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Zero-inflated proportion data models applied to a biological control assay

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  • A. M. C. Vieira
  • J. P. Hinde
  • C. G. B. Demetrio

Abstract

Biological control of pests is an important branch of entomology, providing environmentally friendly forms of crop protection. Bioassays are used to find the optimal conditions for the production of parasites and strategies for application in the field. In some of these assays, proportions are measured and, often, these data have an inflated number of zeros. In this work, six models will be applied to data sets obtained from biological control assays for Diatraea saccharalis , a common pest in sugar cane production. A natural choice for modelling proportion data is the binomial model. The second model will be an overdispersed version of the binomial model, estimated by a quasi-likelihood method. This model was initially built to model overdispersion generated by individual variability in the probability of success. When interest is only in the positive proportion data, a model can be based on the truncated binomial distribution and in its overdispersed version. The last two models include the zero proportions and are based on a finite mixture model with the binomial distribution or its overdispersed version for the positive data. Here, we will present the models, discuss their estimation and compare the results.

Suggested Citation

  • A. M. C. Vieira & J. P. Hinde & C. G. B. Demetrio, 2000. "Zero-inflated proportion data models applied to a biological control assay," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(3), pages 373-389.
    • Handle: RePEc:taf:japsta:v:27:y:2000:i:3:p:373-389
    DOI: 10.1080/02664760021673
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    Cited by:

    1. Helai Huang & Hong Chin, 2010. "Modeling road traffic crashes with zero-inflation and site-specific random effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 445-462, August.
    2. Tian, Guo-Liang & Ma, Huijuan & Zhou, Yong & Deng, Dianliang, 2015. "Generalized endpoint-inflated binomial model," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 97-114.
    3. Daniel B. Hall & Jing Shen, 2010. "Robust Estimation for Zero‐Inflated Poisson Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 237-252, June.
    4. Afrânio M.C. Vieira & Roseli A. Leandro & Clarice G.B. Dem�trio & Geert Molenberghs, 2011. "Double generalized linear model for tissue culture proportion data: a Bayesian perspective," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1717-1731, September.
    5. Gning, Lucien & Ndour, Cheikh & Tchuenche, J.M., 2022. "Modeling COVID-19 daily cases in Senegal using a generalized Waring regression model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    6. María José Olmo-Jiménez & Silverio Vílchez-López & José Rodríguez-Avi, 2022. "cpd: An R Package for Complex Pearson Distributions," Mathematics, MDPI, vol. 10(21), pages 1-15, November.
    7. Jansakul, N. & Hinde, J. P., 2002. "Score Tests for Zero-Inflated Poisson Models," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 75-96, July.
    8. Cai, Tianji & Xia, Yiwei & Zhou, Yisu, 2017. "Generalized Inflated Discrete Models: A Strategy to Work with Multimodal Discrete Distributions," SocArXiv 4r2j3, Center for Open Science.
    9. H. He & W. Wang & J. Hu & R. Gallop & P. Crits-Christoph & Y. Xia, 2015. "Distribution-free inference of zero-inflated binomial data for longitudinal studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2203-2219, October.

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