Model Averaging Methods for Weight Trimming in Generalized Linear Regression Models

In sample surveys where units have unequal probabilities of inclusion, associations between the inclusion probability and the statistic of interest can induce bias. This is true even in regression models, where the estimates of the population slope may be biased if the underlying mean model is misspecified or the sampling is non-ignorable. Weights equal to the inverse of the probability of inclusion are often used to counteract this bias. Highly disproportional sample designs have highly variable weights; weight trimming reduces large weights to a maximum value, reducing variability but introducing bias. Most standard approaches are ad-hoc in that they do not use the data to optimize bias-variance tradeoffs. This manuscript uses Bayesian model averaging to create “data driven ” weight trimming estimators. We develop robust models that approximate fully-weighted estimators when bias correction is of greatest importance, and approximate unweighted estimators when variance reduction is critical