Selection {Bayenet}

Variable selection for a Bayenet object

Description

Variable selection for a Bayenet object

Usage

Selection(obj, sparse)

Arguments

obj

Bayenet object.

sparse

logical flag. If TRUE, spike-and-slab priors will be used to shrink coefficients of irrelevant covariates to zero exactly.

Details

For class ‘Sparse’, the inclusion probability is used to indicate the importance of predictors. Here we use a binary indicator \phi to denote the membership of the non-spike distribution. Take the main effect of the jth genetic factor, X_{j}, as an example. Suppose we have collected H posterior samples from MCMC after burn-ins. The jth G factor is included in the final model at the jth MCMC iteration if the corresponding indicator is 1, i.e., \phi_j^{(h)} = 1. Subsequently, the posterior probability of retaining the jth genetic main effect in the final model is defined as the average of all the indicators for the jth G factor among the H posterior samples. That is, p_j = \hat{\pi} (\phi_j = 1|y) = \frac{1}{H} \sum_{h=1}^{H} \phi_j^{(h)}, \; j = 1, \dots,p. A larger posterior inclusion probability of jth indicates a stronger empirical evidence that the jth genetic main effect has a non-zero coefficient, i.e., a stronger association with the phenotypic trait. Here, we use 0.5 as a cutting-off point. If p_j > 0.5, then the jth genetic main effect is included in the final model. Otherwise, the jth genetic main effect is excluded in the final model. For class ‘NonSparse’, variable selection is based on 95% credible interval. Please check the references for more details about the variable selection.

Value

an object of class ‘Selection’ is returned, which is a list with components:

method

method used for identifying important effects.

effects

a list of indicators of selected effects.

References

Lu, X. and Wu, C. (2023). Bayesian quantile elastic net with spike-and-slab priors.

See Also

Bayenet

Examples

data(dat)
max.steps=5000
fit= Bayenet(X, Y, clin, max.steps, penalty="lasso")
selected=Selection(fit,sparse=TRUE)
selected$Main.G