Any payment received from any entity registered in WI is taxable by WI. That would mostly pertain to work performed in WI for an employer registered to conduct business in WI.
If your *PRIMARY* reason for being in the state is for education, and your intent is to leave the state upon the completion of that education, then your income from a NON-WI source is not taxable or reportable to WI. This is assuming you are claiming and maintaining residency in some other state and you intend to return to that state upon graduation.
What state are you a resident of? How is your research income reported to you (W-2, 1099-misc [which box], 1098-T)?
WI has a reciprocal agreement, on wages, with Illinois, Indiana, Kentucky and Michigan. Scholarships are nor considered income in the state where the school is located. That is income reported on box 5 of a 1098-T is not considered WI source income.
No, you do not change your residency because of the research income. But there may be other reasons.
The general rule is: your report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you worked in and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state.