A robust algorithm for the simultaneous estimation of hierarchical logit models

Estimating simultaneous hierarchical logit models is conditional to the availability of suitable algorithms. Powerful mathematical programs are necessary to maximize the associated non-linear, non-convex, log-likelihood function. Even if classical methods (e.g. Newton-Raphson) can be adapted for relatively simple cases, the need of an e cient and robust algorithm is justi ed to enable practioners to consider a wider class of models. The purpose of this paper is to analyze and to adapt to this context methodologies available in the optimization literature. An algorithm is proposed based on two major concepts from non-linear programming : a trust region method, that ensures robustness and global convergence, and a conjugate gradients iteration, that can be used to solve the quadratic subproblems arising in the estimation process described in this paper. Numerical experiments are nally presented that indicate the power of the proposed algorithm and associate software. Transportation Research Group Department of Mathematics, Facult es Universitaires ND de la Paix, Namur, Belgium E-mail : [email protected]