IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v38y2026icp97-121.html

Robust logistic regression for ordered and unordered responses

Author

Listed:
  • Iannario, Maria
  • Monti, Anna Clara

Abstract

Multinomial regression models and cumulative, adjacent-categories and continuation-ratio models are applied in many fields to analyze unordered or ordered responses with respect to subjects’ profiles. They are typically fitted by maximum likelihood estimators, which unfortunately are sensitive to anomalous data. In order to cope with these data robust M type estimators can be applied. They exploit the properties of the logistic link function and are based on a weighted likelihood approach. The M estimators can be easily implemented numerically, provide reliable inference when data are contaminated and lead to an accurate model specification. Inference based on the M estimators is illustrated in three case studies related to risk attitude in financial investments, diabetes in non-obese adult patients and intensity of chronic pain in aging people.

Suggested Citation

  • Iannario, Maria & Monti, Anna Clara, 2026. "Robust logistic regression for ordered and unordered responses," Econometrics and Statistics, Elsevier, vol. 38(C), pages 97-121.
    • Handle: RePEc:eee:ecosta:v:38:y:2026:i:c:p:97-121
    DOI: 10.1016/j.ecosta.2023.05.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306223000370
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2023.05.004?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
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Miron, Julien & Poilane, Benjamin & Cantoni, Eva, 2022. "Robust polytomous logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    2. Croux, Christophe & Flandre, Cécile & Haesbroeck, Gentiane, 2002. "The breakdown behavior of the maximum likelihood estimator in the logistic regression model," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 377-386, December.
    3. Romina Gambacorta & Maria Iannario, 2013. "Measuring Job Satisfaction with CUB Models," LABOUR, CEIS, vol. 27(2), pages 198-224, June.
    4. Elena Castilla & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2018. "New robust statistical procedures for the polytomous logistic regression models," Biometrics, The International Biometric Society, vol. 74(4), pages 1282-1291, December.
    5. Walter R. Mebane & Jasjeet S. Sekhon, 2004. "Robust Estimation and Outlier Detection for Overdispersed Multinomial Models of Count Data," American Journal of Political Science, John Wiley & Sons, vol. 48(2), pages 392-411, April.
    6. Roy E. Welsch, 1980. "Regression Sensitivity Analysis and Bounded-Influence Estimation," NBER Chapters, in: Evaluation of Econometric Models, pages 153-167, National Bureau of Economic Research, Inc.
    7. Tutz, Gerhard, 1991. "Sequential models in categorical regression," Computational Statistics & Data Analysis, Elsevier, vol. 11(3), pages 275-295, May.
    8. Moustaki, Irini & Victoria-Feser, Maria-Pia, 2006. "Bounded-Influence Robust Estimation in Generalized Linear Latent Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 644-653, June.
    9. Bercedis Peterson & Frank E. Harrell, 1990. "Partial Proportional Odds Models for Ordinal Response Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(2), pages 205-217, June.
    10. Todorov, Valentin & Filzmoser, Peter, 2009. "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i03).
    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. Miron, Julien & Poilane, Benjamin & Cantoni, Eva, 2022. "Robust polytomous logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    2. Gerhard Tutz & Micha Schneider & Maria Iannario & Domenico Piccolo, 2017. "Mixture models for ordinal responses to account for uncertainty of choice," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(2), pages 281-305, June.
    3. Andrew S. Fullerton & Jun Xu, 2018. "Constrained and Unconstrained Partial Adjacent Category Logit Models for Ordinal Response Variables," Sociological Methods & Research, , vol. 47(2), pages 169-206, March.
    4. D'Alberto, R. & Targetti, S. & Schaller, L. & Bartolini, F. & Eichhorn, T. & Haltia, E. & Harmanny, K. & Le Gloux, F. & Nikolov, D. & Runge, T. & Vergamini, D. & Viaggi, D., 2024. "A European perspective on acceptability of innovative agri-environment-climate contract solutions," Land Use Policy, Elsevier, vol. 141(C).
    5. repec:jss:jstsof:10:i01 is not listed on IDEAS
    6. William Magee, 2023. "Earnings, Intersectional Earnings Inequality, Disappointment in One’s Life Achievements and Life (Dis)satisfaction," Journal of Happiness Studies, Springer, vol. 24(1), pages 373-396, January.
    7. Bianco, Ana M. & Martínez, Elena, 2009. "Robust testing in the logistic regression model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4095-4105, October.
    8. Nadine Levratto & Clarisse Nguedam Ntouko & Maarouf Ramadan, 2017. "Institutions and firms’ internationalization: an empirical analysis on three Middle East countries," EconomiX Working Papers 2017-37, University of Paris Nanterre, EconomiX.
    9. Hanna Dudek & Joanna Landmesser, 2012. "Income satisfaction and relative deprivation," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 13(2), pages 321-334, June.
    10. Malpezzi, Stephen, 1998. "Welfare analysis of rent control with side payments: a natural experiment in Cairo, Egypt1," Regional Science and Urban Economics, Elsevier, vol. 28(6), pages 773-795, November.
    11. Yanyuan Ma & Marc G. Genton, 2010. "Explicit estimating equations for semiparametric generalized linear latent variable models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 475-495, September.
    12. Riillo, Cesare Fabio Antonio & Peroni, Chiara, 2022. "Immigration and entrepreneurship in Europe: cross-country evidence," MPRA Paper 114580, University Library of Munich, Germany.
    13. Gennaro Punzo & Rosalia Castellano & Mirko Buonocore, 2018. "Job Satisfaction in the “Big Four” of Europe: Reasoning Between Feeling and Uncertainty Through CUB Models," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 139(1), pages 205-236, August.
    14. Menz, Fredric C. & Vachon, Stephan, 2006. "The effectiveness of different policy regimes for promoting wind power: Experiences from the states," Energy Policy, Elsevier, vol. 34(14), pages 1786-1796, September.
    15. Yiwei Fan & Jiaqi Gu & Guosheng Yin, 2023. "Sparse concordance‐based ordinal classification," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 934-961, September.
    16. Cai, Jing-Heng & Song, Xin-Yuan & Lam, Kwok-Hap & Ip, Edward Hak-Sing, 2011. "A mixture of generalized latent variable models for mixed mode and heterogeneous data," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2889-2907, November.
    17. Bachmann, Kremena & Meyer, Julia & Krauss, Annette, 2024. "Investment motives and performance expectations of impact investors," Journal of Behavioral and Experimental Finance, Elsevier, vol. 42(C).
    18. Ángela González Arbeláez, 2010. "Determinantes del riesgo del crédito comercial en Colombia," Vniversitas Económica, Universidad Javeriana - Bogotá, vol. 0(0), pages 1-69.
    19. Cizek, Pavel, 2008. "Robust and Efficient Adaptive Estimation of Binary-Choice Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 687-696, June.
    20. Steffen Liebscher & Thomas Kirschstein, 2015. "Efficiency of the pMST and RDELA location and scatter estimators," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 63-82, January.
    21. Stefania Capecchi & Maria Iannario & Rosaria Simone, 2018. "Well-Being and Relational Goods: A Model-Based Approach to Detect Significant Relationships," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 135(2), pages 729-750, January.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:eee:ecosta:v:38:y:2026:i:c:p:97-121. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/econometrics-and-statistics .

    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.