IDEAS home Printed from https://ideas.repec.org/a/sae/somere/v49y2020i3p809-834.html
   My bibliography  Save this article

Estimating the Proportion of a Categorical Variable With Probit Regression

Author

Listed:
  • Sergio Martínez
  • Maria Rueda
  • Antonio Arcos
  • Helena Martínez

Abstract

This article discusses the estimation of a population proportion, using the auxiliary information available, which is incorporated into the estimation procedure by a probit model fit. Three probit regression estimators are considered, using model-based and model-assisted approaches. The theoretical properties of the proposed estimators are derived and discussed. Monte Carlo experiments were carried out for simulated data and for real data taken from a database of confirmed dengue cases in Mexico. The probit estimates give valuable results in comparison to alternative estimators. Finally, the proposed methodology is applied to data obtained from an immigration survey.

Suggested Citation

  • Sergio Martínez & Maria Rueda & Antonio Arcos & Helena Martínez, 2020. "Estimating the Proportion of a Categorical Variable With Probit Regression," Sociological Methods & Research, , vol. 49(3), pages 809-834, August.
    • Handle: RePEc:sae:somere:v:49:y:2020:i:3:p:809-834
    DOI: 10.1177/0049124118761771
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0049124118761771
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0049124118761771?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Wu C. & Sitter R. R, 2001. "A Model-Calibration Approach to Using Complete Auxiliary Information From Survey Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 185-193, March.
    2. Cramer,J. S., 2011. "Logit Models from Economics and Other Fields," Cambridge Books, Cambridge University Press, number 9780521188036, September.
    3. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    4. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Siddhartha Chib & Edward Greenberg & Yuxin Chen, 1998. "MCMC Methods for Fitting and Comparing Multinomial Response Models," Econometrics 9802001, University Library of Munich, Germany, revised 06 May 1998.
    2. Bolduc, Denis & Kaci, Mustapha, 1993. "Estimation des modèles probit polytomiques : un survol des techniques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 69(3), pages 161-191, septembre.
    3. Tinessa, Fiore & Marzano, Vittorio & Papola, Andrea, 2020. "Mixing distributions of tastes with a Combination of Nested Logit (CoNL) kernel: Formulation and performance analysis," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 1-23.
    4. Joachim Grammig & Reinhard Hujer & Michael Scheidler, 2005. "Discrete choice modelling in airline network management," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 467-486, May.
    5. Baltas, George & Doyle, Peter, 2001. "Random utility models in marketing research: a survey," Journal of Business Research, Elsevier, vol. 51(2), pages 115-125, February.
    6. GRAMMIG, Joachim & HUJER, Reinhard & SCHEIDLER, Michael, 2001. "The econometrics of airline network management," LIDAM Discussion Papers CORE 2001055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Bunch, David S. & Kitamura, Ryuichi, 1991. "Probit Model Estimation Revisited: Trinomial Models of Household Car Ownership," University of California Transportation Center, Working Papers qt2hr8d4bs, University of California Transportation Center.
    8. Jacques Huguenin & Florian Pelgrin & Alberto Holly, 2009. "Estimation of multivariate probit models by exact maximum likelihood," Working Papers 0902, University of Lausanne, Institute of Health Economics and Management (IEMS).
    9. Samir Ghazouani & Mohamed Goaïed, 1993. "Analyse micro-économétrique de la demande de transport urbain pour la ville de Tunis," Économie et Prévision, Programme National Persée, vol. 108(2), pages 47-62.
    10. Hausman, Jerry A. & Leonard, Gregory K. & McFadden, Daniel, 1995. "A utility-consistent, combined discrete choice and count data model Assessing recreational use losses due to natural resource damage," Journal of Public Economics, Elsevier, vol. 56(1), pages 1-30, January.
    11. Myoung-jae Lee & Sung-jin Kang, 2009. "Strategic Voting and Multinomial Choice In US Presidential Elections," Discussion Paper Series 0907, Institute of Economic Research, Korea University.
    12. Meza, Cristian & Jaffrézic, Florence & Foulley, Jean-Louis, 2009. "Estimation in the probit normal model for binary outcomes using the SAEM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1350-1360, February.
    13. Chihwa Kao & Lung-fei Lee & Mark M. Pitt, 2001. "Simulated Maximum Likelihood Estimation of the Linear Expenditure System with Binding Non-Negativity Constraints," Annals of Economics and Finance, Society for AEF, vol. 2(1), pages 215-235, May.
    14. Robert Kapłon, 2006. "A retrospective review of categorical data analysis – theory and marketing practice," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 16(1), pages 55-72.
    15. Vassilis Argyrou Hajivassiliou, 1993. "Simulating Normal Rectangle Probabilities and Their Derivatives: The Effects of Vectorization," Working Papers _025, Yale University.
    16. Hajivassiliou, Vassilis A. & Ruud, Paul A., 1986. "Classical estimation methods for LDV models using simulation," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 40, pages 2383-2441, Elsevier.
    17. Vassilis A. Hajivassiliou, 1991. "Simulation Estimation Methods for Limited Dependent Variable Models," Cowles Foundation Discussion Papers 1007, Cowles Foundation for Research in Economics, Yale University.
    18. Junsen Zhang & Saul D. Hoffman, 1993. "Discrete-Choice Logit Models," Sociological Methods & Research, , vol. 22(2), pages 193-213, November.
    19. Bunch, David S., 1991. "Estimability in the Multinomial Probit Model," University of California Transportation Center, Working Papers qt1gf1t128, University of California Transportation Center.
    20. Yai, Tetsuo & Iwakura, Seiji & Morichi, Shigeru, 1997. "Multinomial probit with structured covariance for route choice behavior," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 195-207, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:somere:v:49:y:2020:i:3:p:809-834. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.