R package bfa Bayesian Gaussian copula factor models for mixed data. Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models accommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables, the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem, we propose a novel class of Bayesian Gaussian copula factor models that decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this article are implemented in the R package bfa (available from {it}). Supplementary materials for this article are available online.

References in zbMATH (referenced in 20 articles , 1 standard article )

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  1. Lee, Woojoo; Kim, Jeonghwan; Ahn, Jae Youn: The Poisson random effect model for experience ratemaking: limitations and alternative solutions (2020)
  2. Bashir, Amir; Carvalho, Carlos M.; Hahn, P. Richard; Jones, M. Beatrix: Post-processing posteriors over precision matrices to produce sparse graph estimates (2019)
  3. Cui, Ruifei; Bucur, Ioan Gabriel; Groot, Perry; Heskes, Tom: A novel Bayesian approach for latent variable modeling from mixed data with missing values (2019)
  4. Cui, Ruifei; Groot, Perry; Heskes, Tom: Learning causal structure from mixed data with missing values using Gaussian copula models (2019)
  5. Gunawan, D.; Tran, M.-N.; Suzuki, K.; Dick, J.; Kohn, R.: Computationally efficient Bayesian estimation of high-dimensional Archimedean copulas with discrete and mixed margins (2019)
  6. Klein, Nadja; Smith, Michael Stanley: Implicit copulas from Bayesian regularized regression smoothers (2019)
  7. Maleki, Mohsen; Wraith, Darren: Mixtures of multivariate restricted skew-normal factor analyzer models in a Bayesian framework (2019)
  8. Manner, Hans; Stark, Florian; Wied, Dominik: Testing for structural breaks in factor copula models (2019)
  9. Müller, Dominik; Czado, Claudia: Dependence modelling in ultra high dimensions with vine copulas and the graphical lasso (2019)
  10. Edgar Merkle; Yves Rosseel: blavaan: Bayesian Structural Equation Models via Parameter Expansion (2018) not zbMATH
  11. Zhao, Shiwen; Engelhardt, Barbara E.; Mukherjee, Sayan; Dunson, David B.: Fast moment estimation for generalized latent Dirichlet models (2018)
  12. Marbac, Matthieu; Biernacki, Christophe; Vandewalle, Vincent: Model-based clustering of Gaussian copulas for mixed data (2017)
  13. Sun, Jiehuan; Warren, Joshua L.; Zhao, Hongyu: A Bayesian semiparametric factor analysis model for subtype identification (2017)
  14. Gray-Davies, Tristan; Holmes, Chris C.; Caron, François: Scalable Bayesian nonparametric regression via a Plackett-Luce model for conditional ranks (2016)
  15. McParland, Damien; Gormley, Isobel Claire: Model based clustering for mixed data: clustMD (2016)
  16. Creal, Drew D.; Tsay, Ruey S.: High dimensional dynamic stochastic copula models (2015)
  17. Stöber, Jakob; Hong, Hyokyoung Grace; Czado, Claudia; Ghosh, Pulak: Comorbidity of chronic diseases in the elderly: patterns identified by a copula design for mixed responses (2015)
  18. McParland, Damien; Gormley, Isobel Claire; McCormick, Tyler H.; Clark, Samuel J.; Kabudula, Chodziwadziwa Whiteson; Collinson, Mark A.: Clustering south african households based on their asset status using latent variable models (2014)
  19. Gruhl, Jonathan; Erosheva, Elena A.; Crane, Paul K.: A semiparametric approach to mixed outcome latent variable models: estimating the association between cognition and regional brain volumes (2013)
  20. Murray, Jared S.; Dunson, David B.; Carin, Lawrence; Lucas, Joseph E.: Bayesian Gaussian copula factor models for mixed data (2013)