On the overspecification of multinomial and nested logit models
		    due to alternative specific constants

				      by
		     M. Bierlaire, T. Lotan and Ph. Toint

		  Report 95/12            October 24th, 1995

    Alternative specific constants (ASCs), although playing an important role
    in random utility models, have received very little attention in
    theoretical studies.  In this paper, we try to fill this gap by providing
    an analysis of the overspecification caused by  ASCs to the
    log-likelihood function of multinomial and nested logit models.  The
    theoretical results lead directly to a particular strategy of ASC
    specification, called here the {\em orthogonal strategy}. The analysis of
    the relationship between any two arbitrary strategies and the derivation
    of an interesting geometrical property of the orthogonal strategy provide
    a motivation to prefer the latter.