Rear elbow down - vs - Rear elbow elevated.
Starting the swing with "The back elbow up" is on almost all coach's "Bad Advise" list. Initiating the swing with the rear elbow down may constitute the right mechanics for the weight-shift and extension model. In that model, as the swing is initiated, the direction of force of the top hand is directed toward the pitcher. As the batter turns and drives with the top hand, having the elbow already down places the arm in a good driving position for these mechanics at the start of the swing.
With the "stationary axis" model, as the batter initiates the swing, he does not push the top hand toward the pitcher, he instead pulls with the fingers of the top hand back toward the catcher to maximize torque (ala Sammy Sosa). Therefore, his mechanics would want the elbow in a more elevated position (in-line with the direction of pull) to accelerate the bat head back onto the intended plane of the swing. With the elbow flat down at the side, he would not be in as good a position to apply force on the bat opposite to that of the bottom hand (back toward the catcher).
NOTE: Cause of the "uppercut swing".
Dipping of the back shoulder as the front rises is part of the mechanics of a swing with too much of an uppercut. In order to help a player rid himself of these bad habits and swing with the shoulders and arms on a more productive plain, we must first have a good understanding of what is occurring in his swing that is causing the back shoulder to dip. The looping or uppercut swing is most common when the hitter "loads up his swing" in order to hit with more power.
With many players, the top hand is by far the most dominant hand and he feels more powerful when the hand is lowered so that the forearm is in a more horizontal position for driving. Weaker hitters lower the forearm to horizontal much earlier in the swing than do better hitters. In the process of lowering the arm to horizontal, the whole backside drops as he positions his body to turn and extend the arms. The opening of the front side is also more of a body-positioning move rather than to generate body rotation.