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Guevara C.A.,University of Los Andes, Chile
Transportation Research Part A: Policy and Practice | Year: 2015

Endogeneity often arises in discrete-choice models, precluding the consistent estimation of the model parameters, but it is habitually neglected in practical applications. The purpose of this article is to contribute in closing that gap by assessing five methods to address endogeneity in this context: the use of Proxys (PR); the two steps Control-Function (CF) method; the simultaneous estimation of the CF method via Maximum-Likelihood (ML); the Multiple Indicator Solution (MIS); and the integration of Latent-Variables (LV). The assessment is first made qualitatively, in terms of the formulation, normalization and data needs of each method. Then, the evaluation is made quantitatively, by means of a Monte Carlo experiment to study the finite sample properties under a unified data generation process, and to analyze the impact of common flaws. The methods studied differ notably in the range of problems that they can address; their underlying assumptions; the difficulty of gathering proper auxiliary variables needed to apply them; and their practicality, both in terms of the need for coding and their computational burden. The analysis developed in this article shows that PR is formally inappropriate for many cases, but it is easy to apply, and often corrects in the right direction. CF is also easy to apply with canned software, but requires instrumental variables which may be hard to collect in various contexts. Since CF is estimated in two stages, it may also compromise efficiency and difficult the estimation of standard errors. ML guarantees efficiency and direct estimation of the standard errors, but at the cost of larger computational burden required for the estimation of a multifold integral, with potential difficulties in identification, and retaining the difficulty of gathering proper instrumental variables. The MIS method appears relatively easy to apply and requiring indicators that may be easier to obtain in various cases. Finally, the LV approach appears as the more versatile method, but at a high cost in computational burden, problems of identification and limitations in the capability of writing proper structural equations for the latent variable. © 2015 Elsevier Ltd. Source

Fernandez-Oto C.,Free University of Colombia | Clerc M.G.,University of Chile | Escaff D.,University of Los Andes, Chile | Tlidi M.,Free University of Colombia
Physical Review Letters | Year: 2013

We investigate the effect of strong nonlocal coupling in bistable spatially extended systems by using a Lorentzian-like kernel. This effect through front interaction drastically alters the space-time dynamics of bistable systems by stabilizing localized structures in one and two dimensions, and by affecting the kinetics law governing their behavior with respect to weak nonlocal and local coupling. We derive an analytical formula for the front interaction law and show that the kinetics governing the formation of localized structures obeys a law inversely proportional to their size to some power. To illustrate this mechanism, we consider two systems, the Nagumo model describing population dynamics and nonlinear optics model describing a ring cavity filled with a left-handed material. Numerical solutions of the governing equations are in close agreement with analytical predictions. © 2013 American Physical Society. Source

Escaff D.,University of Los Andes, Chile
European Physical Journal D | Year: 2011

Defect interaction (kink-antikink interaction) is studied for a prototypical model for non-local interaction. Mathematically, it is a bistable integrodifferential model, where the non-local interaction is performed due to an integral kernel. The system is able to establish domains where it is in one of its two equilibria, separated by defects. It is shown that the defect interaction depends on the asymptotical behavior of the integral kernel. In the weak non-local regime, when the integral kernel decays faster than an exponential at infinitum, the defect interaction is exponentially weak. Hence, this case is qualitatively similar to the local one. On the other hand, in the strong non-local regime, when the integral kernel decays slower than an exponential at infinitum, the defect interaction is ruled by the asymptotical behavior of the integral kernel. In this case, the defect interaction is stronger, and could be characterized, for instance, by a power law. The effect of this transition (from the weak to strong non-locality) on the domain dynamics is discussed. © 2010 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg. Source

Zegers P.,University of Los Andes, Chile
Entropy | Year: 2015

A set of Fisher information properties are presented in order to draw a parallel with similar properties of Shannon differential entropy. Already known properties are presented together with new ones, which include: (i) a generalization of mutual information for Fisher information; (ii) a new proof that Fisher information increases under conditioning; (iii) showing that Fisher information decreases in Markov chains; and (iv) bound estimation error using Fisher information. This last result is especially important, because it completes Fano's inequality, i.e., a lower bound for estimation error, showing that Fisher information can be used to define an upper bound for this error. In this way, it is shown that Shannon's differential entropy, which quantifies the behavior of the random variable, and the Fisher information, which quantifies the internal structure of the density function that defines the random variable, can be used to characterize the estimation error. © 2015 by the authors; licensee MDPI, Basel, Switzerland. Source

Fernandez R.,University of Los Andes, Chile
Transportation Research Part C: Emerging Technologies | Year: 2010

This paper presents a microscopic model for the study of operations at public transport stops, mainly bus stops and light rail transit stations, from the perspective of the traffic analysis. Firstly, a description of a public transport stop as a traffic mechanism is offered. Then the issue of stop capacity is reviewed, providing typical values of transit system capacities. The most wide-spread analytical model of stop capacity - the Highway Capacity Manual formula - and its components is discussed. Next, a microscopic simulation model as a tool for computing stop capacities and related impacts is described. Results of the calibration and validation of the model are also presented. Two applications are developed to illustrate the model capabilities. The first example deals with a light rail transit station and articulated trams; the second one consists of different classes of buses stopping at a bus stop. It can be concluded from these applications that the proposed model may provide more detailed information about stop operations than other existing approaches. © 2010 Elsevier Ltd. Source

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