Fully Funded PhD: Should my parents still claim me as a dependent on their tax forms?

I am starting my PhD in August, which is fully funded. I will not be living with my parents and they are not supporting me financially at all, but I am still 22 and a "full time student". What are the pros and cons of them still claiming me as a dependent vs. not? In my mind, if I get nothing out of being independent, it makes the most sense for them to get the extra tax break, but not if I get a separate break for being independent. Thank you!