groupSasp: Bayesian Group Shape Adaptive Shrinkage Prior Regression

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

Description

The Group Bayesian Bridge model of Mallick & Yi (2018) adapted to the Shape Adaptive Shrinkage Prior (SASP) of Sillanpää & Mutshinda (2011).

Bridge regression allows you to utilize different Lp norms for the shape of the prior through the shape parameter kappa of the power exponential distribution (also known as generalized Gaussian). Norms of 1 and 2 give the Laplace and Gaussian distributions respectively (corresponding to the LASSO and Ridge Regression). Norms smaller than 1 are very difficult to estimate directly, but have very tall modes at zero and very long, cauchy like tails. Values greater than 2 become increasingly platykurtic, with the uniform distribution arising as it approaches infinity.

The benefit of the shape adaptive shrinkage prior is that one need not pick a specific norm. Hence, if there is uncertainty over whether or not one wishes to choose the L1 norm (LASSO) or L2 norm (Ridge), this integrates over a reasonable range of values. The gamma prior for the norm has an expected value of 1.4, which gives a reasonable compromise between the LASSO and Ridge.

JAGS has no built in power exponential distribution, so the distribution is parameterized as a uniform-gamma mixture just as in Mallick & Yi (2018). The parameterization is given below. For generalized linear models plug-in pseudovariances are used.

Model Specification:

Plugin Pseudo-Variances:

Usage

groupSasp(X, y, idx, family = "gaussian", log_lik = FALSE,
  iter = 10000, warmup = 1000, adapt = 2000, chains = 4,
  thin = 1, method = "parallel", cl = makeCluster(2), ...)

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 an alternative parallel option, choose "rjparallel" or. Otherwise, "rjags" (single core run).
cl	Use parallel::makeCluster(# clusters) to specify clusters for the parallel methods. Defaults to two cores.
...	Other arguments to run.jags.

Value

a runjags 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.

Mallick, H. & Yi, N. (2018). Bayesian bridge regression, Journal of Applied Statistics, 45:6, 988-1008, DOI: 10.1080/02664763.2017.1324565

Mallick, H., & Yi, N. (2014). A New Bayesian Lasso. Statistics and its interface, 7(4), 571–582. doi:10.4310/SII.2014.v7.n4.a12

Sillanpää, S., & Mutshinda, C., (2011). Bayesian shrinkage analysis of QTLs under shape-adaptive shrinkage priors, and accurate re-estimation of genetic effects. Heredity volume 107, pages 405–412. doi: 10.1038/hdy.2011.37

Examples

groupSasp()

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