Combining Statistical Matching and Propensity Score Adjustment for inference from non-probability surveys

Abstract

The convenience of online surveys has quickly increased their popularity for data collection. However, this method is often non-probabilistic as they usually rely on selfselection procedures and internet coverage. These problems produce biased samples. In order to mitigate this bias, some methods like Statistical Matching and Propensity Score Adjustment (PSA) have been proposed. Both of them use a probabilistic reference sample with some covariates in common with the convenience sample. Statistical Matching trains a machine learning model with the convenience sample which is then used to predict the target variable for the reference sample. These predicted values can be used to estimate population values. In PSA, both samples are used to train a model which estimates the propensity to participate in the convenience sample. Weights for the convenience sample are then calculated with those propensities. In this study, we propose methods to combine both techniques. The performance of each proposed method is tested by drawing nonprobability and probability samples from real datasets and using them to estimate population parameters.

Self-Perceived Health, Life Satisfaction and Related Factors among Healthcare Professionals and the General Population: Analysis of an Online Survey, with Propensity Score Adjustment

“…As stated in Section 1, it is known that PSA can reduce the selection bias at the cost of increasing the variance because of the complexity added by the predictive models. However, the bias-variance trade-off is often positive, as the mean square error gets reduced after the application of PSA in certain situations, according to literature [11,14,15,23,24].…”

“…Although the validity of internet research for subjective surveys of personal well-being is well established [8] and online questionnaires are recognised as an important tool for epidemiological research [9], many surveys of this type are subject to self-selection [10,11]. Ref.…”

Does Internet Access Contribute to Residents’ Pro-Environmental Behavior? Evidence from China

“…However, comparing the regression coefficients of the two studies shows that the regression coefficients of this study are much smaller than that of Xiao et al (2022). Because the distribution of netizens and non netizens is not completely random, this paper uses the PSM method can effectively solve the selection bias problem [64], further indicating that the findings of this paper are more realistic. In addition, unlike the study by previous studies [17][18][19], this study finds that Internet access has a greater effect on private-sphere PEB for elderly, women, low educated and rural residents.…”

“…Previous studies use the ordinary least squares (OLS) method for empirical analysis [17][18][19]. However, the PSM method is the best approach to correct the selection bias compared with the OLS method [64]. According to Rosenbaum and Rubin [65], the PSM method obtains unbiased effects on the outcome variables.…”

Enhancing estimation methods for integrating probability and nonprobability survey samples with machine‐learning techniques. An application to a Survey on the impact of the COVID‐19 pandemic in Spain

“…Current reviews of statistical methods of data integration for finite population inference can be seen in Valliant (2020), Buelens et al (2018), andRao (2020). Among the most important methods, we could mention inverse probability weighting (Kim & Wang, 2019;Lee, 2006;Lee & Valliant, 2009), inverse sampling (Kim & Wang, 2019), mass imputation (Rivers, 2007), doubly robust methods (Chen et al, 2019), kernel smoothing methods , or statistical matching combined with propensity score adjustment (PSA; Castro-Martín et al, 2021a). Yang and Kim (2020) provide a good review of some of these techniques.…”