Former private security guard here: in our training, we were told that we, as private citizens, could "arrest" someone, if you're willing to sign your name to an arrest warrant. You'd want to have the cops on the way, and be willing to face a false arrest lawsuit for detaining them, so you'd better be really 100% sure you caught them in the act of doing something illegal.

We were also taught it's almost never worth doing this; basically, if someone's shooting people and you're doing an armed job, yes, use your gun to try and stop them or detain them, but if it's just property damage or theft, call the cops and let them do their thing. The risk to you isn't worth it, nor is the risk of a false arrest lawsuit.