If explanatory variables and a response variable of interest are simultaneously observed, then multivariate models based on vine pair-copula constructions can be fit, from which inferences are based on the conditional distribution of the response variable given the explanatory variables.

For applications, there are things to consider when implementing this idea. Topics include: (a) inclusion of categorical predictors; (b) right-censored response variable; (c) for a pair with one ordinal and one continuous variable, diagnostics for copula choice and assessing fit of copula; (d) use of empirical beta copula; (e) performance metrics for prediction/classification and sensitivity to choice of vine structure and pair-copulas on edges of vine; (f) weighted log-likelihood for ordinal response variable; (g) comparisons with linear regression methods.