Analysis of Multivariate Binary Data Using D-Vine Copula Model

Music City Center 

Multivariate binary data arise in various scientific fields. The Multivariate Probit (MP) model is widely used for analyzing such data. However, it can fail even within a feasible range of binary variable correlations due to its requirement for a positive definite latent correlation matrix. To address this limitation, we propose a pair copula model using D-vine with an assumed dependence structure of either first-order autoregressive or equicorrelation, which overcomes the difficulties associated with the MP model. Our presentation begins with introducing copulas and discussing the differences between D-vine and C-vine pair copula models. We present visualizations illustrating the relationship between the copula parameter and the binary variable correlation coefficient. We then derive the probability mass function (PMF) for bivariate and trivariate binary variables and provide numerical examples. Finally, we present an application of our model to a real-life dataset analysis.

Multivariate Binary

Copula

D-Vine 

International Indian Statistical Association