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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Using King and Zeng's rare-events logit estimator, the two modernization variables remain individually significant and jointly significant when entered together.
“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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BackgroundInfluentialThe Persistent Effect of Geographic Distance in Acquisition Target Selection
Chakrabarti, A., & Mitchell, W. (2013) · Organ. Sci. · doi:10.1287/orsc.1120.0811 · Cited by 195 · see citing works
Hoban, P. R., & Bucklin, R. E. (2015) · Journal of Marketing Research · doi:10.1509/jmr.13.0277 · Cited by 193 · see citing works
“Fortunately, the risk of bias declines dramatically as the number of observed events increases, and it virtually disappears when the number of observed rare events exceeds 6,000, the upper bound published by King and Zeng (2001).”
BackgroundLog-likelihood-based Pseudo-R2 in Logistic Regression
Hemmert, G. A. J., Schons, L., Wieseke, J., & Schimmelpfennig, H. (2018) · Sociological Methods & Research · doi:10.1177/0049124116638107 · Cited by 192 · see citing works
Gassebner, M., Lamla, M. J., & Vreeland, J. R. (2013) · Journal of Conflict Resolution · doi:10.1177/0022002712446132 · Cited by 190 · see citing works
“As shown by King and Zeng (2001), using standard logit regressions in such a setting might lead to an estimation bias.”
Interpretable machine learning for imbalanced credit scoring datasets
Chen, Y., Calabrese, R., & Martin-Barragan, B. (2024) · European Journal of Operational Research · doi:10.1016/j.ejor.2023.06.036 · Cited by 190 · see citing works
Insights Into LSTM Fully Convolutional Networks for Time Series Classification
Karim, F., Majumdar, S., & Darabi, H. (2019) · IEEE Access · doi:10.1109/access.2019.2916828 · Cited by 190 · see citing works
“Class imbalance is handled via a class weighing scheme inspired by King and Zeng [24].”
MethodAssociation of Neighborhood-Level Disadvantage With Alzheimer Disease Neuropathology
Powell, W. R., Buckingham, W. R., Larson, J. L., Vilen, L. H., Yu, M., Salamat, M. S., Bendlin, B. B., Rissman, R. A., & Kind, A. (2020) · JAMA Network Open · doi:10.1001/jamanetworkopen.2020.7559 · Cited by 211 · see citing works
How remote are R&D labs? Distance factors and international innovative activities
Castellani, D., Jiménez, A., & Zanfei, A. (2013) · Journal of International Business Studies · doi:10.1057/jibs.2013.30 · Cited by 167 · see citing works
A-MobileNet: An approach of facial expression recognition
Nan, Y., Ju, J., Hua, Q., Zhang, H., & Wang, B. (2021) · Alexandria Engineering Journal · doi:10.1016/j.aej.2021.09.066 · Cited by 239 · see citing works
Bad Religion? Religion, Collective Action, and the Onset of Armed Conflict in Developing Countries
Basedau, M., Pfeiffer, B., & Vüllers, J. (2016) · Journal of Conflict Resolution · doi:10.1177/0022002714541853 · Cited by 184 · see citing works
Carranza, E. J. M., & Laborte, A. G. (2015) · Natural Resources Research · doi:10.1007/s11053-015-9268-x · Cited by 195 · see citing works
Choice Models and Customer Relationship Management
Kamakura, W., Mela, C. F., Ansari, A., Bodapati, A., Fader, P., Iyengar, R., Naik, P., Neslin, S., Sun, B., Verhoef, P. C., et al. (2005) · Marketing Letters · doi:10.1007/s11002-005-5892-2 · Cited by 178 · see citing works
Workers of the world, unite! Franchise extensions and the threat of revolution in Europe, 1820–1938
Aidt, T. S., & Jensen, P. S. (2014) · European Economic Review · doi:10.1016/j.euroecorev.2014.08.001 · Cited by 191 · see citing works
“In column five, we adopt the rare events logit estimator by King and Zeng (2001) and in column seven we include fixed effects directly in the logic model.”
MethodPapadopoulou-Vrynioti, K., Bathrellos, G. D., Skilodimou, H., Kaviris, G., & Makropoulos, K. (2013) · Engineering Geology · doi:10.1016/j.enggeo.2013.02.009 · Cited by 176 · see citing works
A data-based landslide susceptibility map of Africa
Broeckx, J., Vanmaercke, M., Duchateau, R., & Poesen, J. (2018) · Earth-Science Reviews · doi:10.1016/j.earscirev.2018.05.002 · Cited by 175 · see citing works
Ost, D., Ernst, A., Grosu, H., Lei, X., Diaz-Mendoza, J., Slade, M., Gildea, T., Machuzak, M., Jiménez, C., Toth, J., et al. (2015) · Chest · doi:10.1378/chest.14-1530 · Cited by 171
Heckmann, T., Gegg, K., Gegg, A., & Becht, M. (2014) · Natural hazards and earth system sciences · doi:10.5194/nhess-14-259-2014 · Cited by 169 · see citing works
Exploring the features of agritourism and its contribution to rural development in Italy
Lupi, C., Giaccio, V., Mastronardi, L., Giannelli, A., & Scardera, A. (2017) · doi:10.1016/j.landusepol.2017.03.002 · Cited by 167
Global Supply Chains and Trade Policy
Blanchard, E. J., Bown, C., & Johnson, R. C. (2016) · World Bank, Washington, DC eBooks · doi:10.1596/1813-9450-7536 · Cited by 167 · see citing works
Paying It Forward vs. Rewarding Reputation: Mechanisms of Generalized Reciprocity
Baker, W., & Bulkley, N. (2014) · Organ. Sci. · doi:10.1287/orsc.2014.0920 · Cited by 167 · see citing works
“Fit statistics are not reported because maximum likelihood or a pseudo-R 2 are not meaningful for rare-events models (King and Zeng 2001, Tomz et al. 2003 ).”
InfluentialRobustness Tests for Quantitative Research
Neumayer, E., & Plümper, T. (2017) · Cambridge University Press eBooks · doi:10.1017/9781108233590 · Cited by 166 · see citing works
Timoneda, J. C. (2021) · Social Science Research · doi:10.1016/j.ssresearch.2020.102486 · Cited by 161 · see citing works
Host-genotype dependent gut microbiota drives zooplankton tolerance to toxic cyanobacteria
Macke, E., Callens, M., Meester, L. D., & Decaestecker, E. (2017) · Nature Communications · doi:10.1038/s41467-017-01714-x · Cited by 169 · see citing works
Why Do Countries Adopt Constitutional Review
Ginsburg, T., & Versteeg, M. (2014) · The Journal of Law Economics and Organization · doi:10.1093/jleo/ewt008 · Cited by 159 · see citing works
“King and Zeng (2001) show that, in cases like ours when onsets are rare, standard maximum likelihood procedures may substantially underestimate the probability of an event occurring.”
Landslide susceptibility mapping of the Sera River Basin using logistic regression model
Raja, N., Çiçek, I., Türkoğlu, N., Aydın, O., & Kawasaki, A. (2017) · Natural Hazards · doi:10.1007/s11069-016-2591-7 · Cited by 158 · see citing works
“The sample selection of this study followed the reasoning of King and Zeng (2001): all the landslides events and a random sample of non-events around the current landslide active area were chosen.”
BackgroundMethodBrown, R. P. C., Carmignani, F., & Fayad, G. (2013) · doi:10.1111/twec.12016 · Cited by 156
“15 Corrections are available to estimate models where the binary dependent variable has dozens to thousands of times fewer ones; see for instance King and Zeng (2001). These corrections increase the efficiency of estimates, without altering the sign of the estimated coefficient.”
BackgroundShipilov, A. V., & Li, S. X. (2012) · Organization Science · doi:10.1287/orsc.1100.0568 · Cited by 152 · see citing works
Hydra: An Ensemble of Convolutional Neural Networks for Geospatial Land Classification
Minetto, R., Segundo, M. P., & Sarkar, S. (2018) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2019.2906883 · Cited by 150 · see citing works
“Class weighting methods were: no weighting, FMOW weights (Figure 3) and frequency-based weighting using the balanced heuristic [18] before (Frequency #2) and after (Frequency #1) a manual adjustment. heads, which have slightly different accuracy in the end of the training process.”
MethodManagerss Political Ideology and Gender Inequality within Organizations
Carnahan, S., & Greenwood, B. N. (2016) · Administrative Science Quarterly · doi:10.1177/0001839217708780 · Cited by 170 · see citing works
Should we trust the Z-score? Evidence from the European Banking Industry
Chiaramonte, L., Croci, E., & Poli, F. (2015) · doi:10.1016/j.gfj.2015.02.002 · Cited by 146
Trading and Enforcing Patent Rights
Galasso, A., Schankerman, M. A., & Serrano, C. J. (2011) · The RAND Journal of Economics · doi:10.1111/1756-2171.12020 · Cited by 149 · see citing works
Karra, M., Fink, G., & Canning, D. (2016) · International Journal of Epidemiology · doi:10.1093/ije/dyw062 · Cited by 132 · see citing works
“Furthermore, a low absolute number of deaths in small samples can also give rise to a downward bias in estimates of the true effect size.(16) In this study, we utilize health facility access data that were collected as part of the Service Availability Module in 29 DHS surveys from 21 low- and middle-income countries,…”
MethodGregory, S., Anthopolos, R., Osgood, C., Grotegut, C. A., & Miranda, M. (2013) · JAMA pediatrics · doi:10.1001/jamapediatrics.2013.2904 · Cited by 142 · see citing works
Tuschke, A. C., Sanders, W. G., & Hernández, E. (2013) · Strategic Management Journal · doi:10.1002/smj.2100 · Cited by 132 · see citing works
“We also assessed the robustness of our results to alternative event history estimation procedures including the rare event procedure suggested by King and Zeng (2001), the Cox (1972) proportional hazard model, and piecewise exponential regression (Lee, 2007).”
State capitalism's global reach: Evidence from foreign acquisitions by state-owned companies
Karolyi, G., & Liao, R. (2017) · doi:10.1016/j.jcorpfin.2016.02.007 · Cited by 136
Proximity effects on the dynamics and outcomes of scientific collaborations
Kabo, F. W., Cotton-Nessler, N. C., Hwang, Y., Levenstein, M. C., & owen-Smith, J. (2014) · Research Policy · doi:10.1016/j.respol.2014.04.007 · Cited by 136 · see citing works
- 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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