Skip to main content Accessibility help
×
Home
Hostname: page-component-59df476f6b-6b5bh Total loading time: 0.22 Render date: 2021-05-19T00:29:37.971Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

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

Published online by Cambridge University Press:  09 October 2018

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
E-mail address:

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
Copyright
Copyright © The European Political Science Association 2018 

Access options

Get access to the full version of this content by using one of the access options below.

References

Acemoglu, D, Johnson, S, Robinson, JA Yared, P (2008) Income and Democracy. American Economic Review 98, 808842.10.1257/aer.98.3.808CrossRefGoogle 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, 487495.CrossRefGoogle 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, 133153.CrossRefGoogle Scholar
Buhaug, H Gleditsch, KS (2008) Contagion or Confusion? Why Conflicts Cluster in Space1. International Studies Quarterly 52, 215233.CrossRefGoogle Scholar
Chamberlain, G (1980) Analysis of Covariance with Qualitative Data. The Review of Economic Studies 47, 225238.CrossRefGoogle Scholar
Chassang, S Padro-i Miquel, G (2009) Economic Shocks and Civil War. Quarterly Journal of Political Science 4, 211228.CrossRefGoogle Scholar
Clark, TS Linzer, DA (2015) Should I Use Fixed or Random Effects? Political Science Research and Methods 3, 399408.CrossRefGoogle Scholar
Collier, P Hoeffler, A (2004) Greed and Grievance in Civil War. Oxford Economic Papers 56, 563595.CrossRefGoogle 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, 223240.CrossRefGoogle ScholarPubMed
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, 15.CrossRefGoogle Scholar
Copas, JB (1988) Binary Regression Models for Contaminated Data. Journal of the Royal Statistical Society, Series B 50, 225265.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, 7590.CrossRefGoogle Scholar
Firth, D (1993) Bias Reduction of Maximum Likelihood Estimates. Biometrika 80, 2738.CrossRefGoogle 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, 13601383.CrossRefGoogle Scholar
Green, DP, Kim, SY Yoon, DH (2001) Dirty Pool. International Organization 55, 441468.CrossRefGoogle 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, 98119.CrossRefGoogle 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, 114178. 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, 508535.CrossRefGoogle Scholar
Heinze, G Schemper, M (2002) A Solution to the Problem of Separation in Logistic Regression. Statistics in Medicine 21, 24092419.CrossRefGoogle ScholarPubMed
King, G (2001) Proper Nouns and Methodological Propriety: Pooling Dyads in International Relations Data. International Organization 55, 497507.10.1162/00208180151140667CrossRefGoogle Scholar
Lancaster, T (2000) The Incidental Parameter Problem Since 1948. Journal of Econometrics 95, 391413.CrossRefGoogle 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, 325335.CrossRefGoogle 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, 159185.CrossRefGoogle Scholar
Neyman, J Scott, EL (1948) Consistent Estimates Based on Partially Consistent Observations. Econometrica: Journal of the Econometric Society, 1–32.CrossRefGoogle Scholar
Oneal, JR Russett, B (2001) Clear and Clean: The Fixed Effects of the Liberal Peace. International Organization 55, 469485.CrossRefGoogle 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, 124139.CrossRefGoogle Scholar
Plümper, T Troeger, VE (2011) Fixed-Effects Vector Decomposition: Properties, Reliability, and Instruments. Political Analysis 19, 147164.CrossRefGoogle Scholar
Rainey, C (2016) Dealing with Separation in Logistic Regression Models. Political Analysis 24, 339355.CrossRefGoogle 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, 259282.CrossRefGoogle Scholar
Wright, J (2009) How Foreign Aid Can Foster Democratization in Authoritarian Regimes. American Journal of Political Science 53, 552571.CrossRefGoogle Scholar
Zorn, C (2005) A Solution to Separation in Binary Response Models. Political Analysis 13, 157170.10.1093/pan/mpi009CrossRefGoogle Scholar
Supplementary material: Link

Cook et al. Dataset

Link
Supplementary material: PDF

Cook et al. supplementary material

Cook et al. supplementary material 1

Download Cook et al. supplementary material(PDF)
PDF 104 KB

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *