groupNegLASSO: Group Normal-exponential-gamma Bayesian LASSO

In abnormally-distributed/Bayezilla: Bayesian Models With JAGS and Several Utilities for Data Exploration and Model Evaluation.

Description

This implements the normal-exponential-gamma "hyperlasso" of Griffin & Brown (2011) adapted here to the Kyung et al.'s (2010) group Bayesian LASSO.

This model has normal priors on each coefficient, whose precision is modeled by group specific exponential distributions. The exponential distributions in turn have their respective rate parameters modeled through independent group-level gamma(k_g * 0.50, 1 / lambda^2) distributions, where k_g is the number of predictors in group g. If there is no grouping then this reduces to the negLASSO. Lambda is a single top-level hyperparameter here given a gamma(0.50 , 0.20) prior.

The model specification is given below:



Model Specification:

Usage

groupNegLASSO(X, y, idx, family = "gaussian", log_lik = FALSE,
  iter = 10000, warmup = 1000, adapt = 2000, chains = 4,
  thin = 1, method = "parallel", cl = makeCluster(3), ...)

Arguments

X	the model matrix. Construct this manually with model.matrix()[,-1]
y	the outcome variable
idx	the group labels. Should be of length = to ncol(model.matrix()[,-1]) with the group assignments for each covariate. Please ensure that you start numbering with 1, and not 0.
family	one of "gaussian", "binomial", or "poisson".
log_lik	Should the log likelihood be monitored? The default is FALSE.
iter	How many post-warmup samples? Defaults to 10000.
warmup	How many warmup samples? Defaults to 1000.
adapt	How many adaptation steps? Defaults to 2000.
chains	How many chains? Defaults to 4.
thin	Thinning interval. Defaults to 1.
method	Defaults to "parallel". For another parallel option, choose "rjparallel" or "rjags" for a single core run.
cl	Use parallel::makeCluster(# clusters) to specify clusters for the parallel methods. Defaults to 3.
...	Other arguments to run.jags.

Value

A run.jags object

References

Kyung, M., Gill, J., Ghosh, M., and Casella, G. (2010). Penalized regression, standard errors, and Bayesian lassos. Bayesian Analysis, 5(2):369–411.

Griffin, J. E. and Brown, P. J. (2011), Bayesian Hyper‐LASSOs With Non-Convex Penalization. Australian & New Zealand Journal of Statistics, 53: 423-442. doi:10.1111/j.1467-842X.2011.00641.x

Yuan, Ming; Lin, Yi (2006). Model Selection and Estimation in Regression with Grouped Variables. Journal of the Royal Statistical Society. Series B (statistical Methodology). Wiley. 68 (1): 49–67. doi:10.1111/j.1467-9868.2005.00532.x

Examples

groupNegLASSO()

abnormally-distributed/Bayezilla documentation built on Oct. 31, 2019, 1:57 a.m.