Linking item parameters onto a common scale

Abstract

An item bank typically contains items from several tests that have been calibrated by administering them to different groups of examinees. The parameters of the items must be linked onto a common scale. A linking technique consists of an anchoring design and a transformation method. Four basic anchoring designs are the unanchored, anchor-items, anchor-group, and double-anchor designs. The transformation design consists of the system of equations that is used to translate the anchor information and put the item parameters on a common scale. Several transformation methods are discussed briefly. A simulation study is presented that compared the equivalent-groups method with the anchor-items method, using varying numbers of common items, applied both to the situation in which the groups were equivalent and one in which they were not. The results confirm previous findings that the equivalent-groups method is adequate when the groups are in fact equivalent. When the groups are not equivalent, accurate linking can be obtained with as few as two common items. Linking using a more efficient interlaced anchor-items design can provide accurate linking without the expense of including explicit common items in each of the tests.