TL;DR: Yes! There is!!
I am unfamiliar with sentiment analyses (apart from a quick Wikipedia lookup!), but from an academic perspective, this is touching on UX research using qualitative and quantitative methods. If I had to work with this situation, I would have used the word association (which is essentially a quantitative survey) as a gateway technique to meeting the critical users: the unhappy users that you may lose to your competition.
Let's say someone describes the website/product as 'good' - well -- why is it good? Maybe you leave it at that. How about 'bad'?
Their reason for choosing1 or writing that particular word is definitely something you need to know about as a UX advocate - and qualitative research methods (such as an interview or focus group) can be employed to probe these users further.
Using just the survey is fine for doing a 'temperature check' of how the users experience the website/product. However, to really get the benefits, I would recommend digging deeper. In this approach, your tools would be the research methods (survey, interview), and your framework would be the research methodologies (qualitative, quantitative).
1 Having a list of preselected words makes the analysis easier as there is less interpretation to do - but on the flip side, you may 'box' people in, and lead them to pick certain words. Also keep culture in mind if this is a situation that involves multiple nationalities!