  When fitting statistical models, some predictors are often found to be
correlated with each other, and functioning together. Many group variable
selection methods are developed to select the groups of predictors that are
closely related to the continuous or categorical response. These existing
methods usually assume the group structures are well known. For example,
variables with similar practical meaning, or dummy variables created by
categorical data. However, in practice, it is impractical to know the exact
group structure, especially when the variable dimensional is large. As a
result, the group variable selection results may be selected. To solve the
challenge, we propose a two-stage approach that combines a variable clustering
stage and a group variable stage for the group variable selection problem. The
variable clustering stage uses information from the data to find a group
structure, which improves the performance of the existing group variable
selection methods. For ultrahigh dimensional data, where the predictors are
much larger than observations, we incorporated a variable screening method in
the first stage and shows the advantages of such an approach. In this article,
we compared and discussed the performance of four existing group variable
selection methods under different simulation models, with and without the
variable clustering stage. The two-stage method shows a better performance, in
terms of the prediction accuracy, as well as in the accuracy to select active
predictors. An athlete's data is also used to show the advantages of the
proposed method.
