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Hierarchical shrinkage priors for regression models. (English) Zbl 1384.62225

Summary: In some linear models, such as those with interactions, it is natural to include the relationship between the regression coefficients in the analysis. In this paper, we consider how robust hierarchical continuous prior distributions can be used to express dependence between the size but not the sign of the regression coefficients. For example, to include ideas of heredity in the analysis of linear models with interactions. We develop a simple method for controlling the shrinkage of regression effects to zero at different levels of the hierarchy by considering the behaviour of the continuous prior at zero. Applications to linear models with interactions and generalized additive models are used as illustrations.

MSC:

62J05 Linear regression; mixed models
62F15 Bayesian inference
62J07 Ridge regression; shrinkage estimators (Lasso)
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