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

Abstract

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 probabilitybased 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-basedweb 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 nonprobabilityweb-based survey sampleswith the help ofmachine-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.