Cited by 4,316Statistical Methods and Bayesian InferenceStatistical Methods in EpidemiologySurvey Sampling and Estimation Techniques

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Logistic Regression in Rare Events Data

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King, Gary, Zeng, Langche·2001·Political Analysis

DOI 10.1093/oxfordjournals.pan.a004868

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Abstract

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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“…a certain dyad in a certain year, only one observation is randomly selected when there are more than one observation, reducing the same size from 119,408 to 119,400. check, we also employed the rare events logit models suggested by King and Zeng (2001) and obtained qualitatively similar results.”
A systematic review of studies probing longitudinal associations between anxiety and anorexia nervosa
Lloyd, E. C., Haase, A. M., Foster, C. E., & Verplanken, B. (2019) · Psychiatry Research · doi:10.1016/j.psychres.2019.05.010 · Cited by 49
Policy Narratives and Policy Outcomes: An NPF Examination of Oregon's Ballot Measure 97
McMorris, C., Zanocco, C., & Jones, M. A. (2018) · Policy Studies Journal · doi:10.1111/psj.12263 · Cited by 35
“Consequently, we conduct an alternative estimation method intended to reduce this potential bias (King & Zeng, 2001), utilizing the Firth method, a penalized likelihood approach that reduces small-sample bias in maximum likelihood estimation and is recommended for applications where observed event…”
Detection of phishing websites using a novel twofold ensemble model
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Birth Outcomes of Women Using a Midwife versus Women Using a Physician for Prenatal Care
Weisband, Y. L., Klebanoff, M., Gallo, M., Shoben, A., & Norris, A. (2018) · Journal of midwifery & women's health · doi:10.1111/jmwh.12750 · Cited by 35
Spatial pattern and influencing factors of landslide casualty events
Wang, Y., Lin, Q., & Shi, P. (2018) · Journal of Geographical Science · doi:10.1007/s11442-018-1471-3 · Cited by 35
“According to King and Zeng (2001), too few 1 samples “grossly undervalued” the probability of prediction, and they suggested keeping the rate of 0 samples to 1 samples between 0.2 and 1.”
BackgroundInfluential
How individual characteristics shape the structure of social networks
Girard, Y., Hett, F., & Schunk, D. (2014) · Journal of Economic Behavior & Organization · doi:10.1016/j.jebo.2014.12.005 · Cited by 36
“Overall, the general model looks as 13In addition, we use a rare event logistic regression model developed by King and Zeng (2001).”
Method
Environmental standards as a strategy of international technology transfer
Saikawa, E., & Urpelainen, J. (2014) · doi:10.1016/j.envsci.2013.11.010 · Cited by 35
O poder no Executivo: uma análise do papel da Presidência e dos Ministérios no presidencialismo de coalizão brasileiro (1995-2010)
Batista, M. (2013) · doi:10.1590/s0104-62762013000200009 · Cited by 35
Exploring detection of contact vs. fantasy online sexual offenders in chats with minors: Statistical discourse analysis of self-disclosure and emotion words
Chiu, M. M., Seigfried-Spellar, K. C., & Ringenberg, T. R. (2018) · Child Abuse & Neglect · doi:10.1016/j.chiabu.2018.04.004 · Cited by 35
MoralBERT: A Fine-Tuned Language Model for Capturing Moral Values in Social Discussions
Preniqi, V., Ghinassi, I., Ive, J., Saitis, C., & Kalimeri, K. (2024) · International Conference on Information Technology for Social Good (GoodIT) · doi:10.1145/3677525.3678694 · Cited by 26
“We do so by employing the approach of King and Zeng [44] so that for each class 𝑐 we compute 𝑤𝑒𝑖𝑔ℎ𝑡 𝑐 = 𝑁 / 𝑁 with 𝑁 being the total number of samples in the training data and 𝑁 𝑐 the total number of samples in the training data belonging to class 𝑐 .”
Multimodal metadata assignment for cultural heritage artifacts
Rei, L., Mladenić, D., Dorozynski, M., Rottensteiner, F., Schleider, T., Raphaël Troncy, A., Lozano, J. S., & Gaitán, M. (2022) · Multimedia Systems · doi:10.1007/s00530-022-01025-2 · Cited by 34
“That is, given a text description of a fabric, written in any language, we want to assign exactly one label out of a set of mutually exclusive class labels for each of the properties we wish to predict, i.e., the tasks.”
Background
An Introduction to Multilevel Regression and Post-Stratification for Estimating Constituency Opinion
Hanretty, C. (2020) · Political Studies Review · doi:10.1177/1478929919864773 · Cited by 34
“, submitted), or from general difficulties in explaining rare events with logistic regression models (King and Zeng, 2001).”
Background
A Comparative Analysis of Machine Learning classifiers for Dysphonia-based classification of Parkinson’s Disease
Goyal, J., Khandnor, P., & Aseri, T. (2020) · International Journal of Data Science and Analysis · doi:10.1007/s41060-020-00234-0 · Cited by 34
“It takes value 1 with probability p and value 0 with probability 1 − p [27], where p is given in Eq.”
Background
Association between exposure to the Chinese famine during early life and the risk of chronic kidney disease in adulthood
Lv, S., Shen, Z., Zhang, H., Yu, X., Chen, J., Gu, Y., Ding, X., & Zhang, X. (2020) · Environmental Research · doi:10.1016/j.envres.2020.109312 · Cited by 44
Vanguards of globalization: Organization and political action among America's pro-trade firms
Osgood, I. (2019) · Business and Politics · doi:10.1017/bap.2019.31 · Cited by 34
“45 This strategy of reweighting to eliminate sample selection bias is discussed in King and Zeng (2001).”
Background
Determinants of timeliness in early childhood vaccination among mothers with vaccination cards in Sindh province, Pakistan: a secondary analysis of cross-sectional survey data
Noh, J., Kim, Y.-M., Akram, N., Yoo, K.-B., Cheon, J., Lee, L., Kwon, Y., & Stekelenburg, J. (2019) · BMJ Open · doi:10.1136/bmjopen-2019-028922 · Cited by 34
“Because the number of events were low, logistic regression using Firth's penalised likelihood was conducted in this study.(23) The criterion for significance was p≤0.”
Method
The local geography of transnational terrorism
Marineau, J., Pascoe, H., Braithwaite, A., Findley, M. G., & Young, J. K. (2018) · Conflict Management and Peace Science · doi:10.1177/0738894218789356 · Cited by 34
“We then employ Rare Events Logit (King and Zeng, 2001a, b) and negative binomial models to assess patterns in this form.”
Method
Freedom and Convict Leasing in the Postbellum South
Muller, C. D. (2018) · American Journal of Sociology · doi:10.1086/698481 · Cited by 82
Discretion and Diversion in Albany’s Lead Program
Worden, R., & McLean, S. J. (2018) · Criminal Justice Policy Review · doi:10.1177/0887403417723960 · Cited by 34
“Also see King and Zeng (2001).”
Logistic regression in large rare events and imbalanced data: A performance comparison of prior correction and weighting methods
Maalouf, M., Homouz, D., & Trafali̇s, T. B. (2017) · Computational Intelligence · doi:10.1111/coin.12123 · Cited by 38
“…odd in Equation 22 yields and the logarithm of the odds is which implies that As shown, prior correction is easy to use as it only corrects on 𝛽 0 , 11 , 33 ̃𝛽 0 = ̂𝛽 0 − ln and the modified logit probability is However, according to King and Zeng, 11 the above probability in Equation 27 is…”
BackgroundMethodResultInfluential
Start-up Nation? Slave Wealth and Entrepreneurship in Civil War Maryland
González, F., Marshall, G., & Naidu, S. (2017) · Journal Economic History · doi:10.1017/s0022050717000493 · Cited by 34
Are British Muslims alienated from mainstream politics by Islamophobia and British foreign policy?
Martin, N. S. (2017) · doi:10.1177/1468796816656674 · Cited by 34
“This is a potential source of bias when using maximum likelihood estimation: because far more information is available about failures, the estimate of the successes will be biased downwards (King and Zeng, 2001).”
Method
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Bone, S. A., Lemon, K. N., Voorhees, C. M., Liljenquist, K. A., Fombelle, P. W., DeTienne, K., & Money, R. (2017) · Journal of Marketing Research · doi:10.1509/jmr.14.0232 · Cited by 34
“However, given that our binary event of interest (purchase) was relatively rare and occurred for only 12.9% of the sample, we adopted rare events logistic regression, which Sridhar, Voorhees, and Gopalakrishna (2015) advocate and which was originally introduced by King and Zeng (2001).”
MethodInfluential
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“To conduct the concordance analysis, we adjusted the intercept of the model using correction procedure for rare events data (King & Zeng, 2001).”
Method
Trade policy uncertainty and the WTO
Groppo, V., & Piermartini, R. (2014) · doi:10.2139/ssrn.2553131 · Cited by 34
“We also used the logistic model for rare events (STATA command relogit, which implements the procedure suggested by King and Zeng, 2001).”
Socio-economic Background and Early Post-compulsory Education Pathways: A Comparison between Natives and Second-generation Immigrants in Switzerland
Laganà, F., Chevillard, J., & Gauthier, J. (2013) · European Sociological Review · doi:10.1093/esr/jct019 · Cited by 38
Sound Body, Sound Mind? Asymmetric and Symmetric Fetal Growth Restriction and Human Capital DevelopmentPreprint
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Pu, J.-C., Liu, Y., Chen, Y., Qiu, L.-F., & Cheng, H. (2021) · Information systems research · doi:10.1287/isre.2021.1052 · Cited by 33
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“This unbalanced variable might lead to an unstable regression model, insignificant coefficients, and skewed predicted probabilities [32].”
Background
An international investigation on assurance of integrated reports: Institutions, assurance quality, and assurers
Kılıç, M., Kuzey, C., & Uyar, A. (2021) · doi:10.1016/j.intaccaudtax.2020.100360 · Cited by 33

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
DOI: 10.1093/oxfordjournals.pan.a004868
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
Licence: www.cambridge.org/core/terms (unspecified, 5847 d)
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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Logistic Regression in Rare Events Data

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