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.
Can maximum log likelihood take a value of 0 ?
This boils down to "can a log-likelihood take a value of 0?", to which the answer is "certainly, yes"; log-likelihoods may be positive, negative or zero. Consider, for example, that densities can be greater than 1 and a product of things above and below 1 could happen to come out to be essentially 1.
However - and I suspect this might be the case here - it's common to shift log-likelihoods by arbitrary constants* (as long as it's the same arbitrary constant each time if you're making comparisons). In this situation it's quite possible that they're making it such that the full model has likelihood 0 (besides simplifying things like subsequent likelihood ratio tests, it may well be useful for numerical reasons).
* indeed Fisher defined likelihood up to a multiplicative constant, so some authors at least would say that's not just a common thing to do but actually part of how likelihoods work.