Modeling

Computation of Equilibrium Over Transportation Networks: The Case of Disaggregate Demand Models

Sheffi, Yosef
Carlos Daganzo
1980

The transportation planning forecasting process has been traditionally performed on a sequential, disconnected, heuristic basis, using different methodologies for each one of the stages. In an attempt to improve this situation, a first step toward developing a unified transportation forecasting methodology is described in this paper. This is done by showing how many, seemingly different, problems can be cast as analogous route choice problems on abstract networks and studied with the same methodology. As a consequence of this analogy, it is possible to perform equilibrium analyses and to...

Aggregation with Multinomial Probit and Estimation of Disaggregate Models with Aggregate Data: A New Methodological Approach

Bouthelier, Fernando
Carlos Daganzo
1979

This paper describes an analytic aggregation procedure for disaggregate demand models similar to the one proposed in earlier publications by Westin (1974) and McFadden and Reid (1975). The technique, which uses a multivariate normal approximation for the distribution of the vector of attributes, is based on the multinomial profit algorithm proposed by Daganzo, Bouthelier and Sheffi (1977) and can be applied to an arbitrary number of alternatives. The procedure is computationally so efficient that it enables us to calibrate disaggregate models with aggregate data by maximum likelihood using...

Optimal Sampling Strategies for Statistical Models with Discrete Dependent Variables

Carlos Daganzo
1980

The object of this paper is to improve the cost-effectiveness of data gathering procedures for models with discrete dependent variables. It is assumed throughout the paper that the true value of the parameter vector is approximately known and that, with that information, one must select a statistically optimal number of observations from different population subgroups to refine the accuracy of the estimate. It is shown that the problem can be reduced to a small mathematical program whose objective function can be written after a few preliminary algebraic manipulations. For binary choice...

Estimation of Gap Acceptance Parameters within and Across the Population from Direct Roadside Observation

Carlos Daganzo
1981

This paper explores the feasibility of maximum likelihood as an approach to determine the parameters of gap acceptance functions when these functions vary from individual to individual. Specifically, it is shown that it is theoretically possible to estimate the average critical gap of a population of drivers (or pedestrians) and its variance, within and across individuals, from direct roadside observations. Although the Multinomial Probit Model provides a natural theoretical framework for the estimation of these parameters, the model seems not to be statistically estimable for this...

Errata—Optimal Sampling Strategies for Statistical Models with Discrete Dependent Variables

Carlos Daganzo
1982

Corrections to be made to the article “Optimal Sampling Strategies for Statistical Models with Discrete Dependent Variables” by Carlos F. Daganzo, Transportation Science14, 324–345, 1980.

Goodness-of-Fit Measures and the Predictive Power of Discrete Models

Carlos Daganzo
1982

Although a number of goodness-of-fit measures for discrete choice models have been proposed and are widely in use, there have been few attempts at interpreting their physical meaning at a practical level. This paper presents a family of goodness-of-fit measures, which contains currently used measures such as the pseudo-correlation coefficient and the percent right, and shows how its members are related. More important, it is shown that one of these measures has an interpretation identical to the correlation coefficient of multiple regression in that it can be used to calculate the...

An Investigation of the Accuracy of the Clark Approximation for the Multinomial Probit Model

Horowitz, Joel L.
Sparmann, Jürg M.
Carlos Daganzo
1982

The Clark approximation, in which the maximum of two normally distributed random variables is approximated by a third normally distributed random variable, forms the basis of a relatively inexpensive technique for evaluating the choice probabilities of multinomial probit models. This paper reports the results of a series of numerical experiments in which the accuracy of probit computations based on the Clark approximation was investigated. In contrast to previous investigations, these experiments dealt with the accuracy of the results obtained when the Clark approximation is used for...

Multinomial Probit with Time-Series Data: Unifying State Dependence and Serial Correlation Models

Carlos Daganzo
Sheffi, Y.
1982

This paper develops a general method for treating discrete data sets containing individuals that have made more than one choice under varying stimuli. The multinomial probit model is shown to possess properties that make it very attractive for this application, as with it, it is possible to develop an estimation process that uses all the information in the data, and is both relatively inexpensive and consistent with utility maximization. The method, which is a generalization of Heckman's binary model, can include taste variations and more than two alternatives.

Linear Probit Models: Statistical Properties and Improved Estimation Methods

Sparmann, Jürg M.
Carlos Daganzo
Soheily, Mahboubeh
1983

The multinomial probit model is a statistical tool that is well suited to analyze some transportation problems. Modal split, gap acceptance, and route choice are some examples of application contexts. This paper presents an in-depth analysis of its statistical properties and an estimation method for the trinomial case. In the statistical part of the paper it is shown that for multinomial probit models with specifications that are linear in the parameters, the global maximum of the log-likelihood function is consistent if the data do not exhibit multicollinearity as defined in the text. For...

Unconstrained Extremal Formulation of Some Transportation Equilibrium Problems

Carlos Daganzo
1982

This paper presents transportation equilibrium results that apply to both discrete choice models and network problems. Specifically, it shows that many network equilibrium problems admit an unconstrained extremal formulation and that unconstrained optimization algorithms may be used for their solution. Similar results are derived for equilibrium problems involving discrete choice models. It also shows that a certain class of stochastic networks exhibit unique equilibria and that simulation algorithms with fixed step sizes converge almost surely to the equilibrium point.