FactorCopula-package {FactorCopula}

Factor, bi-factor, second-order and factor tree copula models

Description

Estimation, model selection and goodness-of-fit of (1) factor copula models for mixed continuous and discrete data in Kadhem and Nikoloulopoulos (2021); (2) bi-factor and second-order copula models for item response data in Kadhem and Nikoloulopoulos (2023); (3) factor tree copula models for item response data in Kadhem and Nikoloulopoulos (2022).

Details

This package contains R functions for:

• diagnostics based on semi-correlations (Kadhem and Nikoloulopoulos, 2021, 2023; Joe, 2014) to detect tail dependence or tail asymmetry;

• diagnostics to show that a dataset has a factor structure based on linear factor analysis (Kadhem and Nikoloulopoulos, 2021,2023; Joe, 2014);

• estimation of the factor copula models in Krupskii and Joe (2013), Nikoloulopoulos and Joe (2015), and Kadhem and Nikoloulopoulos (2021);

• estimation of the bi-factor and second-order copula models for item response data in Kadhem and Nikoloulopoulos (2023);

• estimation of the factor tree copula models for item response data in Kadhem and Nikoloulopoulos (2022);

• model selection of the factor copula models in Krupskii and Joe (2013), Nikoloulopoulos and Joe (2015);

• model selection of the bifactor and second-order copula models in Kadhem and Nikoloulopoulos (2023);

• model selection of the factor tree copula models in Kadhem and Nikoloulopoulos (2022);

• goodness-of-fit of the factor copula models in Krupskii and Joe (2013), Nikoloulopoulos and Joe (2015), and Kadhem and Nikoloulopoulos (2021) using the M_2 statistic (Maydeu-Olivares and Joe, 2006). Note that the continuous and count data have to be transformed to ordinal;

• goodness-of-fit of the bi-factor and second-order copula models in Kadhem and Nikoloulopoulos (2023) using the M_2 statistic (Maydeu-Olivares and Joe, 2006).

Author(s)

Sayed H. Kadhem
Aristidis K. Nikoloulopoulos [e-mail]

References

Joe, H. (2014). Dependence Modelling with Copulas. Chapman & Hall, London.

Maydeu-Olivares, A. and Joe, H. (2006). Limited information goodness-of-fit testing in multidimensional contingency tables. Psychometrika, 71, 713–732. doi:10.1007/s11336-005-1295-9.

Kadhem, S.H. and Nikoloulopoulos, A.K. (2021) Factor copula models for mixed data. British Journal of Mathematical and Statistical Psychology, 74, 365–403. doi:10.1111/bmsp.12231.

Kadhem, S.H. and Nikoloulopoulos, A.K. (2023) Bi-factor and second-order copula models for item response data. Psychometrika, 88, 132–157. doi:10.1007/s11336-022-09894-2.

Kadhem, S.H. and Nikoloulopoulos, A.K. (2022) Factor tree copula models for item response data. Arxiv e-prints, <arXiv: 2201.00339>. https://arxiv.org/abs/2201.00339.

Krupskii, P. and Joe, H. (2013) Factor copula models for multivariate data. Journal of Multivariate Analysis, 120, 85–101. doi:10.1016/j.jmva.2013.05.001.

Nikoloulopoulos, A.K. and Joe, H. (2015) Factor copula models with item response data. Psychometrika, 80, 126–150. doi:10.1007/s11336-013-9387-4.