Basics of Operant Conditioning
The theory behind operant conditioning is that an animal can be conditioned to give a specific behavior. You perform this conditioning by either giving the dog a reward for exhibiting the desired behavior or punishing the dog for exhibiting an incorrect behavior.
In the first approach, the dog performs the behavior because she wants to please you. Inappropriate behaviors are extinguished because the dog doesn't receive any pleasure or reward (your praise) when she performs them. In the second approach, the dog gives a specific behavior to avoid pain. The correct behavior is molded by punishing all the incorrect attempts.
Both approaches garner equal results. The rate at which a dog learns with either negative or positive reinforcement is equally fast. Studies also show that the dog's retention rate is similar with both methods. With negative reinforcement, however, the Chihuahua is not providing the behavior you want because she wants to please you; rather, she performs because she is trying to avoid pain. Dogs trained in this manner often show it in their demeanors. Their performances are lackluster, and the obvious sense of joy seen in a dog trained with positive reinforcement is missing. Negative reinforcement training does little to bolster the human-dog bond and doesn't take advantage of the Chihuahua's strong urge to please her human.