IDEAS home Printed from https://ideas.repec.org/a/spr/qualqt/v48y2014i6p3185-3193.html

Ridge regression and its degrees of freedom

Author

Listed:
  • Theo Dijkstra

Abstract

For ridge regression the degrees of freedom are commonly calculated by the trace of the matrix that transforms the vector of observations on the dependent variable into the ridge regression estimate of its expected value. For a fixed ridge parameter this is unobjectionable. When the ridge parameter is optimized on the same data, by minimization of the generalized cross validation criterion or Mallows $$\hbox {C}_{L}$$ C L , additional degrees of freedom are used however. We give formulae that take this into account. This allows of a proper assessment of ridge regression in competitions for the best predictor. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • Theo Dijkstra, 2014. "Ridge regression and its degrees of freedom," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3185-3193, November.
    • Handle: RePEc:spr:qualqt:v:48:y:2014:i:6:p:3185-3193
    DOI: 10.1007/s11135-013-9949-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11135-013-9949-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11135-013-9949-7?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. Bradley Efron, 2004. "The Estimation of Prediction Error: Covariance Penalties and Cross-Validation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 619-632, January.
    2. Paul Anand & Graham Hunter & Ian Carter & Keith Dowding & Francesco Guala & Martin Van Hees, 2009. "The Development of Capability Indicators," Journal of Human Development and Capabilities, Taylor & Francis Journals, vol. 10(1), pages 125-152.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Massimiliano Giacalone & Demetrio Panarello & Raffaele Mattera, 2018. "Multicollinearity in regression: an efficiency comparison between Lp-norm and least squares estimators," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1831-1859, July.
    2. Stefania Corsaro & Valentina De Simone & Zelda Marino & Salvatore Scognamiglio, 2024. "Learning fused lasso parameters in portfolio selection via neural networks," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(5), pages 4281-4299, October.
    3. Minda Ma & Ran Yan & Weiguang Cai, 2017. "An extended STIRPAT model-based methodology for evaluating the driving forces affecting carbon emissions in existing public building sector: evidence from China in 2000–2015," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 89(2), pages 741-756, November.
    4. Ma, Minda & Cai, Wei & Cai, Weiguang, 2018. "Carbon abatement in China's commercial building sector: A bottom-up measurement model based on Kaya-LMDI methods," Energy, Elsevier, vol. 165(PA), pages 350-368.

    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. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    2. Anand, Paul & Lea, Stephen, 2011. "The psychology and behavioural economics of poverty," Journal of Economic Psychology, Elsevier, vol. 32(2), pages 284-293, March.
    3. Yang, Lin, 2017. "The relationship between poverty and inequality: concepts and measurement," LSE Research Online Documents on Economics 103491, London School of Economics and Political Science, LSE Library.
    4. Martin Binder, 2014. "Subjective Well-Being Capabilities: Bridging the Gap Between the Capability Approach and Subjective Well-Being Research," Journal of Happiness Studies, Springer, vol. 15(5), pages 1197-1217, October.
    5. Leßmann, Ortrud, 2011. "Empirische Studien zum Capability Ansatz auf der Grundlage von Befragungen: Ein Überblick," UFZ Discussion Papers 4/2011, Helmholtz Centre for Environmental Research (UFZ), Division of Social Sciences (ÖKUS).
    6. Sieds, 2012. "Complete Volume LXVI n.1 2012," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 66(1), pages 1-296.
    7. Polly Vizard, 2010. "Developing and agreeing a capability list in the British context: What can be learnt from social survey data on ‘rights’?," CASE Papers case142, Centre for Analysis of Social Exclusion, LSE.
    8. Robert A. Cummins & Kenneth C. Land, 2018. "Capabilities, Subjective Wellbeing and Public Policy: A Response to Austin (2016)," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 140(1), pages 157-173, November.
    9. Paul Anand & Laurence S. J. Roope & Anthony J. Culyer & Ron Smith, 2020. "Disability and multidimensional quality of life: A capability approach to health status assessment," Health Economics, John Wiley & Sons, Ltd., vol. 29(7), pages 748-765, July.
    10. Mamatzakis, Emmanuel C. & Tsionas, Mike G., 2021. "Making inference of British household's happiness efficiency: A Bayesian latent model," European Journal of Operational Research, Elsevier, vol. 294(1), pages 312-326.
    11. Jyotishka Datta & Nicholas G. Polson, 2025. "Polynomial Log-Marginals and Tweedie's Formula : When Is Bayes Possible?," Papers 2509.05823, arXiv.org, revised Jan 2026.
    12. Harry G. Barkema & Uta K. Bindl & Lamees Tanveer, 2024. "How Entrepreneurs Achieve Purpose Beyond Profit: The Case of Women Entrepreneurs in Nigeria," Organization Science, INFORMS, vol. 35(3), pages 1042-1071, May.
    13. Simon, Judit & Anand, Paul & Gray, Alastair & Rugkåsa, Jorun & Yeeles, Ksenija & Burns, Tom, 2013. "Operationalising the capability approach for outcome measurement in mental health research," Social Science & Medicine, Elsevier, vol. 98(C), pages 187-196.
    14. Micael Dahlen & Helge Thorbjørnsen, 2022. "Individuals’ Assessments of Their Own Wellbeing, Subjective Welfare, and Good Life: Four Exploratory Studies," IJERPH, MDPI, vol. 19(19), pages 1-10, September.
    15. Hojman, Daniel A. & Miranda, Álvaro, 2018. "Agency, Human Dignity, and Subjective Well-being," World Development, Elsevier, vol. 101(C), pages 1-15.
    16. Cleofas, Jerome Visperas, 2023. "Internet access as a moderator of mental health and satisfaction with life during the COVID-19 pandemic: Evidence from young Filipino undergraduates from income-poor households," Children and Youth Services Review, Elsevier, vol. 155(C).
    17. Yalu Zhang & Qin Gao & Fuhua Zhai & Paul Anand, 2023. "Income and Health in Predicting Older Adults’ Social Capabilities in China: The Mediating Role of Social Engagement," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 165(1), pages 163-180, January.
    18. Younker, James, 2025. "Calculating effective degrees of freedom for forecast combinations and ensemble models," Economics Letters, Elsevier, vol. 247(C).
    19. Delhey, Jan & Steckermeier, Leonie C., 2016. "The Good Life, Affluence, and Self-reported Happiness: Introducing the Good Life Index and Debunking Two Popular Myths," World Development, Elsevier, vol. 88(C), pages 50-66.
    20. Ángeles Sánchez & Jorge Chica-Olmo & Juan de Dios Jiménez-Aguilera, 2018. "A Space–Time Study for Mapping Quality of Life in Andalusia During the Crisis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 135(2), pages 699-728, 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:spr:qualqt:v:48:y:2014:i:6:p:3185-3193. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.