Estimating Multilevel Models on Data Streams

Social scientists are often faced with data that have a nested structure: pupils are nested within schools, employees are nested within companies, or repeated measurements are nested within individuals. Nested data are typically analyzed using multilevel models. However, when data sets are extremely large or when new data continuously augment the data set, estimating multilevel models can be challenging: the current algorithms used to fit multilevel models repeatedly revisit all data points and end up consuming much time and computer memory. This is especially troublesome when predictions are needed in real time and observations keep streaming in. We address this problem by introducing the Streaming Expectation Maximization Approximation (SEMA) algorithm for fitting multilevel models online (or “row-by-row”). In an extensive simulation study, we demonstrate the performance of SEMA compared to traditional methods of fitting multilevel models. Next, SEMA is used to analyze an empirical data stream. The accuracy of SEMA is competitive to current state-of-the-art methods while being orders of magnitude faster. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s11336-018-09656-z) contains supplementary material, which is available to authorized users.