The problem with this line of thinking is that home invasion is a different kind of crime from breaking and entering.

With breaking and entering, the goal is to get what they can with a minimum of fuss. Locked doors, barking dogs, automatic lights, security systems, etc are all great deterrents, because the goal is to get as much as possible while avoiding capture. The table stakes are that the burglar can get in and out without getting caught.

With home invasion, the whole threat profile is different. The operating premise is that the invader will use violence or the threat of it to brutalize the home occupants into facilitating the theft, the escape, and avoidance of prosecution.

Think of how wild animals engage in violence: they will not enter into a violent situation unless trapped (either physically, or by circumstance - e.g. fight or starve), or they think they can win the fight without sustaining any substantial injury. In the case of a home invasion, you are trapped, but the other guy has chosen the fight.

All of that to say, compliance should be done in the light of keeping yourself and those around you together and unharmed, and not willy-nilly. Obviously, don't pick a fight over a TV. But understand that if they continue their breaking-and-entering after they know you're there, compliance may be insufficient to protect your life.

Armed intruders can demand something one minute and something else the next. They may be mentally deranged, they may be sexually devious, there's a good chance they don't have a lot of moral limitations. The issue is not material things. That there's an optimal approach to dealing with them, when you're unarmed, is just not true. You must do what seems best given the situation.

The entire point is that in a home invasion, you have no guarantee the criminal is only interested in your property. If someone deliberately busts into an occupied house, there is a nonzero chance they are also interested in killing or assaulting (sexually or otherwise) the occupants.