Affiliations: [a] Department of Statistics, School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK. E-mail: [email protected] | [b] Department of Mathematics and Statistics, The University of West Florida, Pensacola, FL 32514, USA. E-mail: [email protected]
Abstract: This study attempts to review the existing literature in inference of logistic regression (LR) model parameters. The use of maximum likelihood estimators is unquestionable; however, its use is debatable in small-samples because they may be biased, although they are asymptotically unbiased. Theoretically however, for small-sample cases, bias-correction comes to remedy, though it is not easy to identify how much bias can be reduced. Hence it's use is not popular among it's users in small-sample cases. The LR model analysis is quite often used in real-life data where the data are skewed. However, literature in this area is not widely available. The use of three test statistics (Likelihood ratio, Score, Wald) is common in the LR model. Though the Wald test statistic is more popular, it does not perform as well as the other two. All these tests possess optimal asymptotic properties, but the small-sample behavior is less known.
Keywords: Maximum likelihood, bias correction, linear probability model, likelihood ratio test, score test, Wald test, small sample, simulation