2021
DOI: 10.1017/psrm.2021.9
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Estimating logit models with small samples

Abstract: In small samples, maximum likelihood (ML) estimates of logit model coefficients have substantial bias away from zero. As a solution, we remind political scientists of Firth's (1993, Biometrika, 80, 27–38) penalized maximum likelihood (PML) estimator. Prior research has described and used PML, especially in the context of separation, but its small sample properties remain under-appreciated. The PML estimator eliminates most of the bias and, perhaps more importantly, greatly reduces the variance of the usual ML … Show more

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Cited by 46 publications
(38 citation statements)
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References 38 publications
(61 reference statements)
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“…Frequency, percentages, and cross-tabulation were used to describe the sample. The prevalence of cervical cancer screening was approximately 4% in the female population, rendering the dataset imbalanced or sparse [27][28][29]. Reliance on the Maximum Likelihood Estimation (MLE) based logistic regression will produce coefficients that are biased and unreliable [27][28][29].…”
Section: Discussionmentioning
confidence: 99%
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“…Frequency, percentages, and cross-tabulation were used to describe the sample. The prevalence of cervical cancer screening was approximately 4% in the female population, rendering the dataset imbalanced or sparse [27][28][29]. Reliance on the Maximum Likelihood Estimation (MLE) based logistic regression will produce coefficients that are biased and unreliable [27][28][29].…”
Section: Discussionmentioning
confidence: 99%
“…The prevalence of cervical cancer screening was approximately 4% in the female population, rendering the dataset imbalanced or sparse [27][28][29]. Reliance on the Maximum Likelihood Estimation (MLE) based logistic regression will produce coefficients that are biased and unreliable [27][28][29]. In such situations, a data analyst has a choice among the exact logistic regression, penalized maximum likelihood estimation (PMLE), and the Firth logistic regression.…”
Section: Discussionmentioning
confidence: 99%
See 2 more Smart Citations
“…For logit models this is a relatively small sample size. Such relatively small sample sizes in the logit models could be problematic for producing unbiased estimates (Rainey and McCaskey, 2021). To account for this, models 3 and 4 use a Firth logistic regression model that reduces small sample bias (Rainey and McCaskey, 2021).…”
Section: Empirical Analysismentioning
confidence: 99%