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 28 articles , 1 standard article )

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  1. Alexopoulos, Angelos; Bottolo, Leonardo: Bayesian variable selection for Gaussian copula regression models (2021)
  2. Oh, Rosy; Jeong, Himchan; Ahn, Jae Youn; Valdez, Emiliano A.: A multi-year microlevel collective risk model (2021)
  3. Zhang, Zhenyu; Nishimura, Akihiko; Bastide, Paul; Ji, Xiang; Payne, Rebecca P.; Goulder, Philip; Lemey, Philippe; Suchard, Marc A.: Large-scale inference of correlation among mixed-type biological traits with phylogenetic multivariate probit models (2021)
  4. Lee, Woojoo; Kim, Jeonghwan; Ahn, Jae Youn: The Poisson random effect model for experience ratemaking: limitations and alternative solutions (2020)
  5. Li, Zehang Richard; McComick, Tyler H.; Clark, Samuel J.: Using Bayesian latent Gaussian graphical models to infer symptom associations in verbal autopsies (2020)
  6. Nguyen, Hoang; Ausín, M. Concepción; Galeano, Pedro: Variational inference for high dimensional structured factor copulas (2020)
  7. Roy, Arkaprava; Dunson, David B.: Nonparametric graphical model for counts (2020)
  8. Smith, Michael Stanley; Loaiza-Maya, Rubén; Nott, David J.: High-dimensional copula variational approximation through transformation (2020)
  9. Bashir, Amir; Carvalho, Carlos M.; Hahn, P. Richard; Jones, M. Beatrix: Post-processing posteriors over precision matrices to produce sparse graph estimates (2019)
  10. Cui, Ruifei; Bucur, Ioan Gabriel; Groot, Perry; Heskes, Tom: A novel Bayesian approach for latent variable modeling from mixed data with missing values (2019)
  11. Cui, Ruifei; Groot, Perry; Heskes, Tom: Learning causal structure from mixed data with missing values using Gaussian copula models (2019)
  12. 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)
  13. Klein, Nadja; Smith, Michael Stanley: Implicit copulas from Bayesian regularized regression smoothers (2019)
  14. Loaiza-Maya, Rubén; Smith, Michael Stanley: Variational Bayes estimation of discrete-margined copula models with application to time series (2019)
  15. Maleki, Mohsen; Wraith, Darren: Mixtures of multivariate restricted skew-normal factor analyzer models in a Bayesian framework (2019)
  16. Manner, Hans; Stark, Florian; Wied, Dominik: Testing for structural breaks in factor copula models (2019)
  17. Müller, Dominik; Czado, Claudia: Dependence modelling in ultra high dimensions with vine copulas and the graphical lasso (2019)
  18. Edgar Merkle; Yves Rosseel: blavaan: Bayesian Structural Equation Models via Parameter Expansion (2018) not zbMATH
  19. Zhao, Shiwen; Engelhardt, Barbara E.; Mukherjee, Sayan; Dunson, David B.: Fast moment estimation for generalized latent Dirichlet models (2018)
  20. Marbac, Matthieu; Biernacki, Christophe; Vandewalle, Vincent: Model-based clustering of Gaussian copulas for mixed data (2017)

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