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ReLogit: Rare Events Logistic Regression

  • Micahael Tomz
  • Gary King
  • Langche Zeng

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 shar ply 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 repor ted 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 obser vations but relatively few, and poorly measured, explanator y 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 explanator y 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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Article provided by American Statistical Association in its journal Journal of Statistical Software.

Volume (Year): 08 ()
Issue (Month): i02 ()
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Handle: RePEc:jss:jstsof:08:i02
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  1. Imbens, G. & Lancaster, T., 1991. "Efficient Estimation and Stratified Sampling," Papers 9145, Tilburg - Center for Economic Research.
  2. Imbens, G.W., 1990. "An Efficient Method Of Moments Estimator For Descrete Choice Models With Choice-Based Sampling," Papers 9009, Tilburg - Center for Economic Research.
  3. King, Gary & Zeng, Langche, 2001. "Explaining Rare Events in International Relations," International Organization, Cambridge University Press, vol. 55(03), pages 693-715, June.
  4. Manski, Charles F & Lerman, Steven R, 1977. "The Estimation of Choice Probabilities from Choice Based Samples," Econometrica, Econometric Society, vol. 45(8), pages 1977-88, November.
  5. Amemiya, Takeshi & Vuong, Quang H, 1987. "A Comparison of Two Consistent Estimators in the Choice-based Sampling Qualitative Response Model," Econometrica, Econometric Society, vol. 55(3), pages 699-702, May.
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