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A Conway–Maxwell-multinomial distribution for flexible modeling of clustered categorical data

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  • Morris, Darcy Steeg
  • Raim, Andrew M.
  • Sellers, Kimberly F.

Abstract

Categorical data are often observed as counts resulting from a fixed number of trials in which each trial consists of making one selection from a prespecified set of categories. The multinomial distribution serves as a standard model for such data but assumes that trials are independent and identically distributed. Extensions such as the Dirichlet-multinomial and random-clumped multinomial distribution can express positive association, where trials are more likely to result in a common category due to membership in a common cluster. This work considers a Conway–Maxwell-multinomial (CMM) distribution for modeling clustered categorical data exhibiting positively or negatively associated trials. The CMM distribution features a dispersion parameter which allows it to adapt to a range of association levels and includes several recognizable distributions as special cases. We explore properties of CMM, illustrate its flexible characteristics, identify a method to efficiently compute maximum likelihood (ML) estimates, present simulations of small sample properties under ML estimation, and demonstrate the model via data analysis examples.

Suggested Citation

  • Morris, Darcy Steeg & Raim, Andrew M. & Sellers, Kimberly F., 2020. "A Conway–Maxwell-multinomial distribution for flexible modeling of clustered categorical data," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:jmvana:v:179:y:2020:i:c:s0047259x20302323
    DOI: 10.1016/j.jmva.2020.104651
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    References listed on IDEAS

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    1. Robert E. Gaunt & Satish Iyengar & Adri B. Olde Daalhuis & Burcin Simsek, 2019. "An asymptotic expansion for the normalizing constant of the Conway–Maxwell–Poisson distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 163-180, February.
    2. Sellers, Kimberly F. & Morris, Darcy Steeg & Balakrishnan, Narayanaswamy, 2016. "Bivariate Conway–Maxwell–Poisson distribution: Formulation, properties, and inference," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 152-168.
    3. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
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    8. Kimberly F. Sellers & Sharad Borle & Galit Shmueli, 2012. "The COM‐Poisson model for count data: a survey of methods and applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(2), pages 104-116, March.
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    Cited by:

    1. Corsini, Noemi & Viroli, Cinzia, 2022. "Dealing with overdispersion in multivariate count data," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).

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