Many social science datasets consist of multivariate measurements of different types. For example, a survey may record the sex, education level and income of its participants, thus including measurements that we may consider binary, ordinal and continuous. Two approaches to the analysis of such data include parametric model-based inference and scale-free measures of association. Unfortunately, the former approach is limited in terms of its appropriateness, and the latter is limited in terms of its usefulness.
An old result from statistics says that every multivariate probability distribution can be decomposed into its univariate marginal distributions and a copula, which is a type of joint distribution on the unit cube. In this talk I will discuss the use of such a decomposition for the analysis of multivariate data, in which we can model the marginal distributions of the data nonparametrically, and capture the associations among the variables with the copula. Applications to prediction, imputation and regression will be provided.
