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

Marica Manisera and Paola Zuccolotto

Journal of Multivariate Analysis, 2015, vol. 140, issue C, 302-316

Abstract: 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.

Keywords: Identifiability; Mixture distributions; Likert scales; Categorical ordinal variables; Rating data; Nonlinear CUB (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:140:y:2015:i:c:p:302-316

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DOI: 10.1016/j.jmva.2015.05.011

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