Data from 100 participants is taken. Should I first screen addicts then see the prediction of dark triad and internet addiction or do analysis on all the data?
From the brief question, it is not clear what you are attempting to determine. If your interest is to see if those with internet addiction are more likely to manifest the dark triad or if those with the triad are more likely to be addicted then you would obviously need the entire sample .
In any case a sample of 100 is a minimal sample size to attempt any prediction. If you limit the analyses to a subsample the sample size becomes even more problematic. If half of your sample meets the qualification of Internet addiction (however you are defining it), one or a few atypical individuals could cause you to reach an erroneous conclusion.