Bayesian Latent Variable Model of Mixed Correlated Rank and Beta-Binomial Responses with Missing Data for the International Statistical Literacy Project Poster Competition

Maryam Aghayerashti, Ehsan Bahrami Samani () and Mojtaba Ganjali
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Maryam Aghayerashti: Shahid Beheshti University
Ehsan Bahrami Samani: Shahid Beheshti University
Mojtaba Ganjali: Shahid Beheshti University

Sankhya B: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 8, 210-250

Abstract: Abstract A Bayesian latent variable model of random effect analyzing mixed correlated rank and overdispersed binomial responses with potentially non-random missing values in both types of responses is presented. In this model, the non-random missing values for rank response, called the partial ranking not at random mechanism, is also introduced for analyzing rank data. The random effects method is used to investigate the correlation between the mixed responses. Bayesian-based approach that yields Bayesian estimates of the latent variable model parameters is used. Some simulation studies are conducted to estimate parameters of the proposed models. The model is applied to a real data set from the international statistical literacy project (ISLP) poster competition during 2020-2021 undergraduate students in Iran. In this data set, the mixed data are the responses of questions of the judging form which are answered by an evaluator. Some questions are answered in a rank and others in an overdispersed binomial way. Because the responses collected from the questions are related to the same poster, the responses are dependent. The results of analyzing the posters data are presented to illustrate the method.

Keywords: Primary 62J02; Secondary 62J05; Bayesian analysis; Rank data; Beta-Binomial; Mixed Correlated Responses; Random effect; Latent variable; Partial ranking not at random; ISLP Poster (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13571-023-00307-7

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