Identifiability and Equivalence of GLLIRM Models

The generalized logit–linear item response model (GLLIRM) is a linearly constrained nominal categories model (NCM) that computes the scale and intercept parameters for categories as a weighted sum of basic parameters. This paper addresses the problems of the identifiability of the basic parameters and the equivalence between different GLLIRM models. It is shown that the identifiability of the basic parameters depends on the size and rank of the coefficient matrix of the linear functions. Moreover, two models are observationally equivalent if the product of the respective coefficient matrices has full column rank. Finally, the paper also explores the relations between the parameters of nested models.