  The goal of this article is to select important variables that can
distinguish one class of data from another. A marginal variable selection
method ranks the marginal effects for classification of individual variables,
and is a useful and efficient approach for variable selection. Our focus here
is to consider the bivariate effect, in addition to the marginal effect. In
particular, we are interested in those pairs of variables that can lead to
accurate classification predictions when they are viewed jointly. To accomplish
this, we propose a permutation test called Significance test of Joint Effect
(SigJEff). In the absence of joint effect in the data, SigJEff is similar or
equivalent to many marginal methods. However, when joint effects exist, our
method can significantly boost the performance of variable selection. Such
joint effects can help to provide additional, and sometimes dominating,
advantage for classification. We illustrate and validate our approach using
both simulated example and a real glioblastoma multiforme data set, which
provide promising results.
