Invariance of trait scales across changing samples of items and examin
ees is a central tenet of item response theory (IRT). However, scales
defined by most IRT models are truly invariant with respect to certain
linear transformations of the parameters, The problem is to find the
proper transformation that places separate calibrations on a common sc
ale. A variety of procedures for estimating transformations have been
proposed for unidimensional models. This paper explores some issues in
volved in extending and adapting unidimensional linking procedures for
use with multidimensional IRT models.