# Math Help - A question on profile likelihood confidence interval.

1. ## A question on profile likelihood confidence interval.

It makes sense to me if the likelihood function takes positive values, but what if the likelihood function takes negative max?? The likelihood ratio then does not make sense and the log-likelihood fails since it can't take negative values. I am really confused at the moment and I really hope someone could direct me to the right direction. I assume someone knows about the profile likelihood confidence interval or test so I did not explain much. Thank you!

2. ## Re: A question on profile likelihood confidence interval.

Originally Posted by ld8822
It makes sense to me if the likelihood function takes positive values, but what if the likelihood function takes negative max?? The likelihood ratio then does not make sense and the log-likelihood fails since it can't take negative values. I am really confused at the moment and I really hope someone could direct me to the right direction. I assume someone knows about the profile likelihood confidence interval or test so I did not explain much. Thank you!
Since a likelihood is a conditional probability it cannot be negative.

CB

3. ## Re: A question on profile likelihood confidence interval.

Originally Posted by CaptainBlack
Since a likelihood is a conditional probability it cannot be negative.

CB
thank you so much I didn't realise it!!!!!!!!!!!