BayesGroupBridgeSMU: Unified Bayesian Regularization via Scale Mixture of Uniform...

In himelmallick/UBeRr: Unified Bayesian Regularization via Scale Mixture of Uniform Distributions

Description

Bayesian Group Bridge regression

Usage

BayesGroupBridgeSMU(
  x,
  y,
  alpha = 0.5,
  group = group,
  max.steps = 20000,
  n.burn = 10000,
  n.thin = 1,
  r = 1,
  delta = 0.1,
  posterior.summary.beta = "mean",
  posterior.summary.lambda = "mean",
  posterior.summary.alpha = "mean",
  beta.ci.level = 0.95,
  lambda.ci.level = 0.95,
  alpha.ci.level = 0.95,
  seed = 1234,
  alpha.prior = "none",
  a = 10,
  b = 10,
  update.sigma2 = T
)

Arguments

x	A numeric matrix with standardized predictors in columns and samples in rows.
y	A mean-centered continuous response variable with matched sample rows with x.
alpha	Concavity parameter of the group bridge penalty (the exponent to which the L1 norm of the coefficients are raised). Default is 0.5, the square root. Must be between 0 and 1 (0 exclusive). It can also be estimated from the data by specifying arbitrary non-postive value such as 0.
group	Index of grouping information among the predictors.
max.steps	Number of MCMC iterations. Default is 20000.
n.burn	Number of burn-in iterations. Default is 10000.
n.thin	Lag at which thinning should be done. Default is 1 (no thinning).
r	Shape hyperparameter for the Gamma prior on lambda. Default is 1.
delta	Rate hyperparameter for the Gamma prior on lambda. Default is 0.1.
posterior.summary.beta	Posterior summary measure for beta (mean, median, or mode). Default is 'mean'.
posterior.summary.lambda	Posterior summary measure for lambda (mean or median). Default is 'mean'.
posterior.summary.alpha	Posterior summary measure for alpha (mean or median) when alpha is unknown. Default is 'mean'.
beta.ci.level	Credible interval level for beta. Default is 0.95 (95%).
lambda.ci.level	Credible interval level for lambda. Default is 0.95 (95%).
alpha.ci.level	Credible interval level for alpha when alpha is unknown. Default is 0.95 (95%).
seed	Seed value for reproducibility. Default is 1234.
alpha.prior	Prior distribution on alpha when alpha is unknown. Must be one of 'uniform' and 'beta'.
a	Beta prior distribution shape parameter 1 when ‘alpha.prior' is ’beta'. Default is 10.
b	Beta prior distribution shape parameter 2 when ‘alpha.prior' is ’beta'. Default is 10.
update.sigma2	Whether sigma2 should be updated. Default is TRUE.

Value

A list containing the following components is returned:

time	Computational time in minutes.
beta	Posterior mean or median estimates of beta.
lowerbeta	Lower limit credible interval of beta.
upperbeta	Upper limit credible interval of beta.
lambda	Posterior mean or median estimates of lambda.
lowerlambda	Lower limit credible interval of lambda
upperlambda	Upper limit credible interval of lambda
alpha	Posterior estimate of alpha if alpha is unknown.
alphaci	Posterior credible interval of alpha if alpha is unknown.
beta.post	Post-burn-in posterior samples of beta.
sigma2.post	Post-burn-in posterior samples of sigma2.
lambda.post	Post-burn-in posterior samples of lambda
alpha.post	Post-burn-in posterior samples of alpha if alpha is unknown.

Examples

## Not run: 

################################
# Load the Birthweight Dataset #
################################

library(grpreg)
data(birthwt.grpreg) # Hosmer and lemeshow (1989)
x <- scale(as.matrix(birthwt.grpreg[,-c(1,2)]))
y <- birthwt.grpreg$bwt - mean(birthwt.grpreg$bwt)
group <- c(1,1,1,2,2,2,3,3,4,5,5,6,7,8,8,8)

###########################
# Classical Group Bridge  #
###########################

fit.gbridge <- gBridge(x, y, group=group)
coef.gbridge<-select(fit.gbridge,'BIC')$beta
coef.gbridge[-1][coef.gbridge[-1]!=0]

###############
# Group LASSO #
###############

fit.glasso <- grpreg(x, y, group=group,penalty='grLasso')
coef.glasso<-select(fit.glasso,'BIC')$beta
coef.glasso[-1][coef.glasso[-1]!=0]

##########################
# Bayesian Group Bridge  #
##########################

library(UBR)
fit.BayesGroupBridge<-BayesGroupBridgeSMU(x, y, group = group) 
fit.BayesGroupBridge$beta[which(sign(fit.BayesGroupBridge$lowerbeta) == sign(fit.BayesGroupBridge$upperbeta))]


## End(Not run)

himelmallick/UBeRr documentation built on June 4, 2020, 7:18 a.m.