Three methods of item response theory (IRT) linking--common-item, common-group and a combination of common-item and common-group (referred to as common-common) linking designs were compared using real testing data from an English as second language (ESL) exam program. The methods were considered as "vertical scaling" instead of "equating" because, first, the test was designed to examine three different traits of English ability; multidimensional IRT and factor analysis on testing data confirms that the test was multidimensional. Second, the two test forms are not at the same difficulty level, the averaged difficulty parameters were different by about 0.5, 1.0 or 1.5 standard units, thus the linking was considered vertical. The effects of test length and averaged difficulty level differences were also analyzed. For practical reasons, the anchor test used in the common-item linking design could not represent all the dimensions of the test forms.
Read
