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3) extends over all Ik alternatives in subset k, and Jk denotes the index of the first alternative in this subset. 3) are called the "dissimilarity parameters" of subset k. They are the essential parameters that provide for the flexibility of the nested multinomial logit model. 3). 7) if all Ok equal unity. 4. 4) FNMNL(E;O) - K exp ( - I k=l Each Ok not equal to one introduces a non-zero correlation among the disturbances Ei within the subset k. d. , the assumption of "Independence of Irrelevant Alternatives" that is the major disadvantage of the MNL model.
This leads to a very fast algorithm with a computational effort that increases only quadratically with the number of alternatives in the choice set. Little is known about the analytic properties of the Clark approximation. Empirically, this approximation appears to lead to an overestimate of small choice probabilities. Only in the case of positively correlated variables with comparable variances is the Clark approximation reasonably accurate (McFadden, 1981; Horowitz, sparman, and Daganzo, 1981; Lerman and Manski, 1981).
10) (McFadden, 1981). 4 The Universal Legit Model Another method used to obtain choice probabilities that have similar computational advantages as the MNL model but are not subject to the stringent independence assumption is the universal logit (UL) model (Cox, 1966; McFadden, 1975). 14) Its choice probabilities are exp(Si (v» with functions Si' i=1, •• ,I, that contain all attributes v 1 , ••• ,vI. 7) by an appropriate variable transformation. 4) cannot be separated from each other. In this generality, the UL model does not produce generating functions that are necessarily proper distribution functions.
Analysis of the conservation law for matter and gravitational field introduced by Einstein