Vine copulas for imputation of monotone non-response

Monotone patterns of non-response may occur in longitudinal studies. When the measured variables are dependent it is beneficial to use their joint statistical model to impute the missing values. We propose to use vine copulas to factorize the density of the observed variables into a cascade of bivariate copulas that yield a flexible model of their joint distribution. The structure of the vine depends on the non-response pattern. We build on the work of Aas et al. (2009) and propose a method to select the model, to estimate the parameters of the bivariate copulas of the selected model, and to impute using the constructed model. The imputed values are drawn from the conditional distribution of the missing values, given the observed data. We discuss the generalization of our results to more global non-response patterns.