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

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.