My question on Cross Validated didn't attract any answers yet and it was mentioned by two senior members there (one of which was in meta) that it might be better on Stack Overflow. Could I have opinions on whether that is a good idea ?
First, your goal is to run tasks on your computer for the purpose of crunching some numbers. You're not building software that will be used by anyone else. Thus, this seems to me to be a Stats problem and not necessarily a StackOverflow problem. It is borderline, and if your question were just limited to the coding, it could be on topic... maybe.
However, in the meta question, you're asking specifically about buying hardware. This would definitely be off topic on StackOverflow and would more than likely be considered not constructive on any other StackExchange site, since it could be construed as a shopping question.
However, with some editing to focus the question on the topic of the hardware's effect on the speed of your results, asking more specific questions and being sure not to ask for recommendations or suggestions, this could be on topic on Superuser.
From slhck in the Superuser Chat Room:
I'm going to pick a small nit with @jmort253's answer, but mostly we agree.
The hardware piece of the question is certainly off topic on SO, but the other piece of the question is most certainly not a "stats" question, in that it isn't about the theory. Rather it is a performance related question about a statistical programming language.
However, it is definitely not the case that the only programming questions that are on topic at SO involve "creating software for other people to use". If that were the case, basically every question with the [r] tag (13000+) would be off topic (not to mention Matlab!).
That said, the first half of your question at Cross Validated is probably too broad as currently written to be a good SO question. If you had tried a specific method/technique to speed up your code and it wasn't working, that would be more on topic. As it stands, it would probably simply elicit a variety of recommendations, which isn't the sort of thing we're looking for on SO.
But I also think that the folks active in the [r] tag at SO are likely to contain the people who are most likely to be of some help. It looks like you don't have enough rep to chat there either, so I will post a link to your CV question there and ask if people would be willing to point you in the right direction, at the very least with a comment.
Finally, you might also find people who could help with this kind of problem on the R mixed model mailing list.