extLASSODC: Extended Bayesian LASSO with unpenalized design covariates

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

Description

This is the extended Bayesian LASSO presented by Crispin M. Mutshinda and Mikko J. Sillanpää (2010) which is an improvement on the Baysian LASSO of Park & Casella (2008). Two variants are provided here.

The first version of the model is the original specification in Mutshinda and Sillanpää (2010), labeled "classic" in the options here. This requires you to choose upper limits for the uniform priors on both the top-level shrinkage hyperparameter as well as the local shrinkage parameters. These can be tuned through model comparison if neccessary.

Model Specification:


The second version is the "gamma" prior. This places a gamma(0.50 , 0.20) prior on the top level shrinkage hyperparameter. The individual shrinkage parameters are still given independent uniform(0, local_u) priors just as in the classic version.

Model Specification:


The author of the extended Bayesian Lasso (Sillanpää, personal communication) confirmed that gamma prior on the top level shrinkage parameter does work well in some settings, which is why I opted to include the "gamma" variant.

One really nice feature of the extended Bayesian Lasso is that inclusion probabilities and Bayes Factors for the coefficients are easily obtained. The prior inclusion probability is given by 1/local_u, so for example uniform(0, 2) priors on the shrinkage parameters indicate a 50 probability. Common in Bayesian variable selection is to use a 20 dealing with a high dimensional problem, so for this choose local_u = 5. If you have genuine prior information you can and should use this to guide your choice. If you are unsure, use model comparison to select which value of u to choose. Inclusion indicators are given by a step function based on the marginal individual shrinkage parameter, delta = step(1 - eta). Inlcusion probabilities are then given as the number of 1s that appear in the vector of monte carlo samples out of the total number of iterations. This will appear as the mean for each inclusion indicator in the summary.

Bayes Factors for each cofficient can then be manually derived using the formula below (Mutshinda, & Sillanpää, 2010; 2012).

Usage

extLASSODC(formula, design.formula, data, family = "gaussian",
  eta_prior = "classic", local_u = 2, top_u = 25, log_lik = FALSE,
  iter = 10000, warmup = 10000, adapt = 15000, chains = 4,
  thin = 3, method = "parallel", cl = makeCluster(2), ...)

Arguments

formula	the model formula
design.formula	formula for the design covariates.
data	a data frame.
family	one of "gaussian", "binomial", or "poisson".
eta_prior	one of "classic (default)", or "gamma".
local_u	This must be assigned a value. Default is 2.
top_u	If using eta_prior = "classic" this must be assigned a value. Default is 25.
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 10000.
adapt	How many adaptation steps? Defaults to 15000.
chains	How many chains? Defaults to 4.
thin	Thinning interval. Defaults to 3.
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 run.jags object

References

Li, Z.,and Sillanpää, M. J. (2012) Overview of LASSO-related penalized regression methods for quantitative trait mapping and genomic selection. Theoretical and Applied Genetics 125: 419-435.

Mutshinda, C.M., & Sillanpää, M.J. (2010). Extended Bayesian LASSO for multiple quantitative trait loci mapping and unobserved phenotype prediction. Genetics, 186 3, 1067-75 .

Mutshinda, C. M., and M. J. Sillanpää (2012) A decision rule for quantitative trait locus detection under the extended Bayesian LASSO model. Genetics 192: 1483-1491.

Examples

extLASSODC()

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