Reweighing

Reweighing is the process of adjusting the weights assigned to units in a dataset or sample so that analyses reflect a target distribution or population, rather than the observed sample distribution. It is used to correct sampling bias, address survey nonresponse, or align data with external benchmarks. Weights are typically positive numbers applied during analysis, such as in estimators, regression, or summary statistics.

Common methods include inverse probability weighting, where weights are proportional to the inverse of the probability of inclusion or treatment; post-stratification and raking (iterative proportional fitting) to match known margins; calibration weighting and entropy balancing to satisfy moment constraints; and propensity-score methods in causal inference. In predictive modeling, class weighting adjusts learning algorithms to account for class imbalance.

Applications include survey research to produce population-representative estimates; observational and causal studies to approximate randomized experiments via IPW and related techniques; and machine learning to improve performance on underrepresented groups or outcomes. Reweighing is also used in domain adaptation to compensate for shifts between training and target distributions.

Limitations and considerations include increased estimator variance, sensitivity to weight specification, and potential bias if the model generating weights is misspecified. Weight trimming or stabilization can reduce variability but may introduce bias. Ideally, reweighing relies on observed variables that capture the differences between samples and populations.