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A Marginalized Overdispersed Location Scale Model for Clustered Ordinal Data

Author

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  • Nasim Vahabi

    (University of Florida, Florida)

  • Anoshirvan Kazemnejad

    (Tarbiat Modares University)

  • Somnath Datta

    (University of Florida, Florida)

Abstract

Overdispersion and intra cluster correlation are two important issues in clustered categorical/ordinal data and failure to account for them can result in misleading inferences. Generalized estimating equations and mixed effects models are two common frameworks for analyzing clustered data which are recently combined and extended to the marginalized random effects model. The location scale models are a different extension of the mixed effects models that furthermore allow the variance to vary as a function of covariates. In this paper, we extend a marginalized location scale model for longitudinal ordinal responses by allowing a log-linear model for variance components that facilitates both population-averaged and subject-specific interpretations. We then extend the marginalized location scale model by incorporating an additional random term into the model to handle the overdispersion aspect of the data. We conduct extensive simulation studies to investigate the statistical properties of the maximum likelihood estimators of the model parameters. We illustrate this methodology using a dataset on a children’s growth failure.

Suggested Citation

  • Nasim Vahabi & Anoshirvan Kazemnejad & Somnath Datta, 2018. "A Marginalized Overdispersed Location Scale Model for Clustered Ordinal Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 103-134, December.
    • Handle: RePEc:spr:sankhb:v:80:y:2018:i:1:d:10.1007_s13571-018-0162-5
    DOI: 10.1007/s13571-018-0162-5
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    References listed on IDEAS

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    1. Hyoyoung Choo-Wosoba & Somnath Datta, 2018. "Analyzing clustered count data with a cluster-specific random effect zero-inflated Conway–Maxwell–Poisson distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(5), pages 799-814, April.
    2. Kong, Maiying & Xu, Sheng & Levy, Steven M. & Datta, Somnath, 2015. "GEE type inference for clustered zero-inflated negative binomial regression with application to dental caries," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 54-66.
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    8. Hyoyoung Choo-Wosoba & Steven M. Levy & Somnath Datta, 2016. "Marginal regression models for clustered count data based on zero-inflated Conway–Maxwell–Poisson distribution with applications," Biometrics, The International Biometric Society, vol. 72(2), pages 606-618, June.
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