@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:000355774000003,
	title = {Truncation of vine copulas using fit indices},
	journal = {Journal of Multivariate Analysis},
	volume = {138},
	number = {SI},
	year = {2015},
	month = {JUN},
	pages = {19-33},
	publisher = {Elsevier Inc},
	type = {Article},
	abstract = {Vine copulas are flexible multivariate dependence models, which are built up from a set of bivariate copulas in different hierarchical levels. However, vine copulas have a computational complexity that is increasing quadratically in the number of variables. This complexity can be reduced by focusing on the sub-class of truncated vine copulas, which use only a limited number of hierarchical levels. We propose a new approach to select the adequate number of levels, such that the vine copula is still sufficiently flexible to provide a good fit to given data. The approach is based on fit indices, as used for structural equation models, to measure the goodness of a fitted truncated model. To select such truncated models, we propose methods to effectively explore the search space of truncated vine copulas, so that we are able to improve over previous greedy sequential approaches that optimized over one tree of the vine at each step. This new selection approach is evaluated in a simulation study as well as in two applications to data sets of financial returns. (C) 2015 Elsevier Inc. All rights reserved.},
	keywords = {Fit index, Partial correlation, Truncated vine, Vine copula},
	issn = {0047-259X},
	doi = {10.1016/j.jmva.2015.02.012},
	author = {Brechmann, Eike C. 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}
}
@article { ISI:000275680500009,
	title = {Generating random correlation matrices based on vines and extended onion method},
	journal = {Journal of Multivariate Analysis},
	volume = {100},
	number = {9},
	year = {2009},
	month = {OCT},
	pages = {1989-2001},
	publisher = {Elsevier Inc},
	type = {article},
	abstract = {We extend and improve two existing methods of generating random correlation matrices, the onion method of Ghosh and Henderson [S. Ghosh, S.C. Henderson, Behavior of the norta method for correlated random vector generation as the dimension increases, ACM Transactions on Modeling and Computer Simulation (TOMACS) 13 (3) (2003) 276-294] and the recently proposed method of Joe [H. Joe, Generating random correlation matrices based on partial correlations, journal of Multivariate Analysis 97 (2006) 2177-2189] based on partial correlations. The latteris based on the so-called D-vine. We extend the methodology to any regular vine and study the relationship between the multiple correlation and partial correlations on a regular vine. We explain the onion method in terms of elliptical distributions and extend it to allow generating random correlation matrices from the same joint distribution as the vine method. The methods are compared in terms of time necessary to generate 5000 random correlation matrices of given dimensions. (C) 2009 Elsevier Inc. All rights reserved.},
	keywords = {Correlation matrix, Dependence vines, Onion method, Partial correlation},
	issn = {0047-259X},
	doi = {10.1016/j.jmva.2009.04.008},
	author = {Lewandowski, Daniel and Kurowicka, Dorota and Joe, Harry}
}
@conference { ISI:000238122900008,
	title = {Range of correlation matrices for dependent random variables with given marginal distributions},
	booktitle = {Advances in Distribution Theory, Order Statistics, and Inference},
	series = {Statistics for Industry and Technology},
	year = {2006},
	note = {International Conference on Distribution Theory, Order Statistics, and Inference, Univ Cantabria, Santander, SPAIN, JUN 16-18, 2004},
	pages = {125-142},
	publisher = {Birkhauser Boston},
	organization = {Birkhauser Boston},
	type = {Proceedings Paper},
	abstract = {Let X-1, center dot center dot center dot, X-d be d (d >= 3) dependent random variables with finite variances such that X-j similar to F-j. Results on the set S-d(F-1, center dot center dot center dot, F-d) of possible correlation matrices with given margins are obtained; this set is relevant for simulating dependent random variables with given marginal distributions and a given correlation matrix. When F-1 = (...) = F-d = F, we let S-d(F) denote the set of possible correlation matrices. Of interest is the set of F for which Sd(F) is the same as the set of all non-negative definite correlation matrices; using a construction with conditional distributions, we show that this property holds only if F is a (location-scale shift of a) margin of a (d-1)-dimensional spherical distribution.},
	keywords = {Copula, elliptically contoured, Frechet bounds, Partial correlation, spherically symmetric},
	isbn = {0-8176-4361-3},
	doi = {10.1007/0-8176-4487-3_8},
	author = {Joe, Harry},
	editor = {Balakrishnan, N and Castillo, E and Sarabia, J. M.}
}
