A NOTE ON ITEM HOMOGENEITY DEFINED BY MULTIVARIATE SYMMETRY

Starting from the Lienert and Raatz (1981) model of multivariate axial symmetry for a set of binary items, this note shows that this model i s equivalent to a restricted Rasch model having constant item paramete rs, to the binomial (test) model, to what is called interchangeability by Madansky (1963) and what is called complete symmetry in sociology, while the classical Rasch model is equivalent to the model of quasi s ymmetry. For items having more than two categories this generalizes to the multidimensional Rasch model and restricted versions thereof.