Identifiability of a model for discrete frequency distributions with a multidimensional parameter space

This paper is concerned with the identifiability of models depending on a multidimensional parameter vector, aimed at fitting a probability distribution to discrete observed data, with a special focus on a recently proposed mixture model. Starting from the necessary and sufficient condition derived by the definition of identifiability, we describe a general method to verify whether a specific model is identifiable or not. This procedure is then applied to investigate the identifiability of a recently proposed mixture model for rating data, Nonlinear CUB, which is an extension of a class of mixture models called CUB (Combination of Uniform and Binomial). Formal proofs and a numerical study show that some sufficient conditions for identifiability of Nonlinear CUB are always satisfied, provided that in the estimation procedure one quantity is fixed at a relatively small value.