“…Currently, a large number of studies (e.g., Hanson & Beguin, 2002;Kang & Petersen, 2009;Kim & Cohen, 2002;Meng, 2007;Tong & Kolen, 2007) have explored factors affecting IRT vertical scaling for cell (1, 1) when both assumptions hold, which is nearly true in reality. For cell (0,1) where tests are multidimensional and construct invariant across grades, a few studies (Beguin & Hanson, 2001;Beguin, Hanson, & Glas, 2000;Patz & Yao, 2007;Simon, 2008) have applied multidimensional IRT models to vertical scaling.…”