R2D2 Priors in brms

Function used to set up R2D2(M2) priors in brms. The function does not evaluate its arguments – it exists purely to help set up the model.

Usage

R2D2(mean_R2 = 0.5, prec_R2 = 2, cons_D2 = 0.5, autoscale = TRUE, main = FALSE)

Arguments

mean_R2

Mean of the Beta prior on the coefficient of determination R^2.

prec_R2

Precision of the Beta prior on the coefficient of determination R^2.

cons_D2

Concentration vector of the Dirichlet prior on the variance decomposition parameters. Lower values imply more shrinkage.

autoscale

Logical; indicating whether the R2D2 prior should be scaled using the residual standard deviation sigma if possible and sensible (defaults to TRUE). Autoscaling is not applied for distributional parameters or when the model does not contain the parameter sigma.

main

Logical (defaults to FALSE); only relevant if the R2D2 prior spans multiple parameter classes. In this case, only arguments given in the single instance where main is TRUE will be used. Arguments given in other instances of the prior will be ignored. See the Examples section below.

Details

The prior does not account for scale differences of the terms it is applied on. Accordingly, please make sure that all these terms have a comparable scale to ensure that shrinkage is applied properly.

Currently, the following classes support the R2D2(M2) prior: b (overall regression coefficients), sds (SDs of smoothing splines), sdgp (SDs of Gaussian processes), ar (autoregressive coefficients), ma (moving average coefficients), sderr (SD of latent residuals), sdcar (SD of spatial CAR structures), sd (SD of varying coefficients).

When the prior is only applied to parameter class b, it is equivalent to the original R2D2 prior (with Gaussian kernel). When the prior is also applied to other parameter classes, it is equivalent to the R2D2M2 prior.

Even when the R2D2(M2) prior is applied to multiple parameter classes at once, the concentration vector (argument cons_D2) has to be provided jointly in the the one instance of the prior where main = TRUE. The order in which the elements of concentration vector correspond to the classes' coefficients is the same as the order of the classes provided above.

References

Zhang, Y. D., Naughton, B. P., Bondell, H. D., & Reich, B. J. (2020). Bayesian regression using a prior on the model fit: The R2-D2 shrinkage prior. Journal of the American Statistical Association. https://arxiv.org/pdf/1609.00046

Aguilar J. E. & Bürkner P. C. (2022). Intuitive Joint Priors for Bayesian Linear Multilevel Models: The R2D2M2 prior. ArXiv preprint. https://arxiv.org/pdf/2208.07132

See also

set_prior

Examples

set_prior(R2D2(mean_R2 = 0.8, prec_R2 = 10))
#> b ~ R2D2(mean_R2 = 0.8, prec_R2 = 10)

# specify the R2D2 prior across multiple parameter classes
set_prior(R2D2(mean_R2 = 0.8, prec_R2 = 10, main = TRUE), class = "b") +
  set_prior(R2D2(), class = "sd")
#>                                           prior class coef group resp dpar
#>  R2D2(mean_R2 = 0.8, prec_R2 = 10, main = TRUE)     b                     
#>                                          R2D2()    sd                     
#>  nlpar   lb   ub tag source
#>        <NA> <NA>       user
#>        <NA> <NA>       user