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Title: A Bayesian approach for combining probability and non-probability samples for analytic inference Authors:  Camilla Salvatore - University of Milano-Bicocca (Italy) [presenting]
Silvia Biffignandi - University of Bergamo (Italy)
Joseph Sakshaug - German Institute for Employment Research (Germany)
Arkadiusz Wisniowski - University of Manchester (United Kingdom)
Bella Struminskaya - Utrecht University (Netherlands)
Abstract: The popularity of non-probability sample web-surveys is increasing due to their convenience and relatively low costs. On the contrary, traditional probability-sample surveys are suffering from decreasing response rates, with a consequent increase in survey costs. Integrating the two samples in order to overcome their respective disadvantages is one of the current challenges in the statistical field. Our aim is to combine probability and non-probability samples to improve analytic inference on model parameters. We consider the Bayesian framework, where inference is based on a probability sample and available information about a non-probability sample is provided naturally through the prior. We focus on the logistic regression case and conduct a simulation study under different scenarios based on selection variables, selection probabilities, sample sizes, and prior specifications. We compare the performance of several informative and non-informative priors in terms of mean-squared errors (MSE). Overall, the informative priors reduce the MSE or, in the worst-case situation perform equivalently to the non-informative priors. Finally, we present a real data analysis considering an actual probability-based survey and several volunteer web-surveys which represent different selection scenarios.