Abstract
The logit function is the reciprocal function to the sigmoid logistic function. It maps the interval [0,1] into the real line and is written as
Two traditions are involved in the modern theory of logit models of individual choices. The first one concerns curve fitting as exposed by Berkson (1944), who coined the term ‘logit’ after its close competitor ‘probit’ which is derived from the normal distribution. Both models are by far the most popular econometric methods used in applied work to estimate models for binary variables, even though the development of semiparametric and nonparametric alternatives since the mid-1970s has been intensive (Horowitz and Savin, 2001).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Amemiya, T. 1985. Advanced Econometrics. Cambridge, MA: Harvard University Press.
Andersen, E.B. 1973. Conditional Inference and Models for Measuring. Copenhagen: Mentalhygiejnisk Forlag.
Anderson, S.P., de Palma, A. and Thisse, J.F. 1992. Discrete Choice Theory of Product Differentiation. Cambridge, MA: MIT Press.
Arellano, M. 2003. Discrete choices with panel data. Investigaciones Económicas 27, 423–58.
Berkson, J. 1944. Application of the logistic function to bioassay. Journal of the American Statistical Association 39, 357–65.
Berkson, J. 1951. Why I prefer logits to probits. Biometrics 7, 327–39.
Berkson, J. 1955. Maximum likelihood and minimum chi-square estimates of the logistic function. Journal of the American Statistical Association 50, 130–62.
Berry, S.T., Levinsohn, J.A. and Pakes, A. 1995. Automobile prices in market equilibrium. Econometrica 63, 841–90.
Chamberlain, G. 1984. Panel data. In Handbook of Econometrics, vol. 2, ed. Z. Griliches and M. Intriligator. Amsterdam: North-Holland.
Chamberlain, G. 1992. Binary response models for panel data: identification and information. Unpublished manuscript, Harvard University.
Dagsvik, J. 2002. Discrete choice in continuous time: implications of an intertemporal version of IAA. Econometrica 70, 817–31.
Gouriéroux, C. 2000. Econometrics of Qualitative Dependent Variables. Cambridge: Cambridge University Press.
Gouriéroux, C, Monfort, A. and Trognon, A. 1985. Moindres carrés asymptotiques. Annales de l’INSEE 58, 91–121.
Horowitz, J. 1998. Semiparametric Methods in Econometrics. Berlin: Springer.
Horowitz, J.L. and Savin, N.E. 2001. Binary response models: logits, probits and semiparametrics. Journal of Economic Perspectives 15(4), 43–56.
Lancaster, T. 2000. The incidental parameter problem since 1948. Journal of Econometrics 95, 391–113.
Lewbel, A. 2000. Semiparametric qualitative response model estimation with unknown heteroskedasticity or instrumental variables. Journal of Econometrics 97, 145–77.
Luce, R. 1959. Individual Choice Behavior: A Theoretical Analysis. New York: Wiley.
Magnac, T. 2004. Panel binary variables and sufficiency: generalizing conditional logit. Econometrica 72, 1859–77.
Manski, CF. 1975. The maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3, 205–28.
Manski, CF. 1988. Identification of binary response models. Journal of the American Statistical Association 83, 729–38.
Marschak, J. 1960. Binary choice constraints and random utility indicators. In Mathematical Methods in the Social Sciences, ed. K. Arrow. Stanford: Stanford University Press.
Matzkin, R. 1992. Nonparametric and distribution-free estimation of the binary threshold crossing and the binary choice models. Econometrica 60, 239–70.
McCullagh, P. and Neider, J.A. 1989. Generalized Linear Models. London: Chapman and Hall.
McFadden, D. 1974. Conditional logit analysis of qualitative choice behavior. In Frontiers in Econometrics, ed. P. Zarembka. New York: Academic Press.
McFadden, D. 1984. Econometric analysis of qualitative response models. In Handbook of Econometrics, vol. 2, ed. Z. Griliches and M.D. Intriligator. Amsterdam: North-Holland.
McFadden, D. 2001. Economic choices. American Economic Review 91, 351–78.
McFadden, D. and Train, K. 2000. Mixed MNL models for discrete responses. Journal of Applied Econometrics 15, 447–70.
Rasch, G. 1960. Probabilistic Models for Some Intelligence and Attainment Tests. Copenhagen: Denmark Paedagogiske Institut.
Resnick, S.I. and Roy, R. 1991. Random USC functions, max stable process and continuous choice. Annals of Applied Probability 1, 267–92.
Strauss, D. 1992. The many faces of logistic regression. American Statistician 46, 321–27.
Theil, H. 1969. A multinomial extension of the linear logit model. International Economic Review 10, 251–9.
Thurstone, L. 1927. A law of comparative judgement. Psychological Review 34, 273–86.
Train, K. 2003. Discrete Choice Methods with Simulation. Cambridge: Cambridge University Press.
Editor information
Editors and Affiliations
Copyright information
© 2010 Palgrave Macmillan, a division of Macmillan Publishers Limited
About this chapter
Cite this chapter
Magnac, T. (2010). Logit Models of Individual Choice. In: Durlauf, S.N., Blume, L.E. (eds) Microeconometrics. The New Palgrave Economics Collection. Palgrave Macmillan, London. https://doi.org/10.1057/9780230280816_13
Download citation
DOI: https://doi.org/10.1057/9780230280816_13
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-0-230-23881-7
Online ISBN: 978-0-230-28081-6
eBook Packages: Palgrave Media & Culture CollectionLiterature, Cultural and Media Studies (R0)