Dogs are very tuned into the environment and sometimes they perceive things in the environment as part of the cue or command. They don't "understand' the command in the absence of this environmental cue. The dog understands "sit" in class, or at home in the kitchen before a meal, but they don't understand it at the park or in the pet store. Or they only understand it with a visible treat in your hand. It is a mistaken belief that dogs are stubborn or will 'hold out" on a "sit" until they see a treat. Dog's need to be taught to generalize skills and so it is necessary to train in different places and in absence of lures/food treats.
When you use food as lure, provide a command while enticing the dog to follow the food. The command should slightly precede the presentation of the lure. We want the command to capture the dog's attention, even if he needs the "bribe" of the food to entice him to follow through. Once the dog has successfully completed the behavior, the lure becomes the reward or marker. Dogs can become too dependant on the lure if it is used too long or if it is presented before the command. The lure then becomes PART OF the command.
A lure is like a bribe. The dog knows you have it and he knows that to get it he must offer the behavior requested. To fade the food as a lure, make it less obvious. Obscure food by closing it in your hand, leaving it in your pocket or hide it on a table next to you. when the dog offers the behavior you requested, give your reward marker (RM = "yes!", "good" etc,) present the food and give it to the dog. Begin to wait a little longer between the command and the presentation of the food (RM). Wait the dog out and give him a chance to present the behavior. When he does, give your RM and a food treat with lots of pats and praise!
Training Exercise:
Make the food reward obscure and unpredictable. Have food available in your pocket and various places around the house. Do not cue your dog ahead of time that there will be a food reward.
Praise and reward sits offered without a command. When you sit your dog sitting (or down, etc.) give your RM and reward with food and praise. Do this intermittently, periodically and unpredictably. The dog never knows when you have food and when he will be rewarded. Be subtle about getting the food, don't make a big production of getting it out of your pocket or out of the hiding place. Be quick with the reward. Your verbal marker "yes!" "excellent!" acts as a bridge marking the behavior as soon as it is presented and then followed by a food marker.
After several opportunities over a day or two, begin to request a sit. The dog's attention MUST be on you, and you should have your food handy. Command "sit" and wait a reasonable amount of time for his response. If he doesn't sit, give your "No Reward Marker" -NRM-( "uh oh", "too bad", "no sir", etc.) and walk away. Repeat this periodically and unpredictably. Eventually he will sit when asked. As soon as he does, mark the behavior ("yes!") and give a food reward.
As your dog starts to "get it", raise the bar by expecting him to sit more quickly. Give him minimal response time. When he sits in time, give your RM and a food reward. If he doesn't give your NRM and walk away. Be consistent in your expectation. If you decide he should sit within 2 seconds, don't reward him when he sits within 4 seconds.
When your dog is sitting quickly and reliably in the absence of food, start giving the food lure intermittently. Reward him with your RM and pats and praise every time, but do not reward with food for each occurrence. Reward, for example, every other time, every 3rd time, sometimes give a 'jackpot' ( 2 or 3 pieces) sometimes reward 2 or 3 times in a row. YOU BECOME A TREAT SLOT MACHINE! :) If at anytime he does not sit, NRM and no marker is given.
While practicing this, do not use a leash or collar correction. We want him to learn to sit whether on or off leash!
Good Luck!