Generalized entropy calibration for analyzing voluntary survey data

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 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 a two-step calibration method can be used to smooth the final weights and achieve statistical efficiency. We establish the double robustness and local efficiency of the proposed estimator. Results from a limited simulation study are also presented.