Logistic Regression in Rare Events Data

“In our sample, the rare events problem occurs (King and Zeng 2001) when number and share of positive cases are small.”

“, Probit), are not well-suited to evaluating very rare events [King and Zeng, 2001].”

“01-4) 2 (1-5) Behavioral audiometry Symptomatic Yes 26 4 (1-12) 12 (1-18) 5 (1-22) No 23 4 (1-10) 13 (3-18) 5 (1-16) Asymptomatic Yes 9 5 (3-9) 17 (13-18) 8 (2-10) No 75 4 (1-17) 17 (3-18) 5 (1-13)”

“King and Zeng (2001) argue that the use of traditional binary choices models will underestimate the probability of rare events.”

“A rare event correction [36] was performed (with weights calculated using dataset 2) to allow for interpretable estimates of mortality for the different genotypes despite the case control sampling design.”

“wherewa is a balance weight of attribute a following [24], and note that multiple ya can be 1 for multi-label classification.”

“…models, we applied Firth adjustment, which uses a penalized likelihood estimation model for the multinomial logistic regression to avoid any potential separation issues resulting from the placement of the majority of observations in the undisclosed condition (Firth 1993; King and Zeng 2001).”

“around 8,000 students, a small sample bias due to rare event data is not problematic for this study (King and Zeng, 2001).”

“Rare Events Logistic Regression was proposed by King and Zeng (2001) as appropriate for situations in where a dichotomous dependent variable has relatively few 1s relative to 0s.”

“Logistic regression has been successfully applied in various real-life problems such as cancer detection Kim et al. (2008), medical Boyd et al. (1987); Bagley et al. (2001); Subasi & Erc¸elebi (2005), social science King & Zeng (2001), etc.”

“Second, its probability estimate is biased [5], [6].”

“The high OR and wide confidence interval were most likely due to the small sample size in each cell (85% reported they had regular doctors or places, 17 and 15% reported they did not have regular doctors or places; King & Zeng, 2001; Williams, 2016).”

“Logistic regression in rare events data can be biased, 30,31 and the expected MAE alerts in this study seemed to be very rare.”

“According to King and Zeng [25], applying predictive models (e.g. regression) in rare events datasets (in our case 10%), can benefit from case selection strategies that reduce the number of negative events (in our cases methods that are not in need for refactoring).”

“Penalized logistic regression, using R, was used for sexual and nonsexual violent reoffending as base rates were modest for these outcomes (i.e., 7.4% and 12.9%, respectively; see King & Zeng, 2001).”

“As rare events may bias the logistic regression results, especially when adjusting for multiple confounders, our study utilized Firth’s method of penalized likelihood.(35,36) Finally, as our study is the first population-based study and some of the results may be hypothesisgenerating, further clinical and epidemiologi…”

“Third, we ran our data using several alternate techniques, rare event logistic regression (King and Zeng, 2001), binary logistic regression and”

“Logistic regression (King & Zeng, 2001) is a model used to predict our binary target variable (dropout or non-dropout) from several independent attributes.”

“Although the protest state of the dependent variable is relatively rare (approximately 1 percent of all player–week observations), its absolute frequency (405 observations) is above the threshold for concerns regarding smallsample bias in conventional logistical regression (King and Zeng, 2001; Allison, 2012).”

“We apply a weighted loss function [23] by estimating the inverse class distribution.”

“12) depending on the fact whether the user-item-interaction is observed (weight w1) or missing (weight w0) in Y , then the leading-order effect is that the trained model will predict a different mean (or intercept) for the item (see also [13] for logistic regression).”

“To solve these problemsmore efficiently, researchers and practitioners havemade efforts from various perspectives, such as data sampling [22], feature selection [25,29], costsensitive learning [2,20,24], ensemble learning [4], and kernel-based learning [8], with the considerations of concrete problem characteristics.”

“Considering the unbalanced populations of two classes, we weight the observations of two classes to perform the weighted maximum likelihood estimation as in [1], [25].”

“…the validity of physical violence at work as a predictor of health-related absence from the labor market, a rare event logistic regression model (King & Zeng, 2001) was used for the total follow-up period and for each follow-up year with healthrelated absence from the labor market as the…”

“King and Zeng (2001) describe how class imbalance affects the estimators of Logistic Regression and specifically how the constant term becomes biased and underestimated.”

“…k-ads is biased because the event k-ads tend to have small values of k, whereas a random sample of non-event k-ads would include a disproportionately large number of k-ads with large values of k.2 Therefore, we apply choice-based sampling to create a stratified sample (King and Zeng 2001).”

“‘Tied’ matches are more complex but the decision was made to exclude them as well as they only occur in around 1% of instances and would therefore need rare event techniques, e.g. (King & Zeng, 2001), and would never be predicted over a win or loss anyway.”

“Second, AudStand and ProMinR, as the subdimensions of Accountability, are subject to rare events logistic regression analysis (King and Zeng, 1999a) because the distribution of ExtAss indicates a relatively large difference between the categories of the ExtAss (Kılıç et al., 2020).”

“, the output logit of an ANN for a sample whose size is equal to the number of classes), and weight[c] is the class weight computed for each client independently considering a balanced heuristic inspired by [30].”

“King and Zeng (2001) argue that when collecting data describing rare events, it is not fruitful to collect large but highly unbalanced event data supported by limited predictor variables; rather, it is preferable to sample all available presences (events) and a small subset of absences alongside a…”

“First, as noted by King and Zeng (2001), the rarity of stent implantation (often less than 5% of the time in our sample) can lead to a biased estimation of the standard errors.”

“Besides the bias due to small samples, recent studies (King and Zeng, 2001) have argued that in rare events data the biases in probabilities can be meaningful even with big sample sizes and that these biases result in an underestimation of event probabilities.”

“Multiple imputation using Amelia (available in an Online Appendix) addresses this third problem of missing values on individual variables (King et al. 2001).”

“This is favored over logit models, particularly in scenarios in which the dependent variable contains an excess of zeros, as was the case in this study (King & Zeng, 2001).”

“Further, firthlogit is a technique that is suited to dealing with situations in which the event of interest is rare (cf., Rojas, 2017; Rojas & Stenberg, 2016), which is the case here in the sense that the proportion of deaths from suicide in the data is lower than 5% (King & Zeng, 2001).”

“We tackle this issue by using the idea from [37], during the prediction phase of the neural network.”

“We used the ‘relogit’ command in STATA, which generates approximately unbiased and lower-variance estimates of logit coefficients by correcting for small samples and rare events (King & Zeng, 2001; Zhou & Guillén, 2015).”

“For imbalanced data, such as the data used in this study, it is desirable to build classifiers with good performance on the minority class (23, 28, 29).”

“Here, we adopt one such method that is specifically designed to correct parameter estimates and significance values from logistic regressionmodels (King and Zeng 2001); these models are otherwise identical to the standard binomial generalized linear models (GLM) that normally are used to model host…”

“Participation is a rare, which could lead to bias and underestimation of participation probabilities (King & Zeng 2001).”

“As entrepreneurial activity is relatively uncommon in DUNs we also ran rare events logits to correct for any bias introduced into the results due to the standard logits under-estimating the rare outcome, engagement with entrepreneurial activity (King and Zeng, 2001a; 2001b).”

“Firthlogit is a technique that is suited to dealing with situations in which the event of interest is rare (cf. Rojas and Stenberg 2016), which is the case here in the sense that the proportion of deaths from any cause in the data is lower than 5% (cf. King and Zeng 2001).”

“Estimated program e ects using a rare event logit developed by King and Zeng (2001) are qualitatively similar, and the estimates are also not statistically signi cant.”

“In general, if one category contained none to few observations (e.g., zero larva-to-adult fly survival), we implemented a logistic regression with a penalized likelihood (Firth method) (King and Zeng 2001).”

“Given the high number of zeros, we used a rare event logit regression to control for any possible bias that might arise when analyzing rare events (King and Zeng 2001).”

“The class weights for each class are calculated by the method given by King et al. [38]: where W i is the weight of class i , N is the total number of EEG signals, k is the total number of classes, and N i is the number of EEG signal samples in class i .”

“The relation between and was also examined to further evaluate this method of estimating static values.”

“extremely unbalanced in favor of the “unattached” class (“attached” candidates make up roughly 13% of the development set), we also implement a class-balancing method inspired by (King and Zeng, 2001) which maps class indices to weight values used for weighting the loss function during training.”

“…logit estimator in discrete choice model is asymptotically unbiased, it has been shown that the finite sample bias tends to underestimate the probability of the rare event, and therefore might downward-bias our estimates of the positive effects of the interventions (King and Zeng 2001a,b).”

“All models presented in the tables below employ the subroutine relogit written for use in STATA [46].”

“Zero inflation can pose unique challenges for maximum likelihood regression estimation methods and underestimate the effects of our dependent variable (King and Zeng 2001: 138).”

“To reduce the bias and predict the selectivity for age-classes of fish with very few observations, we used the alternative penalized likelihood estimation method proposed by King and Zeng (2001). Integrated assessment methods are capable of estimating selectivity within models when the data are sufficient.”

“Suicide is a rare event, and the study of rare but significant events poses difficult problems for conventional parametric statistics.(34) Commonly used logistic regression methods can lead to an underestimation of event probabilities, and logit coefficients in models using rare binary outcomes are often inaccurate wh…”