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Addressing Monotone Likelihood in Duration Modelling of Political Events

Published online by Cambridge University Press:  29 June 2020

Noel Anderson Open the ORCID record for Noel Anderson [Opens in a new window] ,
Benjamin E. Bagozzi  and
Ore Koren
Noel Anderson*
Affiliation:
Department of Political Science, University of Toronto, Canada
Benjamin E. Bagozzi
Affiliation:
Deparment of Political Science and International Relations, University of Delaware, USA
Ore Koren
Affiliation:
Department of Political Science, Indiana University, Bloomington, IN, USA
*
*Corresponding author. E-mail: noel.anderson@utoronto.ca
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Abstract

This article provides an accessible introduction to the phenomenon of monotone likelihood in duration modeling of political events. Monotone likelihood arises when covariate values are monotonic when ordered according to failure time, causing parameter estimates to diverge toward infinity. Within political science duration model applications, this problem leads to misinterpretation, model misspecification and omitted variable biases, among other issues. Using a combination of mathematical exposition, Monte Carlo simulations and empirical applications, this article illustrates the advantages of Firth's penalized maximum-likelihood estimation in resolving the methodological complications underlying monotone likelihood. The results identify the conditions under which monotone likelihood is most acute and provide guidance for political scientists applying duration modeling techniques in their empirical research.

Keywords

duration modelsmonotone likelihoodpenalized maximum likelihoodexternal interventionstate partition
Type
Article
Information
British Journal of Political Science , Volume 51 , Issue 4 , October 2021 , pp. 1654 - 1671
Copyright
Copyright © Cambridge University Press 2020

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References

Albert, A and Anderson, JA (1984) On the existence of maximum likelihood estimates in logistic regression models. Biometrika 71(1), 1–10.CrossRefGoogle Scholar
Anderson, N, Bagozzi, B, Koren, O (2020) “Replication Data for: Addressing Monotone Likelihood in Duration Modeling of Political Events”, https://doi.org/10.7910/DVN/OLMVP5, Harvard Dataverse, V1CrossRefGoogle Scholar
Anderson, N (2019) Competitive intervention, protracted conflict, and the global prevalence of civil war. International Studies Quarterly 63(3), 692–706.CrossRefGoogle Scholar
Bagozzi, BE, Joo, MM, Kim, B and Mukherjee, B (2019) A bayesian split population survival model for duration data with misclassified failure events. Political Analysis 27(4), 415–434.CrossRefGoogle Scholar
Balch-Lindsay, D and Enterline, AJ (2000) Killing time: the world politics of civil war duration, 1820–1992. International Studies Quarterly 44(4), 615–642.CrossRefGoogle Scholar
Beger, A et al. (2017) Splitting it up: the spduration split-population duration regression package for time-varying covariates. The R Journal 9(2), 474–486.CrossRefGoogle Scholar
Bennett, DS and Stam, AC (1996) The duration of interstate wars, 1816–1985. American Political Science Review 90(2), 239–257.CrossRefGoogle Scholar
Box-Steffensmeier, JM, Arnold, LW and Zorn, C (1997) The strategic timing of position taking in congress: a study of the north American free trade agreement. American Political Science Review 91(2), 324–338.CrossRefGoogle Scholar
Box-Steffensmeier, JM and Jones, BS (2004) Event History Modeling: A Guide for Social Scientists. New York: Cambridge University Press.CrossRefGoogle Scholar
Bryson, MC and Johnson, ME (1981) The incidence of monotone likelihood in the Cox model. Technometrics 23(4), 381–383.CrossRefGoogle Scholar
Chiba, D, Metternich, NW and Ward, MD (2015) Every story has a beginning, middle, and an end (but not always in that order): predicting duration dynamics in a unified framework. Political Science Research and Methods 3(3), 515–541.CrossRefGoogle Scholar
Cook, SJ, Hays, JC and Franzese, RJ (2020) Fixed effects in rare events data: a penalized maximum likelihood solution. Political Science Research and Methods 8(1), 92–105.CrossRefGoogle Scholar
Cook, SJ, Niehaus, J and Zuhlke, S (2018) A warning on separation in multinomial logistic models. Research & Politics 5(2), 1–5.CrossRefGoogle Scholar
Cunningham, DE (2011) Barriers to Peace in Civil War. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Firth, D (1993) Bias reduction of maximum likelihood estimates. Biometrika 80(1), 27–38.CrossRefGoogle Scholar
Fortna, VP (2008) Does Peacekeeping Work? Shaping Belligerents’ Choices after Civil War. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Gates, S et al. (2006) Institutional inconsistency and political instability: polity duration, 1800–2000. American Journal of Political Science 50(4), 893–908.CrossRefGoogle Scholar
Harden, JJ and Kropko, J (2019) Simulating duration data for the Cox model. Political Science Research and Methods 7(4), 921–928.CrossRefGoogle Scholar
Heinze, G and Dunkler, D (2008) Avoiding infinite estimates of time-dependent effects in small-sample survival studies. Statistics in Medicine 27(30), 6455–6469.CrossRefGoogle ScholarPubMed
Heinze, G and Schemper, M (2001) A solution to the problem of monotone likelihood in Cox regression. Biometrics 57(1), 114–119.CrossRefGoogle ScholarPubMed
Jeffreys, H (1946) An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London: Series A (Mathematical and Physical Sciences) 186(1007), 453–461.Google ScholarPubMed
Johnson, ME et al. (1982) Covariate analysis of survival data: a small-sample study of Cox's model. Biometrics 38(3), 685–698.CrossRefGoogle ScholarPubMed
Jones, BT and Metzger, SK (2019) Different words, same song: advice for substantively interpreting duration models. PS: Political Science & Politics 52(4), 691–695.Google Scholar
Kropko, J and Harden, JJ (2020) Beyond the hazard ratio: generating expected durations from the Cox proportional hazards model. British Journal of Political Science 50(1), 303–320.CrossRefGoogle Scholar
Licht, AA (2011) Change comes with time: substantive interpretation of nonproportional hazards in event history analysis. Political Analysis 19(2), 227–243.CrossRefGoogle Scholar
Licht, AA (2017) Hazards or hassles: the effect of sanctions on leader survival. Political Science Research and Methods 5(1), 143–161.CrossRefGoogle Scholar
Loughin, TM (1998) On the bootstrap and monotone likelihood in the Cox proportional hazards regression model. Lifetime Data Analysis 4(4), 393–403.CrossRefGoogle ScholarPubMed
McCullagh, P and Nelder, JA (1989) Generalized Linear Models, 2nd Edn. London: Chapman and Hall.CrossRefGoogle Scholar
McKibben, HE and Western, SD (2020) Reserved ratification: an analysis of states’ entry of reservations upon ratification of human rights treaties. British Journal of Political Science 50(2), 687–712.CrossRefGoogle Scholar
Omgba, LD (2009) On the duration of political power in Africa: the role of oil rents. Comparative Political Studies 42(3), 416–436.CrossRefGoogle Scholar
Rainey, C (2016) Dealing with separation in logistic regression models. Political Analysis 24(3), 339–355.CrossRefGoogle Scholar
Rainey, C and McKaskey, K (Forthcoming) Estimating logit models with small samples. Political Science Research and Methods.Google Scholar
Regan, PM (2000) Civil Wars and Foreign Powers: Outside Intervention in Intrastate Conflict. Ann Arbor: University of Michigan Press.CrossRefGoogle Scholar
Regan, PM (2002) Third-party interventions and the duration of intrastate conflicts. Journal of Conflict Resolution 46(1), 55–73.CrossRefGoogle Scholar
Ruhe, C (2018) Quantifying change over time: interpreting time-varying effects in duration analyses. Political Analysis 26(1), 90–111.CrossRefGoogle Scholar
Sarkees, MR (2000) The Correlates of War data on war: an update to 1997. Conflict Management and Peace Science 18(1), 123–144.CrossRefGoogle Scholar
Small, M and Singer, JD (1982) Resort to Arms: International and Civil Wars, 1816–1980, 2nd Edn. Beverly Hills, CA: Sage.Google Scholar
Svolik, MW (2008) Authoritarian reversals and democratic consolidation. American Political Science Review 102(2), 153–168.CrossRefGoogle Scholar
Tir, J (2005) Dividing countries to promote peace: prospects for long-term success of partitions. Journal of Peace Research 42(5), 545–562.CrossRefGoogle Scholar
Tsiatis, AA (1981) A large sample study of Cox's regression model. The Annals of Statistics 9(1), 93–108.CrossRefGoogle Scholar
Zorn, C (2005) A solution to separation in binary response models. Political Analysis 13(2), 157–170.CrossRefGoogle Scholar
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