Thanks for the info. I know that but I am confuse with this statement: 

"To claim the EITC, you must be a U.S. citizens or resident alien all year.

If you were a nonresident alien for any part of the tax year, you can only claim the EITC if your filing status is married filing jointly and your spouse is a U.S. citizen or resident alien and you choose to be treated as a U.S. resident."

The wife and kids were as a resident alien only part of year.