ABSTRACT
The logic involved in testing the invariance of relationships among test forms can be applied to shorter and shorter tests, until one treats each item on a form as a one-item test. Then a second falsifiable assumption of linking is that the items within a test form have the same relative difficulty, or that they are in the same relative order with respect to other properties, such as discrimination, as well. DIF analysis can be used as part of the procedure to select common items for linkage across languages, in much the same way as it is often used to select linking items in vertical scaling. DIF analysis works backward from the idea that, if a set of items measure the same construct for two (or more) groups, then the items should be in the same relative order of difficulty, and/or discrimination, for those groups.
