Under the substantial test, I became a resident alien. I've been married for 3 years to a non-resident alien not eligible for a SSN (therefore no income) under a F-2 and we have a 2 year old daughter. Do I file my taxes as head of household or married filing jointly?

If you in fact are a resident alien, you can file jointly with your wife, with her choosing to be treated as a resident alien.

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