A robust algorithm for the simultaneous
		   estimation of hierarchical logit models

				 M. Bierlaire

			Transportation Research Group
			  Department of Mathematics
		    Facultes Universitaires ND de la Paix,
				Namur, Belgium
				       
		   Report 95/3         February 24th, 1995

Keyword : random utility models, non-linear optimization, hierarchical logit
model, discrete choice.

Abstract :

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  efficient  and robust algorithm  is
justified  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  : {\em a trust region method},
that ensures robustness and global convergence, and {\em 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 finally
presented that indicate  the power  of the  proposed algorithm  and  associate
software.