modelassisted

Model-assisted refers to a framework in statistics, especially in survey sampling, where inferences are primarily grounded in the sampling design for validity while auxiliary information is used through a predictive model to improve estimation efficiency. In a model-assisted approach, the estimator combines a working model for the study variable with design-based reasoning. The design-based justification ensures that, under the randomization of the sampling process, estimators are unbiased or consistent, even if the model is misspecified.

A common manifestation is the generalized regression estimator (GREG), which uses auxiliary variables known for all population units to predict the study variable and then adjusts the estimator using these predictions. Calibration of survey weights is another key technique in model-assisted methods, aligning weighted sample totals of auxiliary variables with known population totals to reduce variance without compromising design-based validity.

Model-assisted methods contrast with fully model-based methods, where inferences rely primarily on a probabilistic model for the data and may be sensitive to model misspecification. The model-assisted paradigm seeks to combine the strengths of predictive modeling with the robustness of design-based inference, providing efficiency gains when good auxiliary information is available while preserving validity under the sampling design.

Origins of the approach trace to the work on model-assisted survey sampling in the late 20th century, with notable contributions from researchers who formalized the idea that design-based properties can be retained even when incorporating models for auxiliary information. Applications are widespread in official statistics, national surveys, and any context with reliable auxiliary data.