The Group MCP for Hierarchical Variable Selection in High-Dimensional Logistic Regression

• Activity Number: 299
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 PM
• Sponsor: Biometrics Section
• Author(s): Dingfeng Jiang*+ and Jian Huang and Ying Zhang
• Companies: University of Iowa and University of Iowa and University of Iowa
• Keywords: variable selection ; group structure ; 1-norm group MCP ; 2-norm group MCP ; high dimensional logistic regression

Abstract

Hierarchical structure exists naturally in many variable selection problems. Several methods such as group Lasso (Yuan and Lin 2006; Meier et al 2008) and group bridge (Huang et al 2009; Breheny and Huang 2009) have been proposed to account for group information. This paper proposes the composite of the minimax concave penalty (MCP, Zhang 2010) and the L1 or L2 norm of the coefficients for grouped variables for variable selection. The 1-norm group MCP enables bi-level selection at group and individual levels, while the 2-norm group MCP performs selection at group level. Under such setting, the group lasso can be viewed as a special case of the 2-norm group MCP. Simulation results show that for high-dimensional logistic models with grouping structure, both grouped MCPs have better predictive power than the ungrouped MCP. The grouped MCPs have similar false discover rate and group false discover rate, and both outperform the ungrouped MCP. The grouped MCPs tend to favor models with fewer groups. The 2-norm group MCP is sparser than the 1-norm one at group level. The application of the proposed methods is demonstrated on three microarray gene expression datasets.