It is functional. Usually it is because the person becomes too confused to know they need to use the toilet or too confused to find the bathroom.
Brain Cell Loss. Alzheimer's disease & other neurodegenerative disorders (such as parkinson's) are ultimately devestating because of the loss of brain cells. Eventually, the cells that control the bowels & bladder are effeted & the result is incontinence. That being said, there are certainly things that can be done to help manage like frequent reminders to go to the bathroom & limit fluids in the late evening.