apclm: Bayesian Linear Regression with Adaptive Powered Correlation...

In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description

The adaptive powered correlation prior extends the Zellner-Siow Cauchy g-prior by allowing the crossproduct of the model matrix to be raised to powers other than -1. The power here will be referred to as "lambda". A lambda of 0 results in an identity matrix, which results in a ridge-regression like prior. Under the ridge prior, all coefficients are shrunk towards zero. Positive values of lambda adapt to collinearity by tending to apply shrinkage to entire groups of correlated predictors. Negative values of lambda on the other hand favor sparsity within sets of correlated predictors by tending to apply shrinkage to all but one predictor within a grouping. This can be understood as projecting the information matrix into a new space which leads to a model similar in function to principal components regression (Krishna et al., 2009). Alternatively, this can be viewed as a successor to ridge regression and an alternative to the elastic net. The model is estimated using an optimization routine. Standard errors are computed from the hessian evaluated at the maximum a posteriori estimate.

Additional comments: This particular model is worth the monicker "author's pick". This model seems to perform very well, and is relatively straightforward to estimate. Furthermore, the way it adapts to collinearity seems more flexible than the elastic net.

I recommend only using numeric covariates here.

Usage

apclm(formula, data, lambda = "auto", g = NULL)

Arguments

formula	a model formula
data	a data frame
lambda	a value for the power parameter. defaults to "auto" which means it is jointly estimated with the other model parameters.
g	a value for the g prior. if left as NULL, it defaults to nrow(X)/ncol(X)

Value

a roblm object

References

Zellner, A. & Siow S. (1980). Posterior odds ratio for selected regression hypotheses. In Bayesian statistics. Proc. 1st int. meeting (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley & A. F. M. Smith), 585–603. University Press, Valencia.

Liang, Paulo, Molina, Clyde, & Berger (2008) Mixtures of g Priors for Bayesian Variable Selection, Journal of the American Statistical Association, 103:481, 410-423, DOI: 10.1198/016214507000001337

Krishna, A., Bondell, H. D., & Ghosh, S. K. (2009). Bayesian variable selection using an adaptive powered correlation prior. Journal of statistical planning and inference, 139(8), 2665–2674. doi:10.1016/j.jspi.2008.12.004

abnormally-distributed/cvreg documentation built on May 3, 2020, 3:45 p.m.