Seeking to pursue research project independently (outside of academia)
There are only a few issues. First, yes, you can do such research as long as you haven't signed a contract that gives all of your IP to your employer. This sort of yielding of output is common in industry for employees, but rare, I hope, in academia. 

Second, if your research involves human subjects in any way, you probably have to get vetting on your research proposal from an ethics body. In the US, that would be a university's IRB, or some equivalent. Most reputable journals won't accept a paper involving human subjects without an external ethics review. 

But if there are no impediments, just do your research and submit it in the normal way. If you don't want your university's name attached to it in any way, your affiliation can just be "independent researcher".