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.

Web surveys have replaced Face-to-Face and computer assisted telephone interviewing (CATI) as the main mode of data collection in most countries. This trend was reinforced as a consequence of COVID-19 pandemic-related restrictions. However, this mode still faces significant limitations in obtaining probability-based samples of the general population. For this reason, most web surveys rely on nonprobability survey designs. Whereas probability-based designs continue to be the gold standard in survey sampling, nonprobability web surveys may still prove useful in some situations. For instance, when small subpopulations are the group under study and probability sampling is unlikely to meet sample size requirements, complementing a small probability sample with a larger nonprobability one may improve the efficiency of the estimates. Nonprobability samples may also be designed as a mean for compensating for known biases in probability-based web survey samples by purposely targeting respondent profiles that tend to be underrepresented in these surveys. This is the case in the Survey on the impact of the COVID-19 pandemic in Spain (ESPACOV) that motivates this paper. In this paper, we propose a methodology for combining probability and nonprobability web-based survey samples with the help of machine-learning techniques. We then assess the efficiency of the resulting estimates by comparing them with other strategies that have been used before. Our simulation study and the application of the proposed estimation method to the second wave of the ESPACOV Survey allow us to conclude that this is the best option for reducing the biases observed in our data.

On the Use of Gradient Boosting Methods to Improve the Estimation with Data Obtained with Self-Selection Procedures

In the last years, web surveys have established themselves as one of the main methods in empirical research. However, the effect of coverage and selection bias in such surveys has undercut their utility for statistical inference in finite populations. To compensate for these biases, researchers have employed a variety of statistical techniques to adjust nonprobability samples so that they more closely match the population. In this study, we test the potential of the XGBoost algorithm in the most important methods for estimation that integrate data from a probability survey and a nonprobability survey. At the same time, a comparison is made of the effectiveness of these methods for the elimination of biases. The results show that the four proposed estimators based on gradient boosting frameworks can improve survey representativity with respect to other classic prediction methods. The proposed methodology is also used to analyze a real nonprobability survey sample on the social effects of COVID-19.