Best way I would describe it, is imagining the space offstage, and where you will typically be located before picking an option (near the edge is most likely), as a complete circle. Where you stand is on the fringe of one side of the circle, and the space offstage can form the rest of it. If you think about their positioning, and correlate an option or move to that positioning, you'll cover the person's options better. Also, you have to consider how easily they can evade any aggressive chasing: I'd venture 30% of the failed edgeguards were due to missing an attempt because you underestimated how far he could drift/FF, or you attacked without enough running momentum and had to recover back etc.
For example, you're at the edge, and the opponent has to use Firefox from below stage height. Let's also assume that he's a decent distance out, but close enough where he can angle the Upb onstage barely and land onstage. If you were to draw a circle, you would be on the fringe of one side, offstage somewhere but at ledge/standing height would be the other edge of the circle, and the Fox would be diagonally below you probably inside the circle barrier a bit.
The best choice for this situation could be a Knee right near the edge/below it, or Utilt covering somewhere near the edge. Stomp might not be as good if you have to go low for it, might work the same as Knee or Utilt if you have good timing and use it with a double jump to rise with the hitbox. Fox player might be able to meteor, so again it might stick out as a lesser option. A running weak knee dropped fairly low might work due to his very limited angle choices, but might entail more risk than you actually need to take.
Now say that instead, he's in a less limited position slightly above stage where Side B can easily reach onstage, where he could drop down a bit and sweetspot with Side B, etc. He has a ton of options here, and if you misread with an offstage edgeguard, you could possibly legit die when he gets back and has you offstage. Since his position in the circle can change, and the proper response needed can change, you focus on keeping a good position that might allow you to "switch" responses quickly. A good choice would be to be near the edge, maybe at a distance where you can WD back to grab the edge or at least where Utilt covers it with the tip. You might have killed him with an aggressive choice, but since you don't always know where or when a person will start their choice, moving towards them when they have options is usually risky. Keeping a good position while you wait them out, even if you don't wait for the entire duration, will probably work better because chances are that they start to lose options and flexibility the longer they sit offstage. Fox will keep falling, he can't continue to DJ more, etc.
TL:DR
If a person has a lot of options, or the ability to adjust their offstage positioning quite a bit before being "forced" to choose an option, the best responses are usually waiting or covering the edge. If a person is more limited, either barely escaping hitstun by the time you arrive offstage (You Knee Fox at 40% and run balls deep to knee him again) or getting a nasty knockback angle, then aggressive edgeguards can work better. For Fox specifically, your biggest threat is guessing wrong on his Side B by going offstage, and then dying to his own edgeguard.