Minimizing the effects of floor and ceiling to improve the convergence of log-likelihood

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 log-likelihood. To reveal the benefits of these modifications, we provided a strong 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 under more unstable conditions: on samples with fewer observations and more predictors.