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Bayesian Inference for Zero-Modified Power Series Regression Models

Author

Listed:
  • Katiane S. Conceição

    (Department of Applied Mathematics and Statistics, Institute of Mathematics and Computer Science, University of São Paulo, São Carlos 13566-590, SP, Brazil)

  • Marinho G. Andrade

    (Department of Applied Mathematics and Statistics, Institute of Mathematics and Computer Science, University of São Paulo, São Carlos 13566-590, SP, Brazil)

  • Victor Hugo Lachos

    (Department of Statistics, University of Connecticut, Storrs, CT 06269, USA)

  • Nalini Ravishanker

    (Department of Statistics, University of Connecticut, Storrs, CT 06269, USA)

Abstract

Count data often exhibit discrepancies in the frequencies of zeros, which commonly occur across various application domains. These data may include excess zeros (zero inflation) or, less frequently, a scarcity of zeros (zero deflation). In regression models, both situations can arise at different levels of covariates. The zero-modified power series regression model provides an effective framework for modeling such count data, as it does not require prior knowledge of the type of zero modification, whether zero inflation or zero deflation, and can accommodate overdispersion, equidispersion, or underdispersion present in the data. This paper proposes a Bayesian estimation procedure based on the stochastic gradient Hamiltonian Monte Carlo algorithm, effectively addressing many challenges associated with estimating the model parameters. Additionally, we introduce a measure of Bayesian efficiency to evaluate the impact of prior information on parameter estimation. The practical utility of the proposed method is demonstrated through both simulated and real data across different types of zero modification.

Suggested Citation

  • Katiane S. Conceição & Marinho G. Andrade & Victor Hugo Lachos & Nalini Ravishanker, 2024. "Bayesian Inference for Zero-Modified Power Series Regression Models," Mathematics, MDPI, vol. 13(1), pages 1-30, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:60-:d:1554803
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    References listed on IDEAS

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