Modifications of log-likelihood to measure floor and ceiling effects

Abstract

The problem of complete separation between classes may produce serious difficulties with the successful implementation of logistic regression due to the presence of floor and ceiling effects. To address this problem, the present study proposes two modifications of ordinary loglikelihood. To reveal the benefits of these modifications, we provided a theoretical and experimental basis for comparison with the mostly reported way of penalizing of log-likelihood – the regularization method. From these comparisons, we concluded that the proposed modifications produced less biased estimates and reached higher accuracy on prediction compared to the regularized log-likelihood.