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Logistic Regression in Rare Events Data
Open accessAbstract
We study rare events data, binary dependent variables with dozens to thousands of times fewer ones (events, such as wars, vetoes, cases of political activism, or epidemiological infections) than zeros (“nonevents”). In many literatures, these variables have proven difficult to explain and predict, a problem that seems to have at least two sources. First, popular statistical procedures, such as logistic regression, can sharply underestimate the probability of rare events. We recommend corrections that outperform existing methods and change the estimates of absolute and relative risks by as much as some estimated effects reported in the literature. Second, commonly used data collection strategies are grossly inefficient for rare events data. The fear of collecting data with too few events has led to data collections with huge numbers of observations but relatively few, and poorly measured, explanatory variables, such as in international conflict data with more than a quarter-million dyads, only a few of which are at war. As it turns out, more efficient sampling designs exist for making valid inferences, such as sampling all available events (e.g., wars) and a tiny fraction of nonevents (peace). This enables scholars to save as much as 99% of their (nonfixed) data collection costs or to collect much more meaningful explanatory variables. We provide methods that link these two results, enabling both types of corrections to work simultaneously, and software that implements the methods developed.
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“In columns 5 to 7, we report results using this estimator.The two modernization variables remain individually signi…cant and jointly signi…cant when entered together.”
From From Open to Secret Ballot: Vote Buying and Modernization (2012) · cites this paper as King and Zeng (2001)
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BackgroundWeaver, R. C. (2015) · Social Sciences · doi:10.3390/socsci4041046 · Cited by 5
“Because the population rate in this case is known (q/N ≈ 7 percent), the relogit model allows the author to decrease the large number of non-violators (M = 84,484) in the dataset in order to increase efficiency in carrying out the analysis [68].”
InfluentialCollet, F. H., & Philippe, D. (2013) · Journal of Management Studies · doi:10.1111/joms.12051 · Cited by 57
“Consequently, a random sampling of dyads would yield downward-based estimates because the average probability of alliance formation is small (0.008) (King and Zeng, 2001).”
BackgroundInfluentialA Signaling Perspective on Partner Selection in Venture Capital Syndicates
Hopp, C., & Lukas, C. (2014) · Entrepreneurship Theory and Practice · doi:10.1111/etap.12023 · Cited by 52
Hard times and regime failure: autocratic responses to economic downturns
Tanneberg, D., Stefes, C. H., & Merkel, W. (2013) · Contemporary Politics · doi:10.1080/13569775.2013.773206 · Cited by 79
“Common procedures of statistical analysis such as the binary time-series logistic regression employed here ‘can sharply underestimate the probability of rare events’ (King and Zeng 2001, p. 138).”
MethodA novel generative adversarial network for improving crash severity modeling with imbalanced data
Chen, J.-L., Pu, Z.-Y., Zheng, N., Wen, X., Ding, H., & Guo, X.-C. (2024) · Transportation Research Part C: Emerging Technologies · doi:10.1016/j.trc.2024.104642 · Cited by 51
Commodity prices and banking crises
Eberhardt, M., & Presbitero, A. (2021) · Journal of International Economics · doi:10.1016/j.jinteco.2021.103474 · Cited by 51
Ke, Z.-H., Liu, D., & Brass, D. (2020) · Information systems research · doi:10.2139/ssrn.3607468 · Cited by 51
“To avoid such a bias, we adopted Rare Event logit (ReLogit) (King and Zeng, 2001, 2002) and used logit as a backup.”
BackgroundMethodLandslide susceptibility and mobilization rates in the Mount Elgon region, Uganda
Broeckx, J., Maertens, M., Isabirye, M., Vanmaercke, M., Namazzi, B., Deckers, J., Tamale, J., Jacobs, L., Thiery, W., Kervyn, M., et al. (2018) · Landslides · doi:10.1007/s10346-018-1085-y · Cited by 51
Trading Interests: Domestic Institutions, International Negotiations, and the Politics of Trade
Betz, T. (2017) · Journal of Politics · doi:10.1086/692476 · Cited by 51
Lagged cumulative spruce budworm defoliation affects the risk of fire ignition in Ontario, Canada.
James, P., Robert, L.-E., Wotton, B., Martell, D., & Fleming, R. (2017) · Ecological Applications · doi:10.1002/eap.1463 · Cited by 51
Shany, T., Wang, K., Liu, Y., Lovell, N., & Redmond, S. (2015) · Healthcare technology letters · doi:10.1049/htl.2015.0019 · Cited by 51
The Pacifying Effects of Local Religious Institutions
de Juan, A., Pierskalla, J. H., & Vüllers, J. (2015) · Political Research Quarterly · doi:10.1177/1065912915578460 · Cited by 51
“For example, as an alternative to standard logit, we also estimate rare-events logistic models (King and Zeng 2001) without affecting our main finding (see Section 2 of the supplementary online appendix).14 We also add additional observable covariates that might operate as omitted variables.”
BackgroundMethodEllwanger, N., & Boschma, R. (2015) · doi:10.1111/tesg.12141 · Cited by 51
“In that way, we do not lose consistency or efficiency compared to the full sample (King and Zeng 2001a; King and Zeng 2001b).”
BackgroundUhlig, J., Lücke, C., Vliegenthart, R., Loewe, C., Grothoff, M., Schuster, A., Lurz, P., Jacquier, A., Francone, M., Zapf, A., et al. (2019) · European Radiology · doi:10.1007/s00330-019-06171-2 · Cited by 50
The Determinants and Consequences of Tax Audits: Some Evidence from China
Li, W.-F., Pittman, J., & Wang, Z.-T. (2019) · doi:10.2308/atax-52136 · Cited by 50
Values, Attitudes Toward Interpersonal Violence, and Interpersonal Violent Behavior
Seddig, D., & Davidov, E. (2018) · Frontiers in Psychology · doi:10.3389/fpsyg.2018.00604 · Cited by 71
“In addition, interpersonal violent behavior is a rare event and as such limits the analytical possibilities, which would be otherwise much more flexible for normal data (King and Zeng, 2001).”
BackgroundMingo, S., Morales, F. J., & Dau, L. A. (2018) · Journal of International Business Studies · doi:10.1057/s41267-017-0141-5 · Cited by 55
Krammer, S. M. S. (2016) · Research Policy · doi:10.1016/j.respol.2015.10.014 · Cited by 50
Bank internationalization and firm exports: evidence from matched firm-bank dataPreprint
Bronzini, R., & D'Ignazio, A. (2016) · SSRN Electronic Journal · doi:10.2139/ssrn.2777973 · Cited by 50
From Claims to Violence: Signaling, Outbidding, and Escalation in Ethnic Conflict
Vogt, M., Gleditsch, K., & Cederman, L.-E. (2021) · Journal of Conflict Resolution · doi:10.1177/0022002721996436 · Cited by 49
“For the onset analysis, we use the King and Zeng (2001) rare events logit estimator and drop observations with ongoing civil conflicts.”
Method
Metadata
- Authors
- King, G., & Zeng, L.
- Affiliations
- Harvard University (US)
- George Washington University (US)
- ORCID
- King, Gary
- Venue
- Political Analysis
- Publisher
- Cambridge University Press (CUP)
- Published
- 2001
- Volume
- 9
- Issue
- 2
- Pages
- 137-163
- ISSN
- 1047-1987 (ISSN-L)
- 1476-4989
- OpenAlex
- W2163848058
- Cited by
- 4,316
- References
- 0
- Citations by year
- 2026: 273 · 2025: 223 · 2024: 261 · 2023: 235 · 2022: 277 · 2021: 362 · 2020: 316 · 2019: 307 · 2018: 236 · 2017: 176 · 2016: 205 · 2015: 189 · 2014: 238 · 2013: 185 · 2012: 142
- FWCI
- 61.75
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Political Analysis (publishedVersion)
- Digital Access to Scholarship at Harvard (DASH) (Harvard University) (submittedVersion, cc-by)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- National Science Foundation (9729884, 9753126)
- University of Cambridge
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Survey Sampling and Estimation Techniques
- Keywords
- rare events, logistic regression, binary dependent variables, sampling design, event sampling, war, risk estimation, data collection efficiency
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