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Exploring the Dynamics of Latent Variable Models

Published online by Cambridge University Press:  11 April 2019

Kevin Reuning*
Department of Political Science, Miami University, Oxford, OH 45056, USA. Email:
Michael R. Kenwick
Department of Political Science, Rutgers University, New Brunswick, NJ 08901USA. Email:
Christopher J. Fariss
Department of Political Science, University of Michigan, Ann Arbor, MI 48104, USA. Email:


Researchers face a tradeoff when applying latent variable models to time-series, cross-sectional data. Static models minimize bias but assume data are temporally independent, resulting in a loss of efficiency. Dynamic models explicitly model temporal data structures, but smooth estimates of the latent trait across time, resulting in bias when the latent trait changes rapidly. We address this tradeoff by investigating a new approach for modeling and evaluating latent variable estimates: a robust dynamic model. The robust model is capable of minimizing bias and accommodating volatile changes in the latent trait. Simulations demonstrate that the robust model outperforms other models when the underlying latent trait is subject to rapid change, and is equivalent to the dynamic model in the absence of volatility. We reproduce latent estimates from studies of judicial ideology and democracy. For judicial ideology, the robust model uncovers shocks in judicial voting patterns that were not previously identified in the dynamic model. For democracy, the robust model provides more precise estimates of sudden institutional changes such as the imposition of martial law in the Philippines (1972–1981) and the short-lived Saur Revolution in Afghanistan (1978). Overall, the robust model is a useful alternative to the standard dynamic model for modeling latent traits that change rapidly over time.

Copyright © The Author(s) 2019. Published by Cambridge University Press on behalf of the Society for Political Methodology. 

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Authors’ note: An earlier version of this paper was presented at the annual meeting of the American Political Science Association in Philadelphia, PA (2016) and the Latent Variable Mini-Conference at the Varieties of Democracy Institute at the University of Gothenburg, Sweden (2016). We would like to thank the participants at these conferences and also James Lo, Suzie Linn, Kyle Marquardt, Ryan McMahon, Dan Pemstein, Kevin Quinn, Brigitte Seim, Jeff Staton, Jane Sumner, Alex Tahk, and Anne Whitesell for helpful comments and suggestions. The estimates from this paper along with the code necessary to implement the models in STAN and R are publicly available at a dataverse repository here: (Reuning, Kenwick, and Fariss 2018).

Contributing Editor: R. Michael Alvarez


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