Selection Bias and Continuous‐Time Duration Models: Consequences and a Proposed Solution

This article analyzes the consequences of nonrandom sample selection for continuous-time duration analyses and develops a new estimator to correct for it when necessary. We conduct a series of Monte Carlo analyses that estimate common duration models as well as our proposed duration model with selection. These simulations show that ignoring sample selection issues can lead to biased parameter estimates, including the appearance of (nonexistent) duration dependence. In addition, our proposed estimator is found to be superior in root mean-square error terms when nontrivial amounts of selection are present. Finally, we provide an empirical application of our method by studying whether self-selectivity is a problem for studies of leaders' survival during and following militarized conflicts.

[1]  Paul D. Allison,et al.  Event History Analysis : Regression for Longitudinal Event Data , 1984 .

[2]  James E. Prieger,et al.  A flexible parametric selection model for non‐normal data with application to health care usage , 2002 .

[3]  Adam J. Berinsky,et al.  The Two Faces of Public Opinion , 1999 .

[4]  Thomas Brambor,et al.  Understanding Interaction Models: Improving Empirical Analyses , 2006, Political Analysis.

[5]  William D. Berry,et al.  State Lottery Adoptions as Policy Innovations: An Event History Analysis , 1990, American Political Science Review.

[6]  Jeffrey A. Dubin,et al.  Selection Bias in Linear Regression, Logit and Probit Models , 1989 .

[7]  S. Werner,et al.  The Precarious Nature of Peace: Resolving the Issues, Enforcing the Settlement, and Renegotiating the Terms , 1999 .

[8]  Michael Haas.  Societal Approaches To the Study of War , 1965 .

[9]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1973 .

[10]  G. Maddala.  Limited-dependent and qualitative variables in econometrics: Introduction , 1983 .

[11]  Frederick J. Boehmke,et al.  Using Auxiliary Data to Estimate Selection Bias Models, with an Application to Interest Group Use of the Direct Initiative Process , 2003, Political Analysis.

[12]  Simon Hug,et al.  Selection Bias in Comparative Research: The Case of Incomplete Data Sets , 2003, Political Analysis.

[13]  P. R. Fisk,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1971 .

[14]  Richard J. Timpone.  Structure, Behavior, and Voter Turnout in the United States , 1998, American Political Science Review.

[15]  Curtis S. Signorino.  Strategic Interaction and the Statistical Analysis of International Conflict , 1999, American Political Science Review.

[16]  Karl Derouen.  The Indirect Link: , 1995 .

[17]  Charles R. Shipan,et al.  Delaying Justice(s): A Duration Analysis of Supreme Court Confirmations , 2003 .

[18]  Nathaniel Beck,et al.  Taking Time Seriously: Time-Series-Cross-Section Analysis with a Binary Dependent Variable , 1998 .

[19]  J. Heckman.  Sample selection bias as a specification error , 1979 .

[20]  J. Heckman.  The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models , 1976 .

[21]  G. King,et al.  Unifying Political Methodology: The Likelihood Theory of Statistical Inference , 1989 .

[22]  L. R. Reed,et al.  A unified statistical model of conflict onset and escalation American Journal of Political Science 4 , 2000 .

[23]  R. Michael Alvarez,et al.  Event History Modeling: A Guide for Social Scientists , 2004 .

[24]  John O. Brehm.  The Phantom Respondents: Opinion Surveys and Political Representation , 1993 .

[25]  Philip Verwimp,et al.  Testing the Double-Genocide Thesis for Central and Southern Rwanda , 2003 .

[26]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[27]  Stephen T. Easton,et al.  The Cabinet Stability Controversy: New Perspectives on a Classic Problem , 1992 .

[28]  R. Rosecrance.  Action and Reaction in World Politics: International Systems in Perspective , 1977 .

[29]  Mark J. C. Crescenzi,et al.  Democratic Survival, Peace, and War in the International System , 2003 .

[30]  John Brehm,et al.  Alternative Corrections for Sample Truncation: Applications to the 1988, 1990, and 1992 Senate Election Studies , 1999, Political Analysis.

[31]  Lanny W. Martin,et al.  Wasting Time? The Impact of Ideology and Size on Delay in Coalition Formation , 2003, British Journal of Political Science.

[32]  Brian L. Job,et al.  The President and the Political Use of Force , 1986, American Political Science Review.

[33]  Lung-fei Lee.  Generalized Econometric Models with Selectivity , 1983 .

[34]  Sanford C. Gordon,et al.  Stochastic dependence in competing risks , 2002 .

[35]  Jan Palczewski,et al.  Monte Carlo Simulation , 2008, Encyclopedia of GIS.

[36]  J. Klein,et al.  A partially parametric estimator of survival in the presence of randomly censored data. , 1990, Biometrics.

[37]  Janet M. Box-Steffensmeier,et al.  Time is of the Essence: Event History Models in Political Science , 1997 .

[38]  Nolan McCarty,et al.  Advice and Consent: Senate Responses to Executive Branch Nominations 1885- 1996 , 1999 .

[39]  Murray D Smith,et al.  Modeling Sample Selection Using Archimedean Copulas , 2003 .

[40]  Gary King,et al.  A Unified Model of Cabinet Dissolution in Parliamentary Democracies , 1990 .

[41]  D. Scott Bennett,et al.  Testing Alternative Models of Alliance Duration, 1816-1984 , 1997 .

[42]  D. Scott Bennett,et al.  Parametric Models, Duration Dependence, and Time-Varying Data Revisited , 1999 .

[43]  Anne E. Sartori.  An Estimator for Some Binary-Outcome Selection Models Without Exclusion Restrictions , 2003, Political Analysis.

[44]  Milton C. Chew.  Distributions in Statistics: Continuous Univariate Distributions-1 and 2 , 1971 .

[45]  Christopher Zorn,et al.  Modeling Duration Dependence , 2000, Political Analysis.

[46]  E. Gumbel.  Bivariate Exponential Distributions , 1960 .

[47]  P. Allison.  Event History Analysis , 1984 .

[48]  Nathaniel N. Beck.  Modelling Space and Time: The Event History Approach , 1999 .

[49]  Rudolph Rummel,et al.  Libertarianism and International Violence , 1983 .

[50]  G. Chiozza,et al.  Peace through Insecurity , 2003 .

[51]  P. Schmidt,et al.  Limited-Dependent and Qualitative Variables in Econometrics. , 1984 .

[52]  Ross A. Miller.  Regime Type, Strategic Interaction, and the Diversionary Use of Force , 1999 .

[53]  Randolph M. Siverson,et al.  War and the Survival of Political Leaders: A Comparative Study of Regime Types and Political Accountability , 1995, American Political Science Review.

[54]  A. Lupia,et al.  Coalition Termination and the Strategic Timing of Parliamentary Elections , 1995, American Political Science Review.

[55]  Christopher H. Achen.  The Statistical Analysis of Quasi-Experiments , 2023 .

[56]  D. Diermeier,et al.  The Duration of Cabinet Formation Processes in Western Multi-Party Democracies , 1998, British Journal of Political Science.

[57]  J. Fearon.  Rationalist explanations for war , 1995, International Organization.