Evaluation of available techniques and their combinations to address selection bias in nonprobability surveys

Abstract New survey methodologies that often produce nonprobability samples have recently become very important. However, estimates from nonprobability samples can be subject to selection bias, which is primarily caused by the lack of coverage and the respondent’s ability to decide whether or not to participate in the survey. In such cases, inclusion probabilities can be zero or unknown. When this happens, the estimators normally used in sample surveys are useless, and we must employ methods to reduce this bias. There is a wide variety of techniques to achieve this which depend on the auxiliary information available, but no study has determined which is better among all. In this paper, we briefly explain most of these methods and conduct an extended study to compare their performances. We will study superpopulation models, which require knowledge of the auxiliary variables of all individuals in the population, linear calibration, which requires the population totals of the covariates, and several techniques that use a reference probability sample, such as propensity score adjustment, propensity-adjusted probability prediction, Kernel Weighting, Statistical Matching and, Doubly Robust estimators. In addition, we compare their performance using linear regression or XGBoost as a predictive model, and the design weights in estimating inclusion probabilities or not, and with or without prior variables selection. The study was performed using five different datasets to determine which technique provides accurate and reliable estimates from nonprobability samples.