Equating functions are supposed to be population invariant, meaning that the choice of subpopulation used to compute the equating function should not matter. The extent to which equating functions are population invariant is typically assessed in terms of practical difference criteria that do not account for equating functions' sampling…

Under item response theory, the characteristic curve methods (Haebara and Stocking-Lord methods) are used to link two ability scales from separate calibrations. The linking methods use their respective criterion functions that can be defined differently according to the symmetry- and distribution-related schemes. The symmetry-related scheme…