IDEAS home Printed from https://ideas.repec.org/a/sae/somere/v46y2017i3p604-648.html
   My bibliography  Save this article

Copula Models for Sociology: Measures of Dependence and Probabilities for Joint Distributions

Author

Listed:
  • Mike Vuolo

Abstract

Often in sociology, researchers are confronted with nonnormal variables whose joint distribution they wish to explore. Yet, assumptions of common measures of dependence can fail or estimating such dependence is computationally intensive. This article presents the copula method for modeling the joint distribution of two random variables, including descriptions of the method, the most common copula distributions, and the nonparametric measures of association derived from the models. Copula models, which are estimated by standard maximum likelihood techniques, make no assumption about the form of the marginal distributions, allowing consideration of a variety of models and distributions in the margins and various shapes for the joint distribution. The modeling procedure is demonstrated via a simulated example of spousal mortality and empirical examples of (1) the association between unemployment and suicide rates with time series models and (2) the dependence between a count variable (days drinking alcohol) and a skewed, continuous variable (grade point average) while controlling for predictors of each using the National Longitudinal Survey of Youth 1997. Other uses for copulas in sociology are also described.

Suggested Citation

  • Mike Vuolo, 2017. "Copula Models for Sociology: Measures of Dependence and Probabilities for Joint Distributions," Sociological Methods & Research, , vol. 46(3), pages 604-648, August.
  • Handle: RePEc:sae:somere:v:46:y:2017:i:3:p:604-648
    DOI: 10.1177/0049124115584477
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0049124115584477
    Download Restriction: no

    File URL: https://libkey.io/10.1177/0049124115584477?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. Heinen, Andréas & Rengifo, Erick, 2008. "Multivariate reduced rank regression in non-Gaussian contexts, using copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2931-2944, February.
    2. Junker, Markus & Szimayer, Alex & Wagner, Niklas, 2006. "Nonlinear term structure dependence: Copula functions, empirics, and risk implications," Journal of Banking & Finance, Elsevier, vol. 30(4), pages 1171-1199, April.
    3. Heinen, Andreas & Rengifo, Erick, 2007. "Multivariate autoregressive modeling of time series count data using copulas," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 564-583, September.
    4. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 566-584, December.
    5. Kojadinovic, Ivan & Yan, Jun, 2010. "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i09).
    6. Zimmer, David M. & Trivedi, Pravin K., 2006. "Using Trivariate Copulas to Model Sample Selection and Treatment Effects: Application to Family Health Care Demand," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 63-76, January.
    7. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 566-584, December.
    8. Murray D. Smith, 2005. "Using Copulas to Model Switching Regimes with an Application to Child Labour," The Economic Record, The Economic Society of Australia, vol. 81(s1), pages 47-57, August.
    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. Chandra Bhat & Ipek Sener, 2009. "A copula-based closed-form binary logit choice model for accommodating spatial correlation across observational units," Journal of Geographical Systems, Springer, vol. 11(3), pages 243-272, September.
    2. Bhat, Chandra R. & Eluru, Naveen, 2009. "A copula-based approach to accommodate residential self-selection effects in travel behavior modeling," Transportation Research Part B: Methodological, Elsevier, vol. 43(7), pages 749-765, August.
    3. Eugenio J. Miravete, 2009. "Competing with Menus of Tariff Options," Journal of the European Economic Association, MIT Press, vol. 7(1), pages 188-205, March.
    4. Tzougas, George & Makariou, Despoina, 2022. "The multivariate Poisson-Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," LSE Research Online Documents on Economics 117197, London School of Economics and Political Science, LSE Library.
    5. Pravin Trivedi & David Zimmer, 2017. "A Note on Identification of Bivariate Copulas for Discrete Count Data," Econometrics, MDPI, vol. 5(1), pages 1-11, February.
    6. Prokhorov, Artem & Schmidt, Peter, 2009. "Likelihood-based estimation in a panel setting: Robustness, redundancy and validity of copulas," Journal of Econometrics, Elsevier, vol. 153(1), pages 93-104, November.
    7. Hasebe, Takuya & Vijverberg, Wim P., 2012. "A Flexible Sample Selection Model: A GTL-Copula Approach," IZA Discussion Papers 7003, Institute of Labor Economics (IZA).
    8. Mothafer, Ghasak I.M.A. & Yamamoto, Toshiyuki & Shankar, Venkataraman N., 2018. "A multivariate heterogeneous-dispersion count model for asymmetric interdependent freeway crash types," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 84-105.
    9. Liang Peng & Yongcheng Qi & Ingrid Van Keilegom, 2012. "Jackknife empirical likelihood method for copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 74-92, March.
    10. Chen, Jian & Peng, Liang & Zhao, Yichuan, 2009. "Empirical likelihood based confidence intervals for copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 137-151, January.
    11. Eugenio Miravete, 2014. "Testing for complementarities among countable strategies," Empirical Economics, Springer, vol. 46(4), pages 1521-1544, June.
    12. Jörg Schwiebert, 2016. "Multinomial choice models based on Archimedean copulas," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 333-354, July.
    13. Wanling Huang & Artem Prokhorov, 2014. "A Goodness-of-fit Test for Copulas," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 751-771, October.
    14. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2008. "A multivariate integer count hurdle model: theory and application to exchange rate dynamics," Studies in Empirical Economics, in: Luc Bauwens & Winfried Pohlmeier & David Veredas (ed.), High Frequency Financial Econometrics, pages 31-48, Springer.
    15. Siem Jan Koopman & Rutger Lit & André Lucas & Anne Opschoor, 2018. "Dynamic discrete copula models for high‐frequency stock price changes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 966-985, November.
    16. John Mullahy, 2017. "Individual Results May Vary: Elementary Analytics of Inequality-Probability Bounds, with Applications to Health-Outcome Treatment Effects," NBER Working Papers 23603, National Bureau of Economic Research, Inc.
    17. Stanislav Anatolyev & Nikolay Gospodinov, 2007. "Modeling Financial Return Dynamics by Decomposition," Working Papers w0095, New Economic School (NES).
    18. Lin, Zhongjian & Hu, Yingyao, 2024. "Binary choice with misclassification and social interactions, with an application to peer effects in attitude," Journal of Econometrics, Elsevier, vol. 238(1).
    19. So, Sunha & Lee, Dong-Hee & Jung, Byoung Cheol, 2011. "An alternative bivariate zero-inflated negative binomial regression model using a copula," Economics Letters, Elsevier, vol. 113(2), pages 183-185.
    20. Fantazzini, Dean, 2008. "Econometric Analysis of Financial Data in Risk Management (continuation). Section III: Managing Operational Risk," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 11(3), pages 87-122.

    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:46:y:2017:i:3:p:604-648. 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.