Categorical outcome (or discrete outcome or qualitative response) regression models are models for a discrete dependent variable recording in which of two or more categories an outcome of interest lies. For binary data (two categories) probit and logit models or semiparametric methods are used. For multinomial data (more than two categories) that are unordered, common models are multinomial and...

This paper discusses the representability of discrete logit-type models including multinomial logit and nested logit model from a mathematical approach. It is shown that the logit-type models can be reconstructed from mathematical approximation theory with sigmoidal functions widely used in Neural Network modeling without the basic assumptions such as IIA and iid, and the distribution (or densi...

We consider assortment and price optimization problems under the d-level nested logit model. In the assortment optimization problem, the goal is to find the revenue-maximizing assortment of products to offer, when the prices of the products are fixed. Using a novel formulation of the d-level nested logit model as a tree of depth d, we provide an efficient algorithm to find the optimal assortmen...

We study firms that sell multiple differentiated substitutable products and customers whose purchase behavior follows a Nested Logit model, of which the Multinomial Logit model is a special case. Customers make purchasing decision sequentially under the Nested Logit model: they first select a nest of products and subsequently purchase a product within the selected nest. We consider the general ...

We give a two-line proof of long-standing conjecture Ben-Akiva and Lerman (1985) regarding the random utility representation nested logit model, thus providing renewed straightforward textbook treatment that model. As an application, we provide closed-form formula for correlation between two Fr\'echet variables coupled by Gumbel copula.