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).
Sayed H. Kadhem
Aristidis K. Nikoloulopoulos a.nikoloulopoulos@uea.ac.uk
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).
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. tools:::Rd_expr_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. tools:::Rd_expr_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. tools:::Rd_expr_doi("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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1007/s11336-013-9387-4").