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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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“As pointed out by King and Zeng (2001) rare events data are characterized by “ binary dependent with dozens to thousands of times ( . . . ) fewer ones than zeros ”.”
BackgroundMethodInfluentialHandling Missing Values in Information Systems Research: A Review of Methods and Assumptions
Peng, J., Hahn, J., & Huang, K.-W. (2022) · Information systems research · doi:10.1287/isre.2022.1104 · Cited by 17
Battaglia, D., Cucino, V., Paolucci, E., & Piccaluga, A. (2022) · Studies in Higher Education · doi:10.1080/03075079.2022.2055325 · Cited by 17
“Given the binary and rare nature of our dependent variables, we relied on a specific logit model, based on penalised likelihood (also known as Firth method; King and Zeng 2001).”
MethodA Comparison of Energy-Efficient Seizure Detectors for Implantable Neurostimulation Devices
Manzouri, F., Zöllin, M., Schillinger, S., Dümpelmann, M., Mikut, R., Woias, P., Comella, L. M., & Schulze‐Bonhage, A. (2022) · Frontiers in Neurology · doi:10.3389/fneur.2021.703797 · Cited by 17
“interictal) were imbalanced, the class indices were weighted to balance the weighting of the loss function during the training phase (39).”
BackgroundResource Reconfiguration During Technological Change
Chaturvedi, T., & Prescott, J. (2021) · Strategy Science · doi:10.1287/stsc.2021.0151 · Cited by 17
Danzman, S. B., & Slaski, A. (2021) · The Review of International Organizations · doi:10.1007/s11558-021-09418-0 · Cited by 19
“…1, p value = 0.89 11 χ2 = 0.94, df = 1, p value = 0.33 12 The online appendix is available at the Review of International Organization’s website. literature (King and Zeng 2001), so we confirm in supplementary materials that our results are generally robust to probit and rare events logit (A3-A4).”
ResultInfluentialQuinting, J., & Grams, C. (2021) · Journal of the Atmospheric Sciences · doi:10.1175/jas-d-20-0139.1 · Cited by 17
Testing the Role of Emotion Dysregulation as a Predictor of Juvenile Recidivism
Salinas, K. Z., & Venta, A. C. (2021) · European Journal of Investigation in Health Psychology and Education · doi:10.3390/ejihpe11010007 · Cited by 27
Schmutzler, J., Andonova, V., & Perez-Lopez, J. A. (2021) · International Entrepreneurship and Management Journal · doi:10.1007/s11365-020-00708-4 · Cited by 34
What influences windpower decisions? A statistical analysis of licensing in Norway
Inderberg, T., Theisen, O. M., & Flåm, K. (2020) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2020.122860 · Cited by 17
Correlates of death among SARS-CoV-2 positive veterans: The contribution of lifetime tobacco use
Raines, A. M., Tock, J. L., McGrew, S. J., Ennis, C. R., Derania, J., Jardak, C. L., Lim, J. H., Boffa, J. W., Houtsma, C., Jones, K. R., et al. (2020) · Addictive Behaviours · doi:10.1016/j.addbeh.2020.106692 · Cited by 17
The Dynamics of Repression and Insurgent Practice in the Black Liberation Struggle
Bloom, J. (2020) · American Journal of Sociology · doi:10.1086/711672 · Cited by 22
Is it all about you or your driving? Designing IoT‐enabled risk assessments
Ho, Y., Liu, S., Pu, J., & Zhang, D. (2022) · Production and Operations Management · doi:10.1111/poms.13816 · Cited by 18
“Following the literature on machine learning, we specifically consider four advanced, representative classifiers as the benchmark methods, namely, class-weighted LR (King & Zeng, 2001), nested SVM (Lee & Scott, 2010), cost-sensitive RFs (Devi et al., 2019), and artificial NN (Kim et al., 2005).”
MethodBalanced Symmetric Cross Entropy for Large Scale Imbalanced and Noisy DataPreprint
Huang, F., Li, J., & Zhu, X. (2020) · arXiv.org · doi:10.48550/arxiv.2007.01618 · Cited by 17
Hussain, Z. U., Shah, S. A., Mukherjee, M., & Sheikh, A. (2020) · BMJ Open · doi:10.1136/bmjopen-2019-036099 · Cited by 17
The Early Warning System and policymaking in the European Union
van Gruisen, P., & Huysmans, M. (2020) · European Union Politics · doi:10.1177/1465116520923752 · Cited by 17
Performance of Latent Growth Curve Models with Binary Variables
Newsom, J. T., & Smith, N. A. (2020) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2019.1705825 · Cited by 20
Were, L., Were, E., Wamai, R., Hogan, J., & Galárraga, O. (2020) · BMC Public Health · doi:10.1186/s12889-020-8186-y · Cited by 17
DeMattee, A. J. (2019) · VOLUNTAS International Journal of Voluntary and Nonprofit Organizations · doi:10.1007/s11266-019-00151-2 · Cited by 20
Nier, E., Popa, R., Shamloo, M., & Voinea, L. (2019) · IMF Working Papers · doi:10.5089/9781513509099.001 · Cited by 17
“In reporting our results, we correct for the tendency of logistic regression to underestimate the probability of rare events (King and Zeng (2001)).”
MethodPerformance of asymmetric links and correction methods for imbalanced data in binary regression
Huayanay, A. D. L. C., Bazán, J., Cancho, V. G., & Dey, D. (2019) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2019.1593984 · Cited by 17
“In the application (Section 4) for white wine quality data, the majority of the proposed binary regression models with power link and reverse power link functions obtained better fits than the binary regression models using common link functions and correction methods for rare events as proposed by King and Zeng [5] a…”
BackgroundMethodInfluentialVesco, K. K., Beadle, K., Stoneburner, A. B., Bulkley, J. E., Leo, M., & Clark, A. L. (2019) · Menopause · doi:10.1097/gme.0000000000001198 · Cited by 17
Heads or Tails? Network Effects on Game Purchase Behavior in The Long Tail Market
Kanat, I., Raghu, T. S., & Vinze, A. S. (2018) · Information Systems Frontiers · doi:10.1007/s10796-018-9888-x · Cited by 17
Commodity Price Movements and Banking Crises
Eberhardt, M., & Presbitero, A. (2018) · Social Science Research Network · doi:10.5089/9781484366776.001 · Cited by 17
The Domestic Politics of Preferential Trade Agreements in Hard Times
Mansfield, E. D., & Milner, H. (2017) · World Trade Review · doi:10.1017/s1474745617000428 · Cited by 17
“Second, our results are virtually unchanged when we estimate the model using a rare events logit specification, which accounts for the fact that the establishment of a PTA is an uncommon occurrence (King and Zeng, 2001).”
ResultIf a Global Catastrophic Biological Risk Materializes, at What Stage Will We Recognize It?
Lipsitch, M. (2017) · Health Security · doi:10.1089/hs.2017.0037 · Cited by 17
Arianpoo, N., Aydin, I., & Leung, V. C. M. (2017) · IEEE Transactions on Mobile Computing · doi:10.1109/tmc.2016.2585106 · Cited by 17
“of the system, Naive Bayes classifier is substituted by logistic regression [18].”
BackgroundMethodInfluential
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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