COMPARISON OF SOME CLASSICAL AND META-HEURISTIC OPTIMIZATION TECHNIQUES IN THE ESTIMATION OF THE LOGIT MODEL PARAMETERS.

The aim of this study is to discuss the success of the Genetic Algorithm (GA) approach compared with the conventional Newton-Raphson (NR) and Nelder-Mead (NM) algorithms in the estimation of the Binary Logit Model (BLM) parameters over a simulated data and a real data set on Alopecia disease. NR algorithm requires restrictive assumptions such as the continuity of the objective function and determination of starting points for the model parameters in iterative process. As for the NM algorithm, it does not require differentiable objective function but still suffers from the starting point problem. In this study, the best set of parameters that maximize the likelihood function in BLM is found using both NR and NM algorithms. Then, considering the limitations of the conventional methods, the success of GA is investigated on condition that all the assumptions of the NR and NM methods are satisfied. The results show that when the assumptions of the classical techniques are valid, the GA approach can achieve to obtain very close result to NR and NM. This also implies that it is a good alternative to the NR and NM methods when the requirements of the classical methods cannot be satisfied. Model results of NR, NM and GA are compared in terms of the estimated values and the maximum likelihood function value.