A model robust subsampling approach for Generalised Linear Models in big data settings

In today’s modern era of big data, computationally efficient and scalable methods are needed to support timely insights and informed decision making. One such method is subsampling, where a subset of the big data is analysed and used as the basis for inference rather than considering the whole data set. A key question when applying subsampling approaches is how to select an informative subset based on the questions being asked of the data. A recent approach for this has been proposed based on determining subsampling probabilities for each data point, but a limitation of this approach is that the appropriate subsampling probabilities rely on an assumed model for the big data. In this article, to overcome this limitation, we propose a model robust approach where a set of models is considered, and the subsampling probabilities are evaluated based on the weighted average of probabilities that would be obtained if each model was considered singularly. Theoretical results are derived to inform such an approach. Our model robust subsampling approach is applied in a simulation study and in two real-world applications where performance is compared to current subsampling practices. The results show that our model robust approach outperforms alternative methods.