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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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The Impact of Financial Literacy on Household Health Investment: Empirical Evidence from China
Ling, X., Wang, L., Pan, Y., & Feng, Y. (2023) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph20032229 · Cited by 32
Danesh, A., Ehsani, M., Nejad, F. M., & Zakeri, H. (2022) · International Journal of Crashworthiness · doi:10.1080/13588265.2022.2028471 · Cited by 24
“In fact, algorithms tend to be biased towards major class in imbalanced datasets.(74) Sampling methods can improve the accuracy of the models in prediction of fatal crashes.”
BackgroundRamos, L. A., Blankers, M., van Wingen, G. A., de Bruijn, T., Pauws, S. C., & Goudriaan, A. E. (2021) · Frontiers in Psychology · doi:10.3389/fpsyg.2021.734633 · Cited by 30
“This approach has been shown to be effective even in cases of severe class imbalance (King and Zeng, 2003; Zhu et al., 2018).”
BackgroundMuffoletto, M., Qureshi, A., Zeidan, A., Muizniece, L., Fu, X., Zhao, J., Roy, A., Bates, P., & Aslanidi, O. (2021) · Frontiers in Physiology · doi:10.3389/fphys.2021.674106 · Cited by 24
Monsen, B. (2021) · The Accounting Review · doi:10.2308/tar-2019-0283 · Cited by 42
Rahardja, R., Allan, R., Frampton, C., Morris, A., Mckie, J., & Young, S. (2020) · ANZ journal of surgery · doi:10.1111/ans.16385 · Cited by 24
Ahmed, S., Yap, M. H., Tan, M., & Hasan, M. K. (2020) · medRxiv · doi:10.1101/2020.07.11.20149112 · Cited by 33
“Therefore, we use weighted Categorical Cross-Entropy as our loss function for the feature extraction and classification networks whereby the weighting function is taken from [42].”
MethodExtended Dependence: Trade, Alliances, and Peace
Chen, F. R. (2020) · Journal of Politics · doi:10.1086/709149 · Cited by 24
Role of massa intermedia in human neurocognitive processing
Borghei, A., Cothran, T. P., Brahimaj, B. C., & Sani, S. (2020) · Brain Structure and Function · doi:10.1007/s00429-020-02050-5 · Cited by 28
Machine Learning: The New Language for Applications
Padala, V. S., Gandhi, K., & Dasari, P. (2019) · IAES International Journal of Artificial Intelligence (IJ-AI) · doi:10.11591/ijai.v8.i4.pp411-421 · Cited by 24
“So, it uses a probability model using the sigmoid function [7] as shown Figure 3.”
Is Adolescent Employment Still a Risk Factor for High School Dropout?
Staff, J., Yetter, A. M., Cundiff, K., Ramirez, N. G., Vuolo, M., & Mortimer, J. T. (2019) · Journal of Research on Adolescence · doi:10.1111/jora.12533 · Cited by 24
“Whereas stopping or dropping out of high school is relatively rare, at only 11 percent, the number of those who interrupt their educations in this sample is sufficient to use conventional logistic regression models (King & Zeng 2001).”
Ahmad, M., Allen, M. M. C., Raziq, M. M., & Rehman, W. U. (2019) · Employee Relations · doi:10.1108/er-01-2018-0021 · Cited by 30
Opting-in to prosocial incentives
Schwartz, D., Keenan, E. A., Imas, A., & Gneezy, A. (2019) · Organizational Behavior and Human Decision Processes · doi:10.1016/j.obhdp.2019.01.003 · Cited by 29
The Mafiascum Dataset: A Large Text Corpus for Deception Detection
de Ruiter, B., & Kachergis, G. (2018) · arXiv.org · doi:10.48550/arxiv.1811.07851 · Cited by 24
“For training, the two classes were reweighted using the heuristic devised by King and Zeng (2001).”
MethodLehmann‐Willenbrock, N., & Chiu, M. M. (2017) · Journal of Organizational Behavior · doi:10.1002/job.2256 · Cited by 30
Predictors of Marital Dissolution During a Period of Rapid Social Change: Evidence From South Asia
Jennings, E. A. (2016) · Demography · doi:10.1007/s13524-016-0504-8 · Cited by 24
“Although this is a small proportion, it presents a large enough incidence of marital dissolution to allow for the use of logistic regression with event history analysis (King and Zeng 2001).”
MethodGender, Race, and Dissensus on State Supreme Courts*
Szmer, J., Christensen, R. K., & Kaheny, E. B. (2015) · doi:10.1111/ssqu.12133 · Cited by 24
Deep venous thrombosis in children with sickle cell disease
Boechat, T. D. O., Nascimento, E., Lobo, C. L. D. C., & Ballas, S. (2015) · Pediatric Blood & Cancer · doi:10.1002/pbc.25431 · Cited by 24
Self-administered Questions and Interviewer–Respondent Familiarity
Rodríguez, L., Sana, M., & Sisk, B. (2015) · doi:10.1177/1525822x14549315 · Cited by 24
Stochastic identification of malware with dynamic traces
Storlie, C. B., Anderson, B., Wiel, S. V., Quist, D., Hash, C. L., & Brown, N. (2014) · doi:10.1214/13-aoas703 · Cited by 24
“King and Zeng (2001) point out that, provided the estimates of the regression coefficients [i.”
BackgroundDo asset price drops foreshadow recessions?
Bluedorn, J., Decressin, J., & Terrones, M. E. (2016) · International Journal of Forecasting · doi:10.1016/j.ijforecast.2015.06.005 · Cited by 32
Improved Balanced Classification with Theoretically Grounded Loss Functions
Cortes, C., Mohri, M., & Zhong, Y.-T. (2025) · Neural Information Processing Systems · doi:10.48550/arxiv.2512.23947 · Cited by 23
“…1997, Wallace et al., 2011, Chawla et al., 2002, Yin et al., 2018], threshold adjustments [Fawcett and Provost, 1996, Provost, 2000, Maloof, 2003, King and Zeng, 2001, Collell et al., 2016, Menon et al., 2021, Zhu et al., 2023], and weight normalization methods [Zhang et al., 2019a, Kim and Kim,…”
Application of VGG16 Transfer Learning for Breast Cancer Detection
Fatima, T., & Soliman, H. (2025) · Information · doi:10.3390/info16030227 · Cited by 25
“The class weights were computed using the following formula [35]: class weight = total samples number of classes × samples in class By computing the total number of samples and dividing this value by the combined product of the number of classes and the number of samples per class, this technique…”
Logistic regression versus XGBoost for detecting burned areas using satellite images
Militino, A. F., Goyena, H., Pérez-Goya, U., & Ugarte, M. (2024) · Environmental and Ecological Statistics · doi:10.1007/s10651-023-00590-7 · Cited by 23
“In case of very imbalanced data, the LR can underestimate seriously the probability of success (burned pixels) (King and Zeng 2001).”
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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