I have a new American Standard Cadet 3 that was just installed. After flushing, the water fills into the bowl. However, after several minutes, the water in the bowl slowly drains away and is nearly gone. The flapper appears to be seated well and no sign of leaking. What is causing the water to drain from the bowl like this

Replace the tank water fill valve. Change the flush flapper too. You can get a complete kit from hardware stores.

Sorry for problem with new toilet.
You say water is leaking out of the bowl?

Toilets have 2 parts:
1) Tank: where water is stored for the flush and is sealed with a flapper.
2) Bowl: where water flushes down.

a) If tank is leaking water, then flapper is suspect. Replace flapper and see if that works.
Lift up flapper and run finger around rim to see if there is a rough spot that would indicate flush valve is defective, and needs replacement.
See typical flush valve

b) If bowl is leaking, that is very unusual and would indicate a crack in the porcelain.

If installer sold you the toilet, it is his responsibility to make good on product.
All products are guarantee against workmanship flaws.

As long as the water in the bowl dosent go below the bottom rim your ok there is a trap that the water has to seal that all it needs look at the side of your toilet you will see the trap water saver

theres probably debrie in flush valve, mite also try putting food dye in tank (any color) if it appears in bowl the flapper is seeping water and activating flush valve..

The amount of water in any toilet bowl is determined by its construction and no tank adjustment will ever change that. American Standard has a history of having small water surface areas in their low or ultra low flush toilets. Take a large container of water and pour directly into the bowl. If the ending level remains the same, then that is the manufactured level for your toilet.

Not all tanks completely discharge all of the water when flushed. Measure 1.5 gallons of water into a container. Turn off your water supply to the toilet then flush normally. Replace the water in the tank with your premeasured amount and observe this new water level. You might be surprised to find it is at the same level it always is. Since water weighs more than 8 pounds per gallon, one concept used in todays toilets is to have more than 1.5 gallons of water in the tank and use the extra weight push the water past the flapper at a faster rate while designing the flapper to drop after only 1.5 gallons have passed through.

Check to be sure small tube is flowing inside the ovefow tube. This is the water that flushes the rim holes, and refills the bowl. If you don't have flow clean or replace the float valve.

adjust the float up to make water deeper....make sure no obstructions around the flapper....flapper needs to rest tight to bottom of inside the tank..flapper is the rubber peice that lifts when you push handle

You have a blockage in your drainage system.

in the tank check that the small white hose is not kinked or has fallen away from the center tube where the flush flapper is located the white hose goes into the center and fills the bowl