Mixture of shifted binomial distributions for rating data

Shaoting Li and Jiahua Chen ()
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Shaoting Li: Dongbei University of Finance and Economics
Jiahua Chen: Yunnan University

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 5, No 5, 833-853

Abstract: Abstract Rating data are a kind of ordinal categorical data routinely collected in survey sampling. The response value in such applications is confined to a finite number of ordered categories. Due to population heterogeneity, the respondents may have several different rating styles. A finite mixture model is thus most suitable to fit datasets of this nature. In this paper, we propose a two-component mixture of shifted binomial distributions for rating data. We show that this model is identifiable and propose a numerically stable penalized likelihood approach for parameter estimation. We adapt an expectation-maximization algorithm for the penalized maximum likelihood estimation. Our simulation results show that the penalized maximum likelihood estimator is consistent and effective. We fit the proposed model and other models in the literature to some real-world datasets and find the proposed model can have much better fits.

Keywords: Binomial distribution; Categorical data; Identifiability; EM algorithm; Mixture model; Ordinal data; Rating data (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10463-023-00865-7

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