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Estimating infant mortality in Colombia: some overdispersion modelling approaches

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  • Adrián Quintero-Sarmiento
  • Edilberto Cepeda-Cuervo
  • Vicente Núñez-Antón

Abstract

It is common to fit generalized linear models with binomial and Poisson responses, where the data show a variability that is greater than the theoretical variability assumed by the model. This phenomenon, known as overdispersion, may spoil inferences about the model by considering significant parameters associated with variables that have no significant effect on the dependent variable. This paper explains some methods to detect overdispersion and presents and evaluates three well-known methodologies that have shown their usefulness in correcting this problem, using random mean models, quasi-likelihood methods and a double exponential family. In addition, it proposes some new Bayesian model extensions that have proved their usefulness in correcting the overdispersion problem. Finally, using the information provided by the National Demographic and Health Survey 2005, the departmental factors that have an influence on the mortality of children under 5 years and female postnatal period screening are determined. Based on the results, extensions that generalize some of the aforementioned models are also proposed, and their use is motivated by the data set under study. The results conclude that the proposed overdispersion models provide a better statistical fit of the data.

Suggested Citation

  • Adrián Quintero-Sarmiento & Edilberto Cepeda-Cuervo & Vicente Núñez-Antón, 2012. "Estimating infant mortality in Colombia: some overdispersion modelling approaches," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1011-1036, October.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:5:p:1011-1036
    DOI: 10.1080/02664763.2011.634395
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    References listed on IDEAS

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    1. Murray Aitkin, 1999. "A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 55(1), pages 117-128, March.
    2. J. K. Lindsey, 1999. "On the use of corrections for overdispersion," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 553-561.
    3. Hinde, John & Demetrio, Clarice G. B., 1998. "Overdispersion: Models and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 27(2), pages 151-170, April.
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