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

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.

Type
Original Articles
Information
Political Science Research and Methods , Volume 8 , Issue 1 , January 2020 , pp. 92 - 105
Copyright
Copyright © The European Political Science Association 2018 

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References

Acemoglu, D, Johnson, S, Robinson, JA Yared, P (2008) Income and Democracy. American Economic Review 98, 808–842.10.1257/aer.98.3.808Google Scholar
Beck, N (2011) Is OLS with a Binary Dependent Variable Really OK? Estimating (Mostly) TSCS Models with Binary Dependent Variables and Fixed Effects. Working Paper, Annual Meeting of the Society of Political Methodology.Google Scholar
Beck, N (2015) Estimating Grouped Data Models with a Binary Dependent Variable and Fixed Effects: What Are the Issues? Working Paper, Annual Meeting of the Society of Political Methodology. Available at https://pdfs.semanticscholar.org/65b4/5e49eff7f11a7ce0cb5780a8adcb9f311750.pdf.Google Scholar
Beck, N Katz, JN (2001) Throwing Out the Baby with the Bath Water: A Comment on Green, Kim, and Yoon. International Organization 55, 487–495.Google Scholar
Bell, A Jones, K (2015) Explaining Fixed Effects: Random Effects Modeling of Time-Series Cross-Sectional and Panel Data. Political Science Research and Methods 3, 133–153.Google Scholar
Buhaug, H Gleditsch, KS (2008) Contagion or Confusion? Why Conflicts Cluster in Space1. International Studies Quarterly 52, 215–233.Google Scholar
Chamberlain, G (1980) Analysis of Covariance with Qualitative Data. The Review of Economic Studies 47, 225–238.Google Scholar
Chassang, S Padro-i Miquel, G (2009) Economic Shocks and Civil War. Quarterly Journal of Political Science 4, 211–228.Google Scholar
Clark, TS Linzer, DA (2015) Should I Use Fixed or Random Effects? Political Science Research and Methods 3, 399–408.Google Scholar
Collier, P Hoeffler, A (2004) Greed and Grievance in Civil War. Oxford Economic Papers 56, 563–595.Google Scholar
Cook, SJ, Blas, B, Carroll, RJ Sinha, S (2017) Two Wrongs Make a Right: Addressing Underreporting in Binary Data from Multiple Sources. Political Analysis 25, 223–240.Google Scholar
Cook, SJ McGrath, LF (n.d.) Unit Heterogeneity in Large Datasets with Rare Events. Working Paper, In Progress.Google Scholar
Cook, SJ, Niehaus, J Zuhlke, S (2018) A Warning on Separation in Multinomial Logistic Regression. Research & Politics 5, 1–5.Google Scholar
Copas, JB (1988) Binary Regression Models for Contaminated Data. Journal of the Royal Statistical Society, Series B 50, 225–265.Google Scholar
Fearon, J (2008) Economic Development, Insurgency, and Civil War. In E Helpman (ed), Institutions and Economic Performance. Cambridge, MA: Harvard University Press.Google Scholar
Fearon, JD Laitin, DD (2003) Ethnicity, Insurgency, and Civil War. American Political Science Review 97, 75–90.Google Scholar
Firth, D (1993) Bias Reduction of Maximum Likelihood Estimates. Biometrika 80, 27–38.Google Scholar
Gelman, A, Jakulin, A, Pittau, MG, Su, Y-S et al. (2008) A Weakly Informative Default Prior Distribution for Logistic and Other Regression Models. The Annals of Applied Statistics 2, 1360–1383.Google Scholar
Green, DP, Kim, SY Yoon, DH (2001) Dirty Pool. International Organization 55, 441–468.Google Scholar
Greene, W (2004) The Behaviour of the Maximum Likelihood Estimator of Limited Dependent Variable Models in the Presence of Fixed Effects. The Econometrics Journal 7, 98–119.Google Scholar
Heckman, JJ (1981) The Incidental Parameters Problem and the Problem of Initial Conditions in Estimating a Discrete Time-Discrete Data Stochastic Process and Some Monte Carlo Evidence. In C Manski and D McFadden (eds), Structural Analysis of Discrete Data with Econometric Applications, 114–178. Cambridge, MA: MIT University Press.Google Scholar
Hegre, H Sambanis, N (2006) Sensitivity Analysis of Empirical Results on Civil War Onset. Journal of Conflict Resolution 50, 508–535.Google Scholar
Heinze, G Schemper, M (2002) A Solution to the Problem of Separation in Logistic Regression. Statistics in Medicine 21, 2409–2419.Google Scholar
King, G (2001) Proper Nouns and Methodological Propriety: Pooling Dyads in International Relations Data. International Organization 55, 497–507.10.1162/00208180151140667Google Scholar
Lancaster, T (2000) The Incidental Parameter Problem Since 1948. Journal of Econometrics 95, 391–413.Google Scholar
Lesaffre, E Spiessens, B (2001) On the Effect of the Number of Quadrature Points in a Logistic Random Effects Model: An Example. Journal of the Royal Statistical Society: Series C (Applied Statistics) 50, 325–335.Google Scholar
McGrath, LF (2018) Problems with Penalised Maximum Likelihood and Jeffrey’s Priors to Account for Separation in Large Datasets with Rare Events. Available at https://www.dropbox.com/s/x5csn91nmt09bv8/mcgrath_separation.pdf, accessed 4 May 2018.Google Scholar
Nel, P Righarts, M (2008) Natural Disasters and the Risk of Violent Civil Conflict. International Studies Quarterly 52, 159–185.Google Scholar
Neyman, J Scott, EL (1948) Consistent Estimates Based on Partially Consistent Observations. Econometrica: Journal of the Econometric Society, 1–32.Google Scholar
Oneal, JR Russett, B (2001) Clear and Clean: The Fixed Effects of the Liberal Peace. International Organization 55, 469–485.Google Scholar
Plümper, T Troeger, VE (2007) Efficient Estimation of Time-Invariant and Rarely Changing Variables in Finite Sample Panel Analyses with Unit Fixed Effects. Political Analysis 15, 124–139.Google Scholar
Plümper, T Troeger, VE (2011) Fixed-Effects Vector Decomposition: Properties, Reliability, and Instruments. Political Analysis 19, 147–164.Google Scholar
Rainey, C (2016) Dealing with Separation in Logistic Regression Models. Political Analysis 24, 339–355.Google Scholar
Sambanis, N (2001) Do Ethnic and Nonethnic Civil Wars Have the Same Causes?: A Theoretical and Empirical Inquire (Part 1). Journal of Conflict Resolution 45, 259–282.Google Scholar
Wright, J (2009) How Foreign Aid Can Foster Democratization in Authoritarian Regimes. American Journal of Political Science 53, 552–571.Google Scholar
Zorn, C (2005) A Solution to Separation in Binary Response Models. Political Analysis 13, 157–170.10.1093/pan/mpi009Google Scholar
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