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A flexible zero-inflated model to address data dispersion

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  • Sellers, Kimberly F.
  • Raim, Andrew

Abstract

Excess zeroes are often thought of as a cause of data over-dispersion (i.e. when the variance exceeds the mean); this claim is not entirely accurate. In actuality, excess zeroes reduce the mean of a dataset, thus inflating the dispersion index (i.e. the variance divided by the mean). While this results in an increased chance for data over-dispersion, the implication is not guaranteed. Thus, one should consider a flexible distribution that not only can account for excess zeroes, but can also address potential over- or under-dispersion. A zero-inflated Conway–Maxwell–Poisson (ZICMP) regression allows for modeling the relationship between explanatory and response variables, while capturing the effects due to excess zeroes and dispersion. This work derives the ZICMP model and illustrates its flexibility, extrapolates the corresponding likelihood ratio test for the presence of significant data dispersion, and highlights various statistical properties and model fit through several examples.

Suggested Citation

  • Sellers, Kimberly F. & Raim, Andrew, 2016. "A flexible zero-inflated model to address data dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 68-80.
    • Handle: RePEc:eee:csdana:v:99:y:2016:i:c:p:68-80
    DOI: 10.1016/j.csda.2016.01.007
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    References listed on IDEAS

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    1. 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.
    2. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    3. Daniel B. Hall, 2000. "Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study," Biometrics, The International Biometric Society, vol. 56(4), pages 1030-1039, December.
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    1. Maria De Jesus & Nora Sullivan & William Hopman & Alex Martinez & Paul David Glenn & Saviour Msopa & Brooke Milligan & Noah Doney & William Howell & Kimberly Sellers & Monica C. Jackson, 2023. "Examining the Role of Quality of Institutionalized Healthcare on Maternal Mortality in the Dominican Republic," IJERPH, MDPI, vol. 20(14), pages 1-11, July.
    2. Kimberly F. Sellers & Andrew W. Swift & Kimberly S. Weems, 2017. "A flexible distribution class for count data," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-21, December.
    3. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2021. "On Poisson-exponential-Tweedie models for ultra-overdispersed count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 1-23, March.
    4. Wang, Fan & Li, Heng & Dong, Chao, 2021. "Understanding near-miss count data on construction sites using greedy D-vine copula marginal regression," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    5. Somayeh Ghorbani Gholiabad & Abbas Moghimbeigi & Javad Faradmal, 2021. "Three-level zero-inflated Conway–Maxwell–Poisson regression model for analyzing dispersed clustered count data with extra zeros," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 415-439, November.
    6. Daniel Rodriguez, 2023. "Assessing Area under the Curve as an Alternative to Latent Growth Curve Modeling for Repeated Measures Zero-Inflated Poisson Data: A Simulation Study," Stats, MDPI, vol. 6(1), pages 1-11, February.

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