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Orolan,

Lots of interviews to do, not much time to do them.  Have to go on the worse case scenario theory.  Have to assume Elizabeth has been abducted.  But you also have to rely on statistical information.  Statistically, when a child is either missing, injured, assaulted, or killed the subject is most likely either a family member, or known to the Victim.  We can probably rule out the younger sister, and any other younger siblings, however we have to look at the parents and any close relatives or family friends, primarily males.  The best thing to do is attempt to eliminate as many people from suspicion as quickly as we can while at the same time running other logical leads.  Bringing in dogs may help, but I'm not real familiar with how successful that particular technique has been of late in finding abducted children.  Reason being, most likely if Elizabeth was abducted she was taken to a vehicle not far from the house, so the dogs will only lead us to the curb.  Still worth a try, you don't want to pass up any opportunity.   

Lets jump ahead just a bit.  We've done all the interviews, nothing really relevant has turned up except that we've identifed people who have worked around the house, etc...  Unfortunately we have not had any luck actually turning up hard information as to where Elizabeth is.  We're facing the real possibility that she may be dying or dead.  We need to start getting information, any way we can, and fast.  One particular interview, the handyman (Ricci) shows promise because he is evasive in a lot of his answers.  We're also getting bad vibes from the uncle.  He's reluctant to be forth coming with his assistance, and is making noises that the family may stop cooperating.  He's going to the press, making our job a lot more difficult.

Do we turn to polygraph?  If so who do we polygraph and why?  What do we ask?  Or do we not utilize polygraph?  If not, then what's next?  We may be looking down a dead end street right now, and we're no closer to finding Elizabeth.  Now the heat is really on, we're in day three!

Batman

Batman,

OK. It is true that family members are first on the list of suspects, followed by those that know the layout and routines of the household. Suspecting the parents is a very long shot in this case. The odds of the sister not recognizing her father are slim, and the timeline is entirely too short. If the father did it, and he put her in the car and took her somewhere, then somebody in the house would have heard the car either leaving or coming back. Either the sister or the mother. If he didn't take her in the car, then the dogs have already found her.
So I've eliminated the parents, at least temporarily. So we turn our attention to the uncle. Does he have an alibi? Any reasonable suspicions about him? We can't just make him a suspect because he thinks we're botching the investigation. Assuming no verifiable alibi, we can question him further. We need something a lot stronger than lack of cooperation to justify making him a suspect. What do we have? 
We also have this handyman, Ricci. He's a real piece of work. Evasive, nervous, no verifiable alibi, knowledge of the house and people in it. And he has priors along with an outstanding warrant. Assume that we searched his house and truck, and we found nothing related to Elizabeth. We quickly realize that he may have been responsible for the burglary a few months ago, so we zero in on that. He says he didn't do it, so we ask him to submit to a polygraph. An incident-specific poly, about the burglary only, for now. We could do a GKT, if we have a qualified operator, about Elizabeth. Are we on the right track?

DetJIM,

This is an exercise, not a recounting of the actual events. At this point nobody really knows what happened. If you can't supply any constructive ideas or opinions, kindly take your remarks elsewhere.