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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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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
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
“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
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
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
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
Paying It Forward vs. Rewarding Reputation: Mechanisms of Generalized Reciprocity
Baker, W. E., & Bulkley, N. (2014) · Organization Science · doi:10.1287/orsc.2014.0920 · Cited by 187
“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 198
Timoneda, J. C. (2021) · Social Science Research · doi:10.1016/j.ssresearch.2020.102486 · Cited by 161
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
Why Do Countries Adopt Constitutional Review?
Ginsburg, T., & Versteeg, M. (2013) · The Journal of Law Economics and Organization · doi:10.1093/jleo/ewt008 · Cited by 255
“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
“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
Hydra: An Ensemble of Convolutional Neural Networks for Geospatial Land Classification
Minetto, R., Segundo, M. P., & Sarkar, S. (2019) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2019.2906883 · Cited by 153
“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 174
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
Karra, M., Fink, G., & Canning, D. (2016) · International Journal of Epidemiology · doi:10.1093/ije/dyw062 · Cited by 132
“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
Tuschke, A. C., Sanders, W. G., & Hernández, E. (2013) · Strategic Management Journal · doi:10.1002/smj.2100 · Cited by 132
“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. A., & Liao, R. C. (2016) · Journal of Corporate Finance · doi:10.1016/j.jcorpfin.2016.02.007 · Cited by 142
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
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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