Student-t model

Description

Linear regression with Student-t distributed residuals is also called robust regression.

Definition

For continuous unbounded outcome y and predictors x, the model is:

yiStudentT(ν,ηi,σ)ηi=α+βxi

Parameters needing priors:

  • α (intercept)
  • β (predictor weights)
  • σ (resdiual scale)
  • ν (degrees of freedom)

Prior for α

Prior for β

Prior for ν

Weakly informative gamma prior

A gamma prior that has increasing density from zero to ~30 was analysed and suggested by Juárez and Steel ().

νgamma(2,0.1)

Penalized complexity prior

Simpson et al. ()

See also

References

Juárez, Miguel A., and Mark F. J. Steel. 2010. “Model-Based Clustering of Non-Gaussian Panel Data Based on Skew- t Distributions.” Journal of Business & Economic Statistics 28 (1): 52–66. https://doi.org/10.1198/jbes.2009.07145.
Simpson, Daniel, Håvard Rue, Andrea Riebler, Thiago G. Martins, and Sigrunn H. Sørbye. 2017. “Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors.” Statistical Science 32 (1): 1–28. https://doi.org/10.1214/16-STS576.