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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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Beymer, M., Weiss, R., Bolan, R., Kofron, R., Flynn, R., Pieribone, D., Kulkarni, S. P., & Landovitz, R. (2017) · Open Forum Infectious Diseases · doi:10.1093/ofid/ofx061 · Cited by 17
“In the multivariable logistic regression, we used a penalized likelihood in the model to adjust for the small sample bias caused by the low number of seroconverters in the study [17].”
MethodDouglas, E. (2016) · Child Maltreatment · doi:10.1177/1077559516657890 · Cited by 17
“Rare event logistic regression is used when the dependent variable occurs less than 5% of the time in the data set (King & Zeng, 2001).”
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Ash, K. (2016) · International Interactions · doi:10.1080/03050629.2016.1138108 · Cited by 17
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Kehrberg, J. E. (2015) · Comparative European Politics · doi:10.1057/cep.2014.6 · Cited by 17
Douglas, E. M. (2015) · Journal of Public Child Welfare · doi:10.1080/15548732.2015.1041668 · Cited by 17
“Rare event logistic regression is used when the dependent variable has a binary outcome, but it is especially recommended for use in situations where the dependent variable occurs less than 5% of the time in the dataset (King & Zeng, 2001).”
MethodOccupational Mobility and Depression Among the Foreign-Born in the United States
Ro, A. E. (2013) · Journal of Immigrant and Minority Health · doi:10.1007/s10903-013-9945-y · Cited by 43
“adjusted using the rare outcomes logistic regression command in Stata (relogit) [32] produced smaller coefficients”
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Rawls' Fairness, Income Distribution and Alarming Level of Gini Coefficient
Tao, Y., Wu, X., & Li, C.-S. (2014) · doi:10.48550/arxiv.1409.3979 · Cited by 17
“Since the seminal work of Kuznets (1955), there has emerged a huge and well-developed literature on the theoretical and empirical studies of income inequality (see de la Croix and Doepke 2003; Yang 2013).”
BackgroundInfluentialHegeman, E. E., Dickson, B., & Zachmann, L. J. (2014) · Landscape Ecology · doi:10.1007/s10980-014-0078-z · Cited by 17
“We combined all fires and an equal number of non-fires into a single database (King and Zeng 2001), and then extracted the values of all variables from the data layers.”
Zeigler, S. M., Pierskalla, J. H., & Mazumder, S. (2014) · doi:10.1177/0022002713478561 · Cited by 17
Lardon, A., & Deloof, M. (2014) · doi:10.2139/ssrn.1906429 · Cited by 17
“Rare event logistic regressions correct for the possible underestimation of rare events probabilities (King and Zeng 2001).”
BackgroundBoccio, C. M., Jackson, D. B., & Leal, W. E. (2020) · Addictive Behaviors · doi:10.1016/j.addbeh.2019.106186 · Cited by 13
BIELIK 7B V0.1: POLISH LANGUAGE MODEL - DEVELOPMENT, INSIGHTS, AND EVALUATION
Ociepa, K., Flis, Ł., Wróbel, K., Gwoździej, A., & Kinas, R. (2025) · Computer Science · doi:10.7494/csci.2025.26.4.7689 · Cited by 7
“The standard Weighted Cross-Entropy Loss (King and Zeng, 2001), originating from the weighted exogenous sampling maximum-likelihood estimator, is frequently used in multi-class classification problems (Wu et al., 2024).”
Fissler, T., Lorentzen, C., & Mayer, M. (2022) · arXiv · doi:10.48550/arxiv.2202.12780 · Cited by 7
“We refer to [46] for more information about logistic regression with rare events, e.”
BackgroundMiloslavich, K., & Wardle, M. (2024) · The American Journal of Drug and Alcohol Abuse · doi:10.1080/00952990.2024.2331721 · Cited by 5
“Third, the base rates of certain disorders, for example, opioid use disorder, were very low relative to other SUDs, which may have led to an underestimation of the probability of experiencing anger in lifetime use and SUD variables with lower base rates according to King & Zeng (42).”
Viva la Revolución, or: Do Revolutions Lead to More Democracy?
Boese, V. A. (2015) · Peace Economics, Peace Science and Public Policy · doi:10.1515/peps-2015-0027 · Cited by 1
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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