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Modelling Overdispersion for Complex Survey Data

Author

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  • E.A. Molina
  • T.M.F. Smith
  • R.A. Sugden

Abstract

The population characteristics observed by selecting a complex sample from a finite identified population are the result of at least two processes: the process which generates the values attached to the units in the finite population, and the process of selecting the sample of units from the population. In this paper we propose that the resulting observations by viewed as the joint realization of both processes. We overcome the inherent difflculty in modelling the joint processes of generation and selection by exploring second moment and other simplifying assumptions. We obtain general expressions for the mean and covariance function of the joint processes and show that several overdispersion models discussed in the literature for the analysis of complex surveys are a direct consequence of our formulation, undere particular sampling schemes and population structures. Les caracté d'une population sont observées grâce à un échantillon complexe sélectionnéâ partir d'une poplation finie. Ces caractéristiques sont le résultat de l'échantillon des unités de ette population. Dans cet article, nous considérons que l'observation globale peut être vue comme une réalisation simultanée de ces deux processus. Nous tentons de surmonter la difficulté intrinsèque liée à la modélisation du double processus de génération et de sélection par une étude du moment d'ordre deux et en considérant d'autres hypothèses simplificatrices. Nous obtenons une expression générale pour la moyenne et la covariance liée au sondage complexes, sont une conséquence directe de notre formulation, losque l'on considère un plan de sondage particulier et une population ayant une structure spécifique.

Suggested Citation

  • E.A. Molina & T.M.F. Smith & R.A. Sugden, 2001. "Modelling Overdispersion for Complex Survey Data," International Statistical Review, International Statistical Institute, vol. 69(3), pages 373-384, December.
  • Handle: RePEc:bla:istatr:v:69:y:2001:i:3:p:373-384
    DOI: 10.1111/j.1751-5823.2001.tb00464.x
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    Cited by:

    1. Brajendra C. Sutradhar, 2022. "Multinomial Logistic Mixed Models for Clustered Categorical Data in a Complex Survey Sampling Setup," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 743-789, August.
    2. Brajendra C. Sutradhar, 2023. "Cluster Correlations and Complexity in Binary Regression Analysis Using Two-stage Cluster Samples," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 829-884, February.

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