household urination

Question
Our female beagle is 4 years old. Housetraining her was easy. Late last fall she was the one who discovered we had rats in our crawl space by hearing them, and smell through vents. We had them exterminated, and the crawl cemented and sealed. During this time the dog began urinating, only on the second floor (carpeted, and no indication of rats thru vents etc). She will do this WHILE we are home. The behavior has continued even though the rats have been erradicated. We cannot predict when she will do it, but she appears to have a lot of shame when we find the wet spots (which can be large, not small marking). We have had her checked and there are no physical problems. We have used a dog appeasing collar at the vets suggestion and that hasn't worked either. The frequency is about 1 time per week.

Answer
It's possible your beagle began marking the one area (upstairs) from which she could not smell or hear the vermin.  Beagles are hunting dogs, after all, and she may have been attempting to maintain that territory as a 'statement' to the invaders.  It might also have begun as a nervous response to the 'invasion'.  It has now begun to become habitual, so your best approach would be to not allow her upstairs without your constant supervision.  What you're seeing as 'shame' might be her normal reaction to your anger; even though you may not be overtly attempting to correct her mistakes (a waste of time), your body language alone is communicating your displeasure, and she has NO IDEA what's wrong.  She's following a basic instinct, one she may very well have re engineered based upon emotional or psychological need.  There is NO POINT in disciplining (in any way) a house training mistake.  The only thing one effectively creates by doing this is confusion and anxiety in the dog.  Reinforcing with reward her appropriate elimination outdoors (GO OUT WITH HER, start from scratch as if she were a puppy) while actively preventing her from repeating this behavior in your home will, in combination, probably extinguish the problem.