Sampling of alternatives in Logit Mixture models

Employing a strategy of sampling of alternatives is necessary for various transportation models that have to deal with large choice-sets. In this article, we propose a method to obtain consistent, asymptotically normal and relatively efficient estimators for Logit Mixture models while sampling alternatives. Our method is an extension of previous results for Logit and MEV models. We show that the practical application of the proposed method for Logit Mixture can result in a Naive approach, in which the kernel is replaced by the usual sampling correction for Logit. We give theoretical support for previous applications of the Naive approach, showing not only that it yields consistent estimators, but also providing its asymptotic distribution for proper hypothesis testing. We illustrate the proposed method using Monte Carlo experimentation and real data. Results provide further evidence that the Naive approach is suitable and practical. The article concludes by summarizing the findings of this research, assessing their potential impact, and suggesting extensions of the research in this area.

[1]  Joan L. Walker,et al.  Identification of parameters in normal error component logit-mixture (NECLM) models , 2007 .

[2]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[3]  Bronwyn H Hall,et al.  Estimation and Inference in Nonlinear Structural Models , 1974 .

[4]  K. Train.  Discrete Choice Methods with Simulation , 2003 .

[5]  Michel Bierlaire,et al.  BIOGEME: a free package for the estimation of discrete choice models , 2003 .

[6]  John N. Tsitsiklis,et al.  Introduction to Probability , 2002 .

[7]  Kara M. Kockelman,et al.  STRATEGIC SAMPLING FOR LARGE CHOICE SETS IN ESTIMATION AND APPLICATION , 2012 .

[8]  Sampling of Alternatives for Logit Mixture Models by Inès Azaiez Under the supervision of , 2010 .

[9]  Daniel McFadden,et al.  Modelling the Choice of Residential Location , 1977 .

[10]  Wei-Chun Tseng,et al.  Some Preliminary Evidence on Sampling of Alternatives with the Random Parameters Logit , 1999, Marine Resource Economics.

[11]  Lesley Chiou,et al.  Masking Identification of Discrete Choice Models Under Simulation Methods , 2007 .

[12]  Roger H. von Haefen,et al.  Estimating Mixed Logit Models with Large Choice Sets 1 , 2013 .

[13]  Chandra R. Bhat,et al.  The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models , 2011 .

[14]  Liang-Shyong Duann,et al.  THE ESTIMATION OF DISCRETE CHOICE MODELS WITH LARGE CHOICE SET , 2005 .

[15]  Cristian Angelo Guevara,et al.  A Monte Carlo experiment to analyze the curse of dimensionality in estimating random coefficients models with a full variance-covariance matrix , 2012 .

[16]  Cristian Angelo Guevara,et al.  Change of Scale and Forecasting with the Control-Function Method in Logit Models , 2011, Transp. Sci..

[17]  C. A. Guevara,et al.  Maximum Simulated Likelihood and Expectation-Maximization Methods to Estimate Random Coefficients Logit with Panel Data , 2012 .

[18]  Cristián Angelo Guevara-Cue.  Endogeneity and Sampling of Alternatives in Spatial Choice Models , 2010 .

[19]  Chandra R. Bhat,et al.  Numerical Analysis of Effect of Sampling of Alternatives in Discrete Choice Models , 2004 .

[20]  C. Chorus.  A New Model of Random Regret Minimization , 2010, European Journal of Transport and Infrastructure Research.

[21]  D. McFadden,et al.  MIXED MNL MODELS FOR DISCRETE RESPONSE , 2000 .

[22]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[23]  Moshe Ben-Akiva,et al.  Sampling of alternatives in Multivariate Extreme Value (MEV) models , 2013 .