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Finding Jumps in Otherwise Smooth Curves: Identifying Critical Events in Political Processes

Published online by Cambridge University Press:  04 January 2017

Marc T. Ratkovic  and
Kevin H. Eng
Marc T. Ratkovic*
Affiliation:
Departments of Political Science and Statistics, University of Wisconsin, Madison, 110 North Hall, 1050 Bascom Mall, Madison, WI 53706
Kevin H. Eng
Affiliation:
Department of Statistics, University of Wisconsin, Madison, 1300 University Ave., Madison, WI 53706
*
e-mail: ratkovic@wisc.edu (corresponding author)
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Abstract

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Many social processes are stable and smooth in general, with discrete jumps. We develop a sequential segmentation spline method that can identify both the location and the number of discontinuities in a series of observations with a time component, while fitting a smooth spline between jumps, using a modified Bayesian Information Criterion statistic as a stopping rule. We explore the method in a large-n, unbalanced panel setting with George W. Bush's approval data, a small-n time series with median DW-NOMINATE scores for each Congress over time, and a series of simulations. We compare the method to several extant smoothers, and the method performs favorably in terms of visual inspection, residual properties, and event detection. Finally, we discuss extensions of the method.

Type
Research Article
Information
Political Analysis , Volume 18 , Issue 1 , Winter 2010 , pp. 57 - 77
Copyright
Copyright © The Author 2009. Published by Oxford University Press on behalf of the Society for Political Methodology 

Footnotes

Authors's note: We thank Charles Franklin for providing the presidential approval data and for many useful conversations. We thank Grace Wahba, participants in the University of Wisconsin-Madison's Models and Data Seminar, Sample Survey Seminar, and Fitting Curves to Data Seminar for many useful comments. Replication materials and relevant code are available on the Political Analysis Web site.

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