positive. Thus, a positive "log likelihood" can only be reported when shortcuts are taken to avoid computing a normalizing constant for the probability distribution or else probability densities are involved. Therefore it seems like there's good motivation for this question. – whuber Dec 2 '16 at 23:08
• @whuber agree, I asked so that the question is stated directly. – Tim Dec 2 '16 at 23:12