Survey-weighted generalized linear mixed models - Jan Pablo Burgard; Patricia Dörr (Universität Trier, Fachbereich IV – Volkswirtschaftslehre, 2018)
Regression analysis aims at the revelation of interdependencies and causalities between variables observed in the population. That is, a structure between regressors and regressants that causes the realization of the finite population is assumed, the so-called data generating process or a superpopulation model. When data points occurr in an inherent clustering, mixed models are a natural modelling approach. Given the finite population realization, a consistent estimation of the superpopulation parameters is possible. However, regression analysis seldomly takes place at the level of the finite population. Rather, a survey is conducted on the population and the analyst has to use the sample for regression modeling. Under a correct regression setup, derived estimators are consistent given the sample is non-informative. Though, these conditions are hard to verify, especially when the survey design is complex, employing clustering and unequal selection probabilities. The use of sampling weights may reduce a consequent estimation bias as they could contain additional information about the sampling process conditional on which the data generating process of the sampled units becomes closer to the one of the whole population. [...]
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