I guess that leads me to a very pseudo-ish theory that the MBTI functions are variables in a "function" that outputs a small array of Big 5 personalty values which could then be clustered by the Northwestern study.
Disclaimer: In this case, I mean obviously who knows what else gets effected by our MBTI functions other than the BIg 5.
Not totally sure what you mean, but basically our type is the hard-wiring of our brain, and then due to ingrained personal factors, and how we are choosing to/being prompted to act by our environment/circumstances, we will make use of our hard-wiring in a particular way which will give rise to a set of observable attributes/behaviours.
So, for example take an INFJ who overfocuses on Ti (relevant example for this forum). Then, although their hard-wiring is Ni, then Fe, then Ti etc. they will be emphasising Ti to the degree that they may seem like a Thinker, or be somewhere in the middle of the F/T dichotomy. They may also seem more like a P type. So this INFJ could show the traits associated with the dichotomies of INFJ, INTJ, INFP or INTP, and it would be difficult to tell which they were unless you identified the specific function set that they were using.
As Big 5 is more correlated to the dichotomy approach to types, the resulting behavioural pattern will have some particular associated dichotomy set (and it will be as a spectrum). There is a wide variety of expressions of a particular type, and if you can identify both the underlying cognitive pattern, and how that is being tangibly expressed, then you can deduce how the person differs from their natural inclinations.