Logging plugin usage and interaction for a user study

Hello - I'm wondering what the best way is to go about the following:

I have finished developing my plugin and would like to use it in a user study as part of academic work. I am planning to have participants in my study install the plugin as a JAR and would like to record usage on how often certain actions from my plugin were invoked, how many commits the user examined, etc. and I think the simplest way would be to do this by logging. Is it possible for my plugin to generate a log file that can store this information so that when a user has concluded using my plugin, I can request them to find and send me this generated log file?

Are there any recommendations for what to look into specifically for accomplishing this?

Thank you in advance!