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Estimating overdispersion in sparse multinomial data

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  • Farzana Afroz
  • Matt Parry
  • David Fletcher

Abstract

Multinomial data arise in many areas of the life sciences, such as mark‐recapture studies and phylogenetics, and will often by overdispersed, with the variance being higher than predicted by a multinomial model. The quasi‐likelihood approach to modeling this overdispersion involves the assumption that the variance is proportional to that specified by the multinomial model. As this approach does not require specification of the full distribution of the response variable, it can be more robust than fitting a Dirichlet‐multinomial model or adding a random effect to the linear predictor. Estimation of the amount of overdispersion is often based on Pearson's statistic X2 or the deviance D. For many types of study, such as mark‐recapture, the data will be sparse. The estimator based on X2 can then be highly variable, and that based on D can have a large negative bias. We derive a new estimator, which has a smaller asymptotic variance than that based on X2, the difference being most marked for sparse data. We illustrate the numerical difference between the three estimators using a mark‐recapture study of swifts and compare their performance via a simulation study. The new estimator has the lowest root mean squared error across a range of scenarios, especially when the data are very sparse.

Suggested Citation

  • Farzana Afroz & Matt Parry & David Fletcher, 2020. "Estimating overdispersion in sparse multinomial data," Biometrics, The International Biometric Society, vol. 76(3), pages 834-842, September.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:3:p:834-842
    DOI: 10.1111/biom.13194
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    References listed on IDEAS

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    1. D. J. Fletcher, 2012. "Estimating overdispersion when fitting a generalized linear model to sparse data," Biometrika, Biometrika Trust, vol. 99(1), pages 230-237.
    2. S. R. Paul & D. Deng, 2000. "Goodness of fit of generalized linear models to sparse data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 323-333.
    3. Gary White, 2002. "Discussion comments on: The use of auxiliary variables in capture-recapture modelling. An overview," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(1-4), pages 103-106.
    4. Dianliang Deng & Sudhir R. Paul, 2016. "Goodness of Fit of Product Multinomial Regression Models to Sparse Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 78-95, May.
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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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