Bayesian weight trimming for generalized linear regression models - ARCHIVED

In sample surveys where units have unequal probabilities of inclusion in the sample, associations between the probability of inclusion and the statistic of interest can induce bias. Weights equal to the inverse of the probability of inclusion are often used to counteract this bias. Highly disproportional sample designs have large weights, which can introduce undesirable variability in statistics such as the population mean estimator or population regression estimator. Weight trimming reduces large weights to a fixed cutpoint value and adjusts weights below this value to maintain the untrimmed weight sum, reducing variability at the cost of introducing some bias. Most standard approaches are ad-hoc in that they do not use the data to optimize bias-variance tradeoffs. Approaches described in the literature that are data-driven are a little more efficient than fully-weighted estimators. This paper develops Bayesian methods for weight trimming of linear and generalized linear regression estimators in unequal probability-of-inclusion designs. An application to estimate injury risk of children rear-seated in compact extended-cab pickup trucks using the Partners for Child Passenger Safety surveillance survey is considered.