Fast Estimation of Ideal Points with Massive Data∗

Recently, many scholars have begun to estimate ideological preferences across time and institutions, analyzing data sets that are orders of magnitude larger than a canonical single-chamber roll call matrix for a single time period. To overcome the resulting computational challenges, we propose fast estimation methods for ideal points with massive data. Specifically, we derive the Expectation-Maximization (EM) algorithms to estimate the standard ideal point model with binary, ordinal, and continuous outcome variables. We then extend this methodology to dynamic and hierarchical ideal point models by developing variational EM algorithms for approximate inference. We demonstrate the computational efficiency and scalability of our methodology through a variety of real and simulated data. In cases where a standard Markov chain Monte Carlo algorithm would require several days to compute ideal points, the proposed algorithm can produce essentially identical estimates within minutes. Open-source software is available for implementing the proposed methods.