Copula Models and Methods

This research area focuses on the development of multivariate copula-based models and inference procedures for non-normal multivariate/longitudinal response data.

Multivariate/longitudinal response data abound in many application areas including insurance, risk management, finance, biology, psychometrics, health and environmental sciences. Data from these application areas have different dependence structures including features such as tail dependence. Studying dependence among multivariate response data is an interesting problem in statistical science. The dependence between random variables is completely described by their multivariate distribution. When the multivariate distribution has a simple form, standard methods can be used to make inference. On the other hand one may create multivariate distributions based on particular assumptions, limiting thus their use. For example, most existing models assume rigid margins of the same form (e.g., Gaussian, Student, exponential, Gamma, Poisson, etc.) or limited dependence (e.g., tail independence, positive dependence, etc.). To solve this problem we use copulas (multivariate distributions with uniform margins). Copulas are unified way to model multivariate response data, as they account for the dependence structure and provide a flexible representation of the multivariate distribution. They allow for general dependence modelling, different from assuming simple linear correlation structures and normality. That makes them particularly well suited to the aforementioned application areas.

Specific situations where we have made use of copulas include: (i) models and inference procedures for repeated measures or multivariate discrete (binary, ordinal, count) response in biostatistical, environmental and econometrical applications; (ii) factor copula models for survey data; (iii) vine copula-GARCH models for financial returns; (iv) copula-mixed models for meta-analysis of diagnostic test accuracy studies.

We are committed to making our methods available to the research community. Hence, our methods are disseminated through publicly available software that implements the proposed methodologies. The following R packages are available at the OpenSource R project for statistical computing (see http://cran.r-project.org):

CopulaREMADA [CopulaREMADA on CRAN] [monthly downloads for CopulaREMADA]

FactorCopula [FactorCopula on CRAN] [monthly downloads for FactorCopula]

weightedScores [weightedScores on CRAN] [monthly downloads weightedScores]

References

Kadhem, Sayed H. and Nikoloulopoulos, Aristidis K (2020) Factor copula models for mixed data. British Journal of Mathematical and Statistical Psychology. ISSN 0007-1102 (In Press)
Nikoloulopoulos, Aristidis K (2020) An extended trivariate vine copula mixed model for meta-analysis of diagnostic studies in the presence of non-evaluable outcomes. International Journal of Biostatistics, 16 (2). ISSN 1557-4679
Nikoloulopoulos, Aristidis K (2020) A multinomial quadrivariate D-vine copula mixed model for meta-analysis of diagnostic studies in the presence of non-evaluable subjects. Statistical Methods in Medical Research, 29 (10). pp. 2988-3005. ISSN 0962-2802
Nikoloulopoulos, Aristidis K (2020) Weighted scores estimating equations and CL1 information criteria for longitudinal ordinal response. Journal of Statistical Computation and Simulation, 90 (11). pp. 2002-2022. ISSN 0094-9655
Nikoloulopoulos, Aristidis K. (2019) A D-vine copula mixed model for joint meta-analysis and comparison of diagnostic tests. Statistical Methods in Medical Research, 28 (10-11). pp. 3286-3300. ISSN 0962-2802
Nikoloulopoulos, Aristidis K. and Moffatt, Peter (2019) Coupling couples with copulas: analysis of assortative matching on risk attitude. Economic Inquiry, 57 (1). pp. 654-666. ISSN 0095-2583
Nikoloulopoulos, Aristidis K. (2018) Hybrid copula mixed models for combining case-control and cohort studies in meta-analysis of diagnostic tests. Statistical Methods in Medical Research, 27 (8). pp. 2540-2553. ISSN 0962-2802
Nikoloulopoulos, Aristidis K. (2018) On composite likelihood in bivariate meta-analysis of diagnostic test accuracy studies. AStA Advances in Statistical Analysis, 102 (2). pp. 211-227. ISSN 1863-8171
Nikoloulopoulos, Aristidis K (2017) A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence. Statistical Methods in Medical Research, 26 (5). pp. 2270-2286. ISSN 1477-0334
Nikoloulopoulos, Aristidis K. (2016) Correlation structure and variable selection in generalized estimating equations via composite likelihood information criteria. Statistics in Medicine, 35 (14). pp. 2377-2390. ISSN 0277-6715
Nikoloulopoulos, Aristidis K. (2016) Comment on ‘A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence’. Statistical Methods in Medical Research, 25 (2). 988–991. ISSN 0962-2802
Nikoloulopoulos, Aristidis K (2016) Efficient estimation of high-dimensional multivariate normal copula models with discrete spatial responses. Stochastic Environmental Research and Risk Assessment, 30 (2). pp. 493-505. ISSN 1436-3240
Nikoloulopoulos, Aristidis K (2015) A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution. Statistics in Medicine, 34 (29). pp. 3842-3865. ISSN 0277-6715
Nikoloulopoulos, Aristidis K and Joe, H (2015) Factor copula models for item response data. Psychometrika, 80 (1). pp. 126-150. ISSN 0033-3123
Nikoloulopoulos, Aristidis K (2013) On the estimation of normal copula discrete regression models using the continuous extension and simulated likelihood. Journal of Statistical Planning and Inference, 143 (11). pp. 1923-1937. ISSN 0378-3758
Nikoloulopoulos, Aristidis K (2013) Copula-based models for multivariate discrete response data. In: Copulae in Mathematical and Quantitative Finance, Lecture Notes in Statistics. Springer-Verlag Berlin Heidelberg, pp. 231-249.
Genest, Christian, Nikoloulopoulos, Aristidis K., Rivest, Louis-Paul and Fortin, Mathieu (2013) Predicting dependent binary outcomes through logistic regressions and meta-elliptical copulas.Brazilian Journal of Probability and Statistics, 27 (3). pp. 265-284.
Nikoloulopoulos, Aristidis K., Joe, Harry and Li, Haijun (2012) Vine copulas with asymmetric tail dependence and applications to financial return data. Computational Statistics and Data Analysis, 56 (11). pp. 3659-3673.
Nikoloulopoulos, Aristidis K (2012) Comment on "Two-dimensional toxic dose and multivariate logistic regression, with application to decompression sickness" by Li, J. and Wong, W.K.Biostatistics, 13 (1). pp. 1-3. ISSN 1468-4357
Nikoloulopoulos, Aristidis K., Joe, Harry and Chaganty, N. Rao (2011) Weighted scores method for regression models with dependent data. Biostatistics, 12 (4). pp. 653-665. ISSN 1468-4357
Joe, Harry, Li, Haijun and Nikoloulopoulos, Aristidis K (2010) Tail dependence functions and vine copulas. Journal of Multivariate Analysis, 101 (1). pp. 252-270.
Nikoloulopoulos, Aristidis K and Karlis, D (2010) Modeling multivariate count data using copulas. Communications in Statistics: Simulation and Computation, 39 (1). pp. 172-187. ISSN 1532-4141
Nikoloulopoulos, Aristidis K and Karlis, Dimitris (2009) Finite normal mixture copulas for multivariate discrete data modeling. Journal of Statistical Planning and Inference, 139 (11). pp. 3878-3890.
Nikoloulopoulos, Aristidis K, Joe, Harry and Li, Haijun (2009) Extreme value properties of multivariate t copulas. Extremes, 12 (2). pp. 129-148.
Nikoloulopoulos, Aristidis K and Karlis, D (2008) Multivariate logit copula model with an application to dental data. Statistics in Medicine, 27 (30). pp. 6393-6406. ISSN 1097-0258
Nikoloulopoulos, Aristidis K and Karlis, D (2008) Fitting copulas to bivariate earthquake data: the seismic gap hypothesis revisited. Environmetrics, 19 (3). pp. 251-269. ISSN 1099-095X
Nikoloulopoulos, Aristidis K and Karlis, D (2008) Copula model evaluation based on parametric bootstrap. Computational Statistics and Data Analysis, 52 (7). pp. 3342-3353.
Nikoloulopoulos, Aristidis K and Karlis, D (2008) On modeling count data: a comparison of some well-known discrete distributions. Journal of Statistical Computation and Simulation, 78 (3). pp. 437-457. ISSN 1563-5163

Research Team

Dr. Aristidis K. Nikoloulopoulos, Mr. Sayed H. Kadhem