Logistic Regression Equivalent Weights for Survey Inference: Construction and Asymptotic Properties

Abstract

Equivalent weights from regression models provide a bridge between design-based and model- based survey inference. We develop a frequentist survey-weighting framework for logistic regres- sion equivalent weights under categorical poststratification. Because the logistic model-based population estimator is nonlinear in the observed outcomes, we define equivalent weights through a local first-order representation, with each weight given by the scaled derivative of the popula- tion estimator with respect to the corresponding observed outcome. This construction yields an explicit closed-form expression in terms of the fitted logistic model and population cell structure. We establish convergence of the effective sample size ratio, asymptotic linearity of the resulting weighted estimator, and a consistent plug-in variance estimator under a finite-cell superpop- ulation framework. Simulation results examine population recovery, regression performance, effective sample size, and the finite-sample behavior of the asymptotic variance approximation. The results show that logistic equivalent weighting provides competitive finite-sample point esti- mation and approximately valid plug-in variance estimation, effective sample size is competitive with alternative model-based weighting in the settings considered. An application to the Fu- ture of Families and Child Wellbeing Study illustrates the construction and use of the proposed weights and variance estimator in an empirical survey setting. We emphasize the relationship between logistic equivalent weighting and recent work on locally equivalent weights for non- linear multilevel regression and poststratification, while focusing specifically on the frequentist interpretation of the weights, their survey-weight properties, and their use for inference.