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Fixed effects in rare events data: a penalized maximum likelihood solution

Published online by Cambridge University Press:  09 October 2018

Scott J. Cook*
Department of Political Science, Texas A&M University, 2010 Allen Building, College Station, TX 77843, USA
Jude C. Hays
Department of Political Science, University of Pittsburgh, 4600 Wesley W. Posvar Hall Pittsburgh, PA 152603, USA
Robert J. Franzese
Department of Political Science, University of Michigan, 5700 Haven Hall, Ann Arbor, MI 48109, USA
*Corresponding author. Email:


Most agree that models of binary time-series-cross-sectional data in political science often possess unobserved unit-level heterogeneity. Despite this, there is no clear consensus on how best to account for these potential unit effects, with many of the issues confronted seemingly misunderstood. For example, one oft-discussed concern with rare events data is the elimination of no-event units from the sample when estimating fixed effects models. Many argue that this is a reason to eschew fixed effects in favor of pooled or random effects models. We revisit this issue and clarify that the main concern with fixed effects models of rare events data is not inaccurate or inefficient coefficient estimation, but instead biased marginal effects. In short, only evaluating event-experiencing units gives an inaccurate estimate of the baseline risk, yielding inaccurate (often inflated) estimates of predictor effects. As a solution, we propose a penalized maximum likelihood fixed effects (PML-FE) estimator, which retains the complete sample by providing finite estimates of the fixed effects for each unit. We explore the small sample performance of PML-FE versus common alternatives via Monte Carlo simulations, evaluating the accuracy of both parameter and effects estimates. Finally, we illustrate our method with a model of civil war onset.

Original Articles
Copyright © The European Political Science Association 2018 

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