Efficiency of propensity score adjustment and calibration on the estimation from non-probabilistic online surveys

One of the main sources of inaccuracy in modern survey techniques, such as online and smartphone surveys, is the absence of an adequate sampling frame that could provide a probabilistic sampling. This kind of data collection leads to the presence of high amounts of bias in final estimates of the survey, specially if the estimated variables (also known as target variables) have some influence on the decision of the respondent to participate in the survey. Various correction techniques, such as calibration and propensity score adjustment or PSA, can be applied to remove the bias. This study attempts to analyse the efficiency of correction techniques in multiple situations, applying a combination of propensity score adjustment and calibration on both types of variables (correlated and not correlated with the missing data mechanism) and testing the use of a reference survey to get the population totals for calibration variables. The study was performed using a simulation of a fictitious population of potential voters and a real volunteer survey aimed to a population for which a complete census was available. Results showed that PSA combined with calibration results in a bias removal considerably larger when compared with calibration with no prior adjustment. Results also showed that using population totals from the estimates of a reference survey instead of the available population data does not make a difference in estimates accuracy, although it can contribute to slightly increment the variance of the estimator