SOME CLARIFICATIONS OF THE TUCKALS2 ALGORITHM APPLIED TO THE IDIOSCALPROBLEM

Kroonenberg and de Leeuw have suggested fitting the IDIOSCAL model by the TUCKALS2 algorithm for three-way components analysis. In theory, t his is problematic because TUCKALS2 produces two possibly different co ordinate matrices, that are useless for IDIOSCAL unless they are equal . Kroonenberg has claimed that, when IDIOSCAL is fitted by TUCKALS2, t he resulting coordinate matrices will be identical. In the present pap er, this claim is proven valid when the data matrices are semidefinite . However, counterexamples for indefinite matrices are also constructe d, by examining the global minimum in the case where the data matrices have the same eigenvectors. Similar counterexamples have been conside red by ten Berge and Kiers in the related context of CANDECOMP/PARAFAC to fit the INDSCAL model.