I am De Vincentis Francesco, a Statistics student form University Federico II in Naples (Italy). In this time I work on my thesis in “Variable Selection” and I’d like to apply Bayesian approach to modeling a “hccframe” dataset with 56 observations, 45 regressor, Y ordinal response (Normal, Cirrhosis, Tumor). My first approach is frequentist mode with shrinkage estimator ( Ridge, Lasso and Elastic Net).
What do You suggest me with bayesian approach?
Could I apply this shrinkage method with “brms” package?
Thank you for your attention!
Yes you can! Welcome to the Stan community.
You might find this post useful by the author of the {bmrs} package: Help with lasso example in brms - #7 by paul.buerkner
What you are looking for is called the Horsehoe Prior (Regularized horseshoe priors in brms — horseshoe • brms) which is better than the LASSO prior (Set up a lasso prior in brms — lasso • brms) in bayesian models.
Also see these references:
- Carvalho, C. M., Polson, N. G., & Scott, J. G. (2009). Handling Sparsity via the Horseshoe. Artificial Intelligence and Statistics, 73–80. http://proceedings.mlr.press/v5/carvalho09a.html
- Park, T., & Casella, G. (2008). The Bayesian Lasso. Journal of the American Statistical Association, 103(482), 681-686.
- Piironen, J., & Vehtari, A. (2017a). On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior. Artificial Intelligence and Statistics, 905–913. http://proceedings.mlr.press/v54/piironen17a.html
- Piironen, J., & Vehtari, A. (2017b). Sparsity information and regularization in the horseshoe and other shrinkage priors. Electronic Journal of Statistics, 11(2), 5018–5051. https://doi.org/10.1214/17-EJS1337SI
- Ari Vehtari - Model assessment, selection and inference after selection
- Michael Betancourt — Bayes Sparse Regression
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projpred would be another alternative. In its version 2.4.0, the augmented-data projection and the latent projection were introduced, which both add support for ordinal models.
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