Fosgerau, Mogens and McFadden, Daniel and Bierlaire, Michel (2010): Choice probability generating functions.
There is a more recent version of this item available. 

PDF
MPRA_paper_24214.pdf Download (325kB)  Preview 
Abstract
This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choiceprobability generating function (CPGF) with specific properties, and that every function with these specific properties is consistent with a RUM. The choice probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized by logarithmic mixtures of their associated CPGF. The paper relates CPGF to multivariate extreme value distributions, and reviews and extends methods for constructing generating functions for applications. The choice probabilities of any ARUM may be approximated by a crossnested logit model. The results for ARUM are extended to competing risk survival models.
Item Type:  MPRA Paper 

Original Title:  Choice probability generating functions 
Language:  English 
Keywords:  Discrete choice; random utility; mixture models; duration models; logit; generalised extreme value; multivariate extreme value 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C35  Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions 
Item ID:  24214 
Depositing User:  Mogens Fosgerau 
Date Deposited:  03. Aug 2010 09:59 
Last Modified:  16. Mar 2015 10:56 
References:  Antonelli, G. (1886) Sulla Teoria Matematica della Economia Politica in H. S. J. Chipman, L. Hurwicz (ed.), Preferences, Utility, and Demand Harcourt BraceJovanovich New York. Bates, J. (2003) Economic evaluation and transport modelling: theory and practice in K. W. Axhausen (ed.), Moving through nets: the physical and social dimensions of travel Elsevier. Bierlaire, M. (2006) A theoretical analysis of the crossnested logit model Annals of operations research 144(1), 287–300. Bierlaire, M., Bolduc, D. and McFadden, D. (2008) The estimation of Generalized Extreme Value models from choicebased samples Transportation Research Part B: Methodological 42(4), 381–394. Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values SpringerVerlag. Dagsvik, J. (1995) How large is the class of generalized extreme value random utility models? Journal of Mathematical Psychology 39(1), 90–98. Daly, A. and Bierlaire, M. (2006) A General and Operational Representation of Generalised Extreme Value Models Transportation Research Part B: Methodological 40(4), 285–305. Daly, A. J. and Zachary, S. (1978) Improved multiple choice in D. A. Hensher and M. Q. Dalvi (eds), Determinants of travel demand Saxon House Sussex. de Palma, A. and Kilani, K. (2007) Invariance of conditional maximum utility Journal of Economic Theory 132(1), 137–146. Diewert, E. (1974) Applications of Duality Theory in M. Intriligator and D. Kendrick (eds), Frontiers of Quantitative Economics North Holland Amsterdam. Fisher, R. A. and Tippett, L. H. C. (1928) Limiting forms of the frequency distribution of the largest or smallest member of a sample Mathematical Proceedings of the Cambridge Philosophical Society 24, 180–190. Gnedenko, B. (1943) Sur La Distribution Limite Du Terme Maximum D’Une S´erie Al´eatoire The Annals of Mathematics 44(3), 423–453. Translated and reprinted in: Breakthroughs in Statistics, Vol. I, 1992, eds. S. Kotz and N.L. Johnson, SpringerVerlag, pp. 195225. Gorman,W. M. (1953) Community Preference Fields Econometrica 21(1), 63–80. Gumbel, E. (1958) Statistics of Extremes Columbia University Press New York. Houthakker, H. (1950) Revealed Preference and the Utility Function Economica 17, 159–174. Ib´a˜nez, J. N. and Batley, R. P. (2008) On the integrability conditions for discrete travel choice in A. for European Transport (ed.), Proceedings of the European Transport Conference. Ib´a˜nez, N. (2007) On the compatibility of probabilistic choice systems with random utility maximization Working paper 592 ITS, University of Leeds. Joe, H. (1997) Multivariate Models and Dependence Concepts Vol. 73 of Monographs on Statistics and Applied Probability Chapman and Hall/CRC. Johnson, N., Kotz, S. and Balakrishnan, N. (1995) Continuous univariate distributions Vol. 2 2nd edn John Wiley New York. Kalbfleisch, J. D. and Prentice, R. L. (2002) The statistical analysis of failure time data Vol. 360 of Wiley series in probability and statistics 2nd edn Wiley. Koning, R. and Ridder, G. (2003) Discrete Choice and Stochastic Utility Maximization Econometrics Journal 6, 1–27. Lindberg, P. O., Eriksson, E. A. and Mattsson, L.G. (1995) Invariance of achieved utility in random utility models Environment & Planning A 27(1), 121–142. MasColell, A., Whinston, M. and Green, J. (1995) Microeconomic Theory Oxford Press Oxford. McFadden, D. and Train, K. (2000) Mixed MNL Models for Discrete Response Journal of Applied Econometrics 15(5), 447–470. McFadden, D. (1974) The measurement of urban travel demand Journal of Public Economics 3, 303–328. McFadden, D. (1978) Modelling the choice of residential location in A. Karlquist et al. (ed.), Spatial interaction theory and residential location NorthHolland Amsterdam pp. 75–96. McFadden, D. (1981) Econometric models of probabilistic choice in C. Manski and D. McFadden (eds), Structural analysis of discrete data with econometric application MIT Press Cambridge, Mass. McFadden, D. L. (2005) Revealed stochastic preference: a synthesis Economic Theory 26(2), 245–264. McFadden, D. and Richter, M. (1990) Stochastic Rationality and Revealed Stochastic Preference in M. R. J. Chipman, D. McFadden (ed.), Preferences, Uncertainty, and Optimality: Essays in honor of Leonid Hurwicz Westview Press Boulder and Oxford pp. 161–186. Miller, K. S. and Samko, S. G. (2001) Completely monotonic functions Integr. Transf. and Spec. Funct. 12(4), 389–402. Nelsen, R. B. (2006) An introduction to copulas Springer Series in Statistics 2 edn Springer. Richter, M. (1966) Revealed Preference Theory Econometrica 34, 635–645. Robertson, C. A. and Strauss, D. J. (1981) A characterization theorem for random utility variables Journal of Mathematical Psychology 23(2), 184–189. Samuelson, P. (1947) Foundations of Economic Analysis Harvard Press Cambridge. Smith, T. E. (1984) A choice probability characterization of generalized extreme value models Applied Mathematics and Computation 14(1), 35 – 62. Sreehari, M. (2009) General maxstable laws Extremes 12(2), 187–200. Strauss, D. (1979) Some results on random utility models Journal of Mathematical Psychology 20(1), 35–52. Varian, H. (1993) Microeconomic Analysis Norton New York. Vovsha, P. (1997) CrossNested Logit Model: an application to mode choice in the TelAviv metropolitan area Transportation Research Record 1607, 6–15. Williams, H. (1977) On the formation of travel demand models and economic measures of user benefit Environment and Planning 9A, 285–344. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/24214 
Available Versions of this Item
 Choice probability generating functions. (deposited 03. Aug 2010 09:59) [Currently Displayed]