  We investigate leading order deviations from general relativity that violate
the Einstein equivalence principle in the gravitational standard model
extension. We show that redshift experiments based on matter waves and clock
comparisons are equivalent to one another. Consideration of torsion balance
tests, along with matter wave, microwave, optical, and M\"ossbauer clock tests,
yields comprehensive limits on spin-independent Einstein equivalence
principle-violating standard model extension terms at the $10^{-6}$ level.
