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Abstract:
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An informative sampling design assigns unit inclusion probabilities to be correlated with the response variable of interest. Model inference performed on the observed sample taken from the population will be biased for the population generative model. A popular approach that produces asymptotically unbiased inference employs marginal inclusion probabilities to form sampling weights used to exponentiate each likelihood contribution of a pseudo likelihood. Posterior consistency restricts sampling designs to those under which pairwise inclusion dependencies limit to $0$. There are sampling designs excluded by this restriction; for example, a two-stage cluster design where the number of clusters increases with population size, but the number of units in each cluster remains relatively fixed. We propose a more general approach that forms the pseudo likelihood with weights based on pairwise or second order inclusion probabilities, which admits a broader class of sampling designs to achieve consistency by shifting restrictions to pairwise factorizations of third and fourth order inclusion probabilities, but allows for pairwise unit inclusion dependencies.
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