Recalibration of Predicted Probabilities Using the “Logit Shift”: Why Does It Work, and When Can It Be Expected to Work Well?
Recalibration of Predicted Probabilities Using the “Logit Shift”: Why Does It Work, and When Can It Be Expected to Work Well?
复制标题
使用“Logit Shift”重新校准预测概率：为什么它有效，什么时候可以有效？
作者：
Evan T. R. Rosenman;Cory McCartan;Santiago Olivella
摘要：预测模型的输出通常通过将低层次的预测与在更高聚合层次上定义的已知量进行协调来重新校准。例如，对美国选举中个体层面的投票概率进行预测的模型可以进行调整，使其聚合结果与每个县观察到的投票总数相匹配，从而产生校准更好的预测。在本研究报告中，我们为最常用的重新校准策略之一提供了理论基础，该策略通俗地称为“逻辑斯蒂变换”。通常它被视为一种启发式调整策略（即找到逻辑斯蒂尺度上的一个常数修正量，使得聚合预测与目标总数相匹配），我们表明逻辑斯蒂变换为一种有原则但计算上不实用的调整策略提供了一种快速且准确的近似：根据观察到的总数计算后验预测概率。在推导出近似质量的分析界限之后，我们使用蒙特卡罗模拟说明了其准确性。我们还讨论了逻辑斯蒂变换在重新校准预测时效果较差的情况：当目标总数仅针对高度异质的群体定义时，以及当原始预测正确地捕捉到真实个体概率的均值，但未能捕捉到其分布形状时。
Abstract The output of predictive models is routinely recalibrated by reconciling low-level predictions with known quantities defined at higher levels of aggregation. For example, models predicting vote probabilities at the individual level in U.S. elections can be adjusted so that their aggregation matches the observed vote totals in each county, thus producing better-calibrated predictions. In this research note, we provide theoretical grounding for one of the most commonly used recalibration strategies, known colloquially as the “logit shift.” Typically cast as a heuristic adjustment strategy (whereby a constant correction on the logit scale is found, such that aggregated predictions match target totals), we show that the logit shift offers a fast and accurate approximation to a principled, but computationally impractical adjustment strategy: computing the posterior prediction probabilities, conditional on the observed totals. After deriving analytical bounds on the quality of the approximation, we illustrate its accuracy using Monte Carlo simulations. We also discuss scenarios in which the logit shift is less effective at recalibrating predictions: when the target totals are defined only for highly heterogeneous populations, and when the original predictions correctly capture the mean of true individual probabilities, but fail to capture the shape of their distribution.
种族两极分化投票的地理分布：校准地区一级的调查
影响因子：
6.8
作者：
KURIWAKI, SHIRO;ANSOLABEHERE, STEPHEN;DAGONEL, ANGELO;YAMAUCHI, SOICHIRO
通讯作者：
YAMAUCHI, SOICHIRO