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- W4300924554 abstract "Bimodal truncated count distributions are frequently observed in aggregate survey data and in user ratings when respondents are mixed in their opinion. They also arise in censored count data, where the highest category might create an additional mode. Modeling bimodal behavior in discrete data is useful for various purposes, from comparing shapes of different samples (or survey questions) to predicting future ratings by new raters. The Poisson distribution is the most common distribution for fitting count data and can be modified to achieve mixtures of truncated Poisson distributions. However, it is suitable only for modeling equi-dispersed distributions and is limited in its ability to capture bimodality. The Conway-Maxwell-Poisson (CMP) distribution is a two-parameter generalization of the Poisson distribution that allows for over- and under-dispersion. In this work, we propose a mixture of CMPs for capturing a wide range of truncated discrete data, which can exhibit unimodal and bimodal behavior. We present methods for estimating the parameters of a mixture of two CMP distributions using an EM approach. Our approach introduces a special two-step optimization within the M step to estimate multiple parameters. We examine computational and theoretical issues. The methods are illustrated for modeling ordered rating data as well as truncated count data, using simulated and real examples." @default.
- W4300924554 created "2022-10-04" @default.
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- W4300924554 date "2013-09-02" @default.
- W4300924554 modified "2023-09-24" @default.
- W4300924554 title "Modeling Bimodal Discrete Data Using Conway-Maxwell-Poisson Mixture Models" @default.
- W4300924554 doi "https://doi.org/10.48550/arxiv.1309.0579" @default.
- W4300924554 hasPublicationYear "2013" @default.
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