A Research On SCAD-FLR Model And Its Application

The Firth Logistic model was first proposed by D.Firth in 1993,aiming to remove the bias in parametric problems caused by maximum likelihood estimation.Maximum likelihood estimation is the classical method of Logistic model,but the estimators are asymptotic biased,especially for small data.The Firth Logistic model penalized the likelihood by an item based on the information matrix,which can "advanced" remove bias.Since the Firth Logistic model has been proposed,there are two mainstream applications.Firstly,in the case of rare event,the bias in coefficients of the Logistic model is very large,and it tends to underestimate the probability of the event.Second,for separated data,the most common warning is the fitted probability is zero or one,even may come out monotone likelihood,the algorithm does not convergence or even if the number of iterations is reached,the estimated value is returned,some estimation coefficients tend to be infinite,and the coefficients are no longer reliable.The Firth Logistic model can effectively deal with rare events or separated data,and always return finite coefficients.First of all,through numerical simulation,it is found that small data or rare events are the root reasons for the failure of the Logistic model,rather than the proportion of samples.Meanwhile,through simulation for the two cases:complete separation and quasi-complete separation,the applicability of Firth Logistic model is proved.Whether it is small data or rare event,or separated data,the number of target class events is always limited.Objectively,the number of explanatory variables is limited.Therefore,selecting important variables and building a sparse model is a necessary and important thing.Based on this,this paper introduces SCAD(Smoothly Clipped Absolute Deviation)method into the Firth Logistic model,build SCAD-FLR model,achieves the dual purpose of obtain stable and reasonable estimators and variable selection.The optimal parameter is selected by the five-fold cross validation,and the Gauss-Seidel Newton-Raphson Algorithm is used for optimization.Through a comprehensive and sufficient stochastic simulation,the performance of the model is investigated and the model paradigm is determined.Finally,the availability and superiority of the model are verified in real data.