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A combined overdispersed and marginalized multilevel model

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  • Iddi, Samuel
  • Molenberghs, Geert

Abstract

Overdispersion and correlation are two features often encountered when modeling non-Gaussian dependent data, usually as a function of known covariates. Methods that ignore the presence of these phenomena are often in jeopardy of leading to biased assessment of covariate effects. The beta-binomial and negative binomial models are well known in dealing with overdispersed data for binary and count data, respectively. Similarly, generalized estimating equations (GEE) and the generalized linear mixed models (GLMM) are popular choices when analyzing correlated data. A so-called combined model simultaneously acknowledges the presence of dependency and overdispersion by way of two separate sets of random effects. A marginally specified logistic-normal model for longitudinal binary data which combines the strength of the marginal and hierarchical models has been previously proposed. These two are brought together to produce a marginalized longitudinal model which brings together the comfort of marginally meaningful parameters and the ease of allowing for overdispersion and correlation. Apart from model formulation, estimation methods are discussed. The proposed model is applied to two clinical studies and compared to the existing approach. It turns out that by explicitly allowing for overdispersion random effect, the model significantly improves.

Suggested Citation

  • Iddi, Samuel & Molenberghs, Geert, 2012. "A combined overdispersed and marginalized multilevel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1944-1951.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1944-1951
    DOI: 10.1016/j.csda.2011.11.021
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    References listed on IDEAS

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    4. Tony Vangeneugden & Geert Molenberghs & Geert Verbeke & Clarice G.B. Dem�trio, 2011. "Marginal correlation from an extended random-effects model for repeated and overdispersed counts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(2), pages 215-232, September.
    5. Patrick J. Heagerty, 1999. "Marginally Specified Logistic-Normal Models for Longitudinal Binary Data," Biometrics, The International Biometric Society, vol. 55(3), pages 688-698, September.
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    Cited by:

    1. Iddi Samuel & Nwoko Esther O., 2017. "Effect of covariate misspecifications in the marginalized zero-inflated Poisson model," Monte Carlo Methods and Applications, De Gruyter, vol. 23(2), pages 111-120, June.
    2. Iraj Kazemi & Fatemeh Hassanzadeh, 2021. "Marginalized random-effects models for clustered binomial data through innovative link functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 197-228, June.
    3. Aregay, Mehreteab & Shkedy, Ziv & Molenberghs, Geert, 2013. "A hierarchical Bayesian approach for the analysis of longitudinal count data with overdispersion: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 233-245.
    4. Özgür Asar & Ozlem Ilk, 2016. "First-order marginalised transition random effects models with probit link function," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(5), pages 925-942, April.

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