So much depends on whether the test piece or component is compressed under lubricated or bonded conditions, and in the latter case shape factor, ie the ratio of the area to which the force is applied to the force-free area, also comes into plsy. At small compressive deformations the relationship between stress and strain is approximately linear when the compessed surfaces are fully lubricated, so the compression modulus is constant. When the rubber is bonded to metal or another rigid substrate lateral movement is confined and the stress will rise disproportionately with the compressive strain. There is plenty on this subject on the web and I would also suggest looking through the test method ISO 7743: 2011, which gives a simple explanation of the facrors involved.
Afraid I do not really follow cloa's argument, but the influence of strain history is correct.
