A covariance regression model

Peter D. Hoff, Xiaoyue Niu

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a multivariate response vector as a parsimonious quadratic function of explanatory variables. The approach is analogous to the mean regression model, and is similar to a factor analysis model in which the factor loadings depend on the explanatory variables. Using a random-effects representation, parameter estimation for the model is straightforward using either an EM-algorithm or an MCMC approximation via Gibbs sampling. The proposed methodology provides a simple but flexible representation of heteroscedasticity across the levels of an explanatory variable, improves estimation of the mean function and gives better calibrated prediction regions when compared to a homoscedastic model.

Original languageEnglish (US)
Pages (from-to)729-753
Number of pages25
JournalStatistica Sinica
Issue number2
StatePublished - Apr 2012

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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