Discrete analogues to Principal Components Analysis (PCA) are intended to handle discrete or positive-only data, for instance sets of documents. The class of methods is appropriately called multinomial PCA because it replaces the Gaussian in the probabilistic formulation of PCA with a multinomial. Experiments to date, however, have been on small data sets, for instance, from early information r...

nonlinear knapsack problems (nkp) are the alternative formulation for the multiple-choice knapsack problems. a powerful approach for solving nkp is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...

Several characterizations of the joint multinomial distribution of two discrete random vectors are derived assuming conditional multinomial distributions.

Many discrete choice contexts in transportation deal with large choice sets, including destination, route, and vehicle choices. Model estimation with large numbers of alternatives remains computationally expensive. In the context of the multinomial logit (MNL) model, limiting the number of alternatives in estimation by simple random sampling (SRS) yields consistent parameter estimates, but esti...

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...

Demand estimation based on discrete choice theory has become an important tool in Marketing and empirical Industrial Organization. In particular, estimation techniques have been developed that allow the use of individual-based discrete choice methods in situations where only aggregate data are available (e.g. Berry et al. 1995). In essence, these methods allow making inferences on the distribut...

In 2011, Lake Erie experienced a record-setting harmful algal bloom (HAB), posing significant risks to ecosystem services, including its $1.5 billion sport fishing industry. Using a mail survey of 3,000 Ohio recreational anglers and a choice experiment, this article provides the first empirical evidence in the US to link HABs to damages to Great Lakes recreational anglers. We account for the he...

The application of compositional data analysis through log ratio transformations corresponds to a multinomial logit model for the shares themselves. This model is characterized by the property of Independence of Irrelevant Alternatives (IIA). IIA states that the odds ratio –in this case the ratio of shares – is invariant to the addition or deletion of outcomes to the problem. It is exactly this...

This study examines the customer satisfaction of the telecommunications service in Kurdistan region of Iraq. The purpose is to identify the key factors that determine the customer satisfaction of the telecommunications services. A conceptual model is specified and a number of hypotheses are tested with a sample of 1,458 Kurdish mobile phone users in 2010. Discrete choice methodology is used to ...

Categorical distributions are ubiquitous in machine learning, e.g., in classification, language models, and recommendation systems. They are also at the core of discrete choice models. However, when the number of possible outcomes is very large, using categorical distributions becomes computationally expensive, as the complexity scales linearly with the number of outcomes. To address this probl...