Does the altitude or attitude of an aircraft affect GPS accuracy? Of course we are assuming an effective signal is being received.

I live near Idaho Falls, Idaho with a field elev of 5300ft. If I shoot an approach will GPS be more or less accurate then landing at Seattle or LA?

Does the accuracy of GPS change with aircraft altitude or attitude?
Altitude has little effect, as long as you don't descent into a valley. Mountains shield the GPS signal, resulting generally in lower accuracy and lower integrity levels.

Attitude does matter, steep turns can result in the airframe shielding GPS signals from the antenna. Again, the effect is a lower accuracy and integrity.