Logistic Regression in Rare Events Data

“King and Zeng (2001a) posit that, for logit models with unknown sampling probability, as in our set-up, the constant term is biased but the parameter estimates remain largely unbiased.”

“We find that an estimator that uses the profit-based loss function has the same statistical properties as the weighted estimator for endogenously stratified samples (Cosslett 1993, Donkers, et al. 2003, King and Zeng 2001a, 2001b, Manski and Lerman 1977).”

“…adopt sampling and analytic methods that provide sufficient statistical power to detect career orientation–mobility behavior relations, such as contrast group sampling, logistic regression, or event history/survival analysis (G. King & Zeng, 2001; Tutz & Schmid, 2016; Woo, Chae, Jebb, & Kim, 2016).”

“The data we use on this work belong to rare events data, binary dependent variables with dozens to thousands of times fewer ones (events, cases of fraudulent use, or epidemiological infections) than zeros ( ‘ nonevents ’ ) King and Zeng (2001).”

“Fourth, we use STATA to conduct rare event analysis (King & Zeng, 2001) and penalized maximum likelihood estimation (Firth, 1993) to provide a bias-corrected and more robust analysis for the turnover of enthusiastic group (p 3.8”

“%) is much higher than the proportion of ties in the population (less than 0.005%), logistic regressions may be biased (KING and ZENG, 2001; SORENSON et al., 2006).”

“Various solutions have been proposed for reducing this bias, including the use of rare-events logistic regression (RE-), a profile-likelihood method proposed by King and Zeng (2001). In this paper, we compare results from RE- and standard- logistic regression to determine if and when these small sample corrections mat…”

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

“For this reason, rare event logistic models may be more appropriate to estimate models based on a case–control design (King and Zeng 2001; Sorenson et al. 2006).10 The strategy is to select all the “cases” for which the event is realized (pi j = 1, we observe a realized tie in the population as…”

“Since bankruptcy is a rare event (1.3%, 1412 cases in the sample of 109,454 answering the question), it is necessary to use a rare events adjusted version of logistic regression (King & Zeng, 2001).”

“…only a small percentage of the total number of observations were positive observations), this procedure relieves much of the spatial bias, and because only negative observations were filtered out of the dataset, class imbalance is also addressed here (King and Zeng 2001, Robinson et al. 2017).”

“Relationships depicted in Table 1 (first row) were backtransformed to regression coefficients while a rare events correction of the intercept (King and Zeng, 2001) was conducted to consider the low portion of landslide presences in the area (∼ 0.002 % of the cells were envisaged to represent…”

“Typically, the bias in logistic regressions with skewed data concerns underestimations of the effects (King & Zeng, 2001).”

“Logistic regression [33] Logistic regression models the probability of a binary outcome by fitting a linear function to the input features and applying a logistic (sigmoid) function to obtain the predicted class probabilities. depict this linkage in the following Table 2.”

“Likewise, five of our activity regressions exhibited at least one level of the dependent variable as sufficiently small enough to be considered a rare event [85].”

“It has been extensively employed in many areas of engineering and applied sciences, such as in the medical [3, 32] and social sciences [14].”

“Firth models account for such disproportionate distributions in a binary dependent variable (Firth 1993; King and Zeng 2001).”

“Conventional learning methods will run into a problem with such kind of unbalanced data [2].”

“Consistent with King and Zeng (2001) and Hansen and Løvås (2004), for each multipartner alliance formed in each year t, it was matched with two D ow nl oa de d fr om in fo rm s. or g by [ 35 .9 .1 94 .1 34 ] on 1 8 Se pt em be r 20 14 , a t 1 2: 42 .”

“Yet, according to King and Zeng (2001a, 2001b), the rare events issue makes the results less significant than they really are; thus producing conversative results.”

“The results should be interpreted with caution, however, as logistic regression has well-known problems in modeling rare events [50].”

“Logistic regression is known to underestimate the probability of such rare events when applied to small samples (King and Zeng 2001).”

“The relogit command in STATA was used because it can provide approximately unbiased and lower-variance estimates of logit coe ffi cients for small samples and rare events (King & Zeng, 2001).”

“However, this small number of resignations may be problematic because King and Zeng (2001) show that coefficient estimates”

“This model is comprised of multiple input nodes, a neural network with hidden layers, and an output layer.”

“Our preferred specification is based on the linear probability model because it has been shown that the parameter estimates of nonlinear models might not be consistent when there are too many “0” in the dependent variable (King and Zeng, 2001), which is the case in this article.”

“Stata: Release 14.”

“We calculate the weight for each document category by N Nl (King and Zeng, 2001), where N is the number of documents in each language and Nl is the number of documents labeled by the category.”

“Logistic regression models for rare events were also fit for testing association between immune response and clinical response as sensitivity analysis (29).”

“Using this static data set, we applied King’s rare events logit model (King and Zeng 2001) to analyze the impact of demographic similarity with workgroup seniors and peers on a junior attorney’s chance of promotion.”

“Because the pooled model is less susceptible to small sample bias it can reveal effects that might otherwise be underestimated if the model is presented separately for each country in the sample (cf. King and Zeng, 2001).”

“This leads to the following regression model, where all regression co-ef fi cients are bias-corrected for rare events as described in King and Zeng (2001): where m is a k (cid”

“The log transformation of the probability p is called the logit of p or logit (p) (King and Zeng, 2001).”

“This means that classes with fewer samples receive higher weights, making them more influential in the learning process 72 .”

“With only one pandemic every few decades, the data set for testing the prediction of such rare events is inadequate, a problem that challenges predictions in many fields beyond infectious diseases (King and Zeng, 2001; Hansson, 2006).”

“5% of the total, we check for the robustness of the estimates of logistic regression by also estimating the models using rare events logistic regression (King and Zeng (2000), King and Zeng (2001)).”

“Note that researchers should not apply our rules of thumb to rare events data (King and Zeng, 2001), because the recommendations are overly conservative in that scenario.”

“, β̂n by correcting the intercept β̂0 as indicated in [34] :”

“[14] Researchers in these fields benefit from Firth’s method’s ability to produce reliable estimates, even when working with sparse data.”

“Because not eating for a whole day is a rare situation, we risk bias in using the standard logistic regression model [33].”

“This test helped us to determine whether the HLM method we employed produced inaccurate estimates due to the low probability of starting a business in our sample (King & Zeng, 2001).”

“We use the default method provided in h2o, described in [31], which creates a balanced class distribution.”

“Using (linear) logistic regression or similar will give biased probability estimates (King and Zeng 2001).”

“Therefore, we consider the logistic regression classifier suitable for rate factor aggregation if the intercept is either omitted from the model or appropriate corrections [35] are applied by actuaries.”

“This result confirms what other researchers suggested that the numbers of positive and negative samples should be kept equal to ensure optimal regression (Breslow and Cain 1988; Schill et al. 1993; King and Zeng 2001).”

“As the values of these probability estimates scale with the ratio between the numbers of landslide (L) and no-landslide (NL) pixels used in the model calibration (King and Zeng, 2001), we stress that Broeckx et al. (2018) applied a ~4:1 L/NL ratio.”

“Second, commonly used data collection strategies are inefficient for rare event data [42].”

“…compared to the total number of observations (0.12 %), it is high enough in absolute value – we have a total of 2,597 link formation events in our sample – thus making our results statistically significant (see King and Zeng, 2001; Nesta et al., 2010, for a more detailed discussion on the topic).”

“When the modeled event probability is small, traditional logit regressions produce biased coefficients estimates (King and Zeng 1999, 2001; Tomz et al. 1999).”

“%) reflected an extreme condition that reflected high (or conversely low) prevalence rates which standard logistic regression may not be optimal to use (King & Zeng, 2001).”

“Here, we focus on measures of HRO (1) shaming and (2) local presence to reflect these two concepts, respectively (Murdie and Bhasin 2011; Murdie and Davis 2012). First, to capture HRO shaming, following Ron et al. (2005) and Hafner-Burton (2008), we use the natural log of the count of all Amnesty International press r…”

“In datasets such as ours, where non-events make up the greater part of the data, there is a danger that the effects of independent variables on the occurrence of an event may be seriously underestimated (King and Zeng, 2001).”

“Such a percentage indicates that the sample is well balanced in terms of default and nondefault populations, thereby suggesting that our analysis should not be biased (King and Zeng 2001).”

“This approach provided for an unbiased estimation of the coefficients by accounting for the rate at which the collaborative and conflictual ties would form in the population as opposed to the matched sample (King & Zeng, 2001).”

“To account for the rare events nature of syndication data, we used the rare events corrections implemented by King and Zeng (1999a, 2001) as the relogit command in STATA.”