A covariance regression model

Peter D. Hoff; Xiaoyue Niu

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arXiv · 1102.5721

A covariance regression model

Peter D. Hoff·Xiaoyue Niu

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Abstract

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.

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BibTeX RIS

Peter D. Hoff, Xiaoyue Niu. 2011-02-28. A covariance regression model. https://arxiv.org/abs/1102.5721

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