Modelling Overdispersion for Complex Survey Data |
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Authors: | EA Molina TMF Smith RA Sugden |
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Institution: | Departmenent de Matemáticas Puras y Aplicadas, Universidad Simón Bolívar, Caracas, Venezuela;Department of Mathematics, The University of Southmapton, UK;Department of Mathematical and Computing Sciences, Goldsmiths College, University of London, UK |
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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. |
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Keywords: | Categorical data Inclusion probability Generation process Model-based inference Overdispersion Randomization inference Sampling design Selection Underdispersion |
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