Day 3

9:30 Copula modelling for discrete data

We suggest  models that admit a wide range of dependence, such as the multivariate normal (MVN) copula (Nikoloulopoulos, 2013a,2013b,2016).Given its wide range of dependence, MVN copula provides often the best fit or nearly the best fit  for discrete data (Nikoloulopoulos et al., 2011).  However MVN copula is inadequate to model multivariate data with refection asymmetry or tail dependence (Nikoloulopoulos et al., 2012).  Vine copula constructions are suitable for modelling this kind of data since by using as bivariate blocks asymmetric bivariate copulas tail asymmetry can be accommodated, i.e., more probability in one or both joint tails can be obtained (Panagiotelis et al., 2012).

11:00 Coffee/Tea and Refreshments

11:30 Factor copula models

Factor models based on copulas are proposed for multivariate discrete data (Nikoloulopoulos and Joe, 2015). The factor copula models have interpretations of latent maxima/minima (in comparison with latent means) and can lead to more probability in the joint upper or lower tail compared with factor models based on the discretized multivariate normal distribution.

13:00 Lunch

14:00 Copula modelling for discrete in practice

This talk fits MVN, vine and factor copula models to real multivariate discrete response data in  the R package CopulaModel (Joe and Krupskii, 2014).

16:00 Close


  • Joe, H. and Krupskii, P. (2014). CopulaModel: Dependence Modeling with Copulas. R package version 0.6. 
  • Nikoloulopoulos, A. K. (2013a). Copula-based models for multivariate discrete response data. In Durante, F., Ha¨rdle, W., and Jaworski, P., editors, Copulae in Mathematical and Quantitative Finance, pages 231–249. Springer.
  • Nikoloulopoulos, A. K. (2013b). On the estimation of normal copula discrete regression models using the continuous extension and simulated likelihood. Journal of Statistical Planning and Inference, 143:1923–1937.
  • Nikoloulopoulos, A. K., Joe, H., and Chaganty, N. R. (2011). Weighted scores method for regression models with dependent data. Biostatistics, 12:653–665.
  • Nikoloulopoulos, A.K. (2016). Efficient estimation of high-dimensional multivariate normal copula models with discrete spatial responses in Stochastic Environmental Research and Risk Assessment, 30: 493-505
  • Nikoloulopoulos, A.K. and Joe, H. (2015) Factor copula models for item response data. Psychometrika, 80:126-150
  • Nikoloulopoulos, A. K., Joe, H., and Li, H. (2012). Vine copulas with asymmetric tail dependence and applications to financial return data. Computational Statistics and Data Analysis, 56:3659–3673.
  • Panagiotelis, A., Czado, C., and Joe, H. (2012). Pair copula constructions for multivariate discrete data. Journal of the American Statistical Association, 107:1063–1072.