Generalized entropy calibration for analyzing voluntary survey data

TL;DR

This paper introduces a unified generalized entropy calibration method for analyzing voluntary survey data, addressing selection bias and improving estimation efficiency under ignorable sampling mechanisms.

Contribution

It develops a novel calibration weighting framework using generalized entropy, linking it to regression models and proposing a two-step calibration for efficiency.

Findings

The method effectively controls selection bias in voluntary surveys.

Two-step calibration improves statistical efficiency when a regression model is available.

Simulation results demonstrate the approach's practical effectiveness.

Abstract

Statistical analysis of voluntary survey data is an important area of research in survey sampling. We consider a unified approach to voluntary survey data analysis under the assumption that the sampling mechanism is ignorable. Generalized entropy calibration is introduced as a unified tool for calibration weighting to control the selection bias. We first establish the relationship between the generalized calibration weighting and its dual expression for regression estimation. The dual relationship is critical in identifying the implied regression model and developing model selection for calibration weighting. Also, if a linear regression model for an important study variable is available, then two-step calibration method can be used to smooth the final weights and achieve the statistical efficiency. Asymptotic properties of the proposed estimator are investigated. Results from a limited simulation study are also presented.