@article { ISI:000351843300007,
	title = {Factor copula models for item response data},
	journal = {Psychometrika},
	volume = {80},
	number = {1},
	year = {2015},
	month = {MAR},
	pages = {126-150},
	publisher = {Springer},
	type = {Article},
	abstract = {Factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses. 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 (or multidimensional normal ogive model). Details on maximum likelihood estimation of parameters for the factor copula model are given, as well as analysis of the behavior of the log-likelihood. Our general methodology is illustrated with several item response data sets, and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data.},
	keywords = {Conditional independence, factor model dependence structure, latent variable model, limited information, Partial correlation},
	issn = {0033-3123},
	doi = {10.1007/s11336-013-9387-4},
	author = {Nikoloulopoulos, Aristidis K. and Joe, Harry}
}
@article { ISI:000355774000005,
	title = {Structured factor copula models: Theory, inference and computation},
	journal = {Journal of Multivariate Analysis},
	volume = {138},
	number = {SI},
	year = {2015},
	month = {JUN},
	pages = {53-73},
	publisher = {Elsevier Inc},
	type = {Article},
	abstract = {In factor copula models for multivariate data, dependence is explained via one or several common factors. These models are flexible in handling tail dependence and asymmetry with parsimonious dependence structures. We propose two structured factor copula models for the case where variables can be split into non-overlapping groups such that there is homogeneous dependence within each group. A typical example of such variables occurs for stock returns from different sectors. The structured models inherit most of dependence properties derived for common factor copula models. With appropriate numerical methods, efficient estimation of dependence parameters is possible for data sets with over 100 variables. We apply the structured factor copula models to analyze a financial data set, and compare with other copula models for tail inference. Using model-based interval estimates, we find that some commonly used risk measures may not be well discriminated by copula models, but tail-weighted dependence measures can discriminate copula models with different dependence and tail properties. (C) 2014 Elsevier Inc. All rights reserved.},
	keywords = {Bi-factor model, Conditional independence, Dependence measure, Factor analysis, Tail asymmetry, Tail dependence, Truncated vine},
	issn = {0047-259X},
	doi = {10.1016/j.jmva.2014.11.002},
	author = {Krupskii, Pavel and Joe, Harry}
}
@article { ISI:000322290500006,
	title = {Factor copula models for multivariate data},
	journal = {Journal of Multivariate Analysis},
	volume = {120},
	year = {2013},
	month = {SEP},
	pages = {85-101},
	publisher = {Elsevier Inc},
	type = {Article},
	abstract = {General conditional independence models ford observed variables, in terms of p latent variables, are presented in terms of bivariate copulas that link observed data to latent variables. The representation is called a factor copula model and the classical multivariate normal model with a correlation matrix having a factor structure is a special case. Dependence and tail properties of the model are obtained. The factor copula model can handle multivariate data with tail dependence and tail asymmetry, properties that the multivariate normal copula does not possess. It is a good choice for modeling high-dimensional data as a parametric form can be specified to have O(d) dependence parameters instead of O(d(2)) parameters. Data examples show that, based on the Akaike information criterion, the factor copula model provides a good fit to financial return data, in comparison with related truncated vine copula models. (C) 2013 Elsevier Inc. All rights reserved.},
	keywords = {Conditional independence, Factor analysis, Pair-copula construction, Partial correlation, Tail asymmetry, Tail dependence, Truncated vine},
	issn = {0047-259X},
	doi = {10.1016/j.jmva.2013.05.001},
	author = {Krupskii, Pavel and Joe, Harry}
}
