A comparison of algorithms for maximum likelihood estimation of choice models

Maximum likelihood estimation (MLE) is often avoided in econometric and other statistical applications due to computational considerations despite its strong theoretical appeal. Recent advances in non-linear optimization provide feasible alternative methods for calculating MLE's, especially when special structure may be exploited, as for example in probabilistic choice models. This paper examines a range of quasi-Newton methods and gives numerical comparisons based on the multinomial logit model and a non-independence of irrelevant alternative model. Among the issues considered are step determination and methods of approximating the Hessian. These include standard secant updates (DFP and BFGS), statistical approximations (BHHH), and recently developed approaches which use model switching.