IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/128489.html

Robust tobit regression for censored observations using extended Box-Cox Transformations

Author

Listed:
  • Riani, Marco
  • Atkinson, Anthony C.
  • Corbellini, Aldo
  • Morelli, Gianluca

Abstract

Truncated regression data often occur in measuring consumer behaviour involving infrequent purchases. We consider data with truncation of the upper and lower tails of the response distribution at arbitrary values. If, in addition, the distribution of responses is also skewed, we use robust transformations of the response with the parametric Yeo–Johnson transformation to provide approximate normality for both positive and negative responses. Tests for the value of the transformation parameter use the signed square root of the loglikelihood ratio test. To achieve robustness we use the Forward Search which fits the model to data subsets of increasing size and so orders the observations by closeness to the fitted model. Monitoring the statistic for transformation during the Forward Search indicates an appropriate transformation. We initially exhibit the properties of our procedure on simulated data. Our practical regression analysis is of 493 observations derived from loyalty card data. 100 of the responses are censored at zero and there are ten explanatory variables.

Suggested Citation

  • Riani, Marco & Atkinson, Anthony C. & Corbellini, Aldo & Morelli, Gianluca, 2025. "Robust tobit regression for censored observations using extended Box-Cox Transformations," LSE Research Online Documents on Economics 128489, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:128489
    as

    Download full text from publisher

    File URL: https://researchonline.lse.ac.uk/id/eprint/128489/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. L. Aït Hennani & M. Lemdani & E. Ould Saïd, 2019. "Robust regression analysis for a censored response and functional regressors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(1), pages 221-243, January.
    2. Anthony C. Atkinson & Marco Riani & Andrea Cerioli, 2018. "Cluster detection and clustering with random start forward searches," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(5), pages 777-798, April.
    3. Shiller, Robert J., 1999. "The Et Interview: Professor James Tobin," Econometric Theory, Cambridge University Press, vol. 15(6), pages 867-900, December.
    4. Lankford, R Hamilton & Wyckoff, James H, 1991. "Modeling Charitable Giving Using a Box-Cox Standard Tobit Model," The Review of Economics and Statistics, MIT Press, vol. 73(3), pages 460-470, August.
    5. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
    6. Michelli Barros & Manuel Galea & Víctor Leiva & Manoel Santos-Neto, 2018. "Generalized Tobit models: diagnostics and application in econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 145-167, January.
    7. Thomas W. Zuehlke, 2021. "Estimation of a type 2 Tobit model with generalized Box-Cox transformation," Applied Economics, Taylor & Francis Journals, vol. 53(17), pages 1952-1975, April.
    8. Fabrizio Carlevaro & Yves Croissant, 2020. "On the use of the Box-Cox transformation in censored and truncated regression models," Post-Print hal-03347607, HAL.
    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. Marco Riani & Anthony C. Atkinson & Aldo Corbellini & Gianluca Morelli, 2025. "Robust tobit regression for censored observations using extended Box–Cox transformations," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 34(3), pages 385-408, July.
    2. Karling, Maicon J. & Durante, Daniele & Genton, Marc G., 2024. "Conjugacy properties of multivariate unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 204(C).
    3. Jean‐Paul Chaze, 2005. "Assessing household health expenditure with Box–Cox censoring models," Health Economics, John Wiley & Sons, Ltd., vol. 14(9), pages 893-907, September.
    4. Danúbia R. Cunha & Jose Angelo Divino & Helton Saulo, 2022. "On a log-symmetric quantile tobit model applied to female labor supply data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(16), pages 4225-4253, December.
    5. Calcagno, R. & Renneboog, L.D.R., 2004. "Capital Structure and Managerial Compensation : The Effects of Renumeration Seniority," Discussion Paper 2004-120, Tilburg University, Center for Economic Research.
    6. Simplice A. Asongu & Mushfiqur Rahman & Mohammad Alghababsheh, 2022. "Information Technology, Business Sustainability and Female Economic Participation in Sub-Saharan Africa," Working Papers 22/057, European Xtramile Centre of African Studies (EXCAS).
    7. Andrés Felipe Martínez, 2006. "Determinantes de la supervivencia de empresas industriales en el área metropolitana de Cali 1994-2003," Ensayos Sobre Economía Regional (ESER) 2320, Banco de la República - Economía Regional.
    8. Renneboog, L.D.R. & Szilagyi, P.G., 2009. "Shareholder Activism through the Proxy Process," Other publications TiSEM cc25d736-2965-4511-b100-1, Tilburg University, School of Economics and Management.
    9. Guillermo Martínez-Flórez & Roger Tovar-Falón & Héctor W. Gómez, 2024. "Mathematical Formalization and Applications to Data with Excess of Zeros and Ones of the Unit-Proportional Hazard Inflated Models," Mathematics, MDPI, vol. 12(22), pages 1-23, November.
    10. Brannlund, Runar & Nordstrom, Jonas, 2004. "Carbon tax simulations using a household demand model," European Economic Review, Elsevier, vol. 48(1), pages 211-233, February.
    11. Eunsil Seok & Akhgar Ghassabian & Yuyan Wang & Mengling Liu, 2024. "Statistical Methods for Modeling Exposure Variables Subject to Limit of Detection," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 16(2), pages 435-458, July.
    12. Lynne, Gary D. & Franklin Casey, C. & Hodges, Alan & Rahmani, Mohammed, 1995. "Conservation technology adoption decisions and the theory of planned behavior," Journal of Economic Psychology, Elsevier, vol. 16(4), pages 581-598, December.
    13. Giovanni Marin & Francesca Lotti, 2017. "Productivity effects of eco-innovations using data on eco-patents," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 26(1), pages 125-148.
    14. Dennis Coates & Brad Humphreys, 2011. "Game Attendance and Competitive Balance in the National Hockey League," Working Papers 2011-08, University of Alberta, Department of Economics.
    15. Getachew A. Dagne, 2016. "A growth mixture Tobit model: application to AIDS studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(7), pages 1174-1185, July.
    16. Rama Lionel Ngenzebuke, 2016. "Female say on income and child outcomes: Evidence from Nigeria," WIDER Working Paper Series 134, World Institute for Development Economic Research (UNU-WIDER).
    17. Gerko Vink & Laurence E. Frank & Jeroen Pannekoek & Stef Buuren, 2014. "Predictive mean matching imputation of semicontinuous variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(1), pages 61-90, February.
    18. Simplice A. Asongu & Nicholas M. Odhiambo, 2022. "The of role economic growth in modulating mobile connectivity dynamics for financial inclusion in developing countries," Working Papers of the African Governance and Development Institute. 22/013, African Governance and Development Institute..
    19. Laeven, Luc, 2001. "Insider Lending and Bank Ownership: The Case of Russia," Journal of Comparative Economics, Elsevier, vol. 29(2), pages 207-229, June.
    20. Steven Yen & Hung-Hao Chang & Tsui-Fang Lin, 2013. "Out-of-pocket expenditures on traditional and Western medicine in Taiwan," International Journal of Public Health, Springer;Swiss School of Public Health (SSPH+), vol. 58(4), pages 583-592, August.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    Statistics

    Access and download statistics

    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:ehl:lserod:128489. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.