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

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  • 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
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    References listed on IDEAS

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    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. 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.
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