I want to provide my insight into sooner vs. later. It's only my opinion, so bear with me.
Booth's process is very transparent and there was an article about it on Poets and Quants. Two people read your file and both have to agree. If one doesn't, than the file goes through a third person to decide.
Therefore, IMO, the people who receive the invites in the later days are the ones who needed to be further evaluated.
With that said, I have heard NUMEROUS cases in which the candidates who needed to be 'further' evaluated ended up being very interesting to the adcom post interview and even got in with scholarships. Whereas, some candidates that seemed to have no red flags ended up coming flat and getting dinged.
So in the end, you never know. I just don't think the interview invite process is 100% random.