Estimation of ideological positions among
voters, legislators, and other actors is central to many subfields
of political science. Recent applications include large data sets
of various types including roll calls, surveys, textual and social
media data. To overcome the resulting computational challenges, we
propose fast estimation methods for ideal points with massive data.
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.