Exploring the Dynamics of Latent Variable Models
47 Pages Posted: 26 Aug 2016 Last revised: 26 Feb 2017
Date Written: October 3, 2016
Researchers face a tradeoff when applying latent variable models to accommodate temporal interdependence in 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 experiences discrete temporal changes. We address this tradeoff by investigating two new approaches for modeling and evaluating latent variable estimates: a robust dynamic model and a finite mixture model that nests together the static and dynamic models. These new models are capable of minimizing bias and accommodating volatile changes in the latent trait. A simulation study demonstrates that the robust dynamic model outperforms other models when the underlying latent trait is characterized by volatile changes, and is equivalent to the dynamic model in the absence of volatile changes. We also reproduce latent estimates from studies of judicial ideology and democracy. For judicial ideology, the robust dynamic model provides new evidence about the strategic nature of judicial choices. For democracy, the robust dynamic 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).
Keywords: Latent Variables, Dynamic Latent Variables, IRT, Political Methodology
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