Increasingly, statisticians are faced with the problem of identifying interesting subsets of
predictors from among a large number of candidates. Existing methods for variable selection, such
as stochastic search algorithms, tend to explore the model space too slowly in large dimensions.
Shotgun stochastic search (SSS) algorithms have been proposed as an efficient alternative. As
current SSS algorithms rely on conjugacy, they are not appropriate for generalized linear models
without use of approximation methods. This article compares the frequently used Laplace
approximation with two alternatives based on Variational Bayes methods. The comparison is
illustrated using several simulated data examples and an application to the problem of predicting
conception using data on timing of intercourse in the menstrual cycle. This application also
illustrates the problem of selection of interactions.