Relative Variable Importance and Backward Variable Selection for High-Dimensional Response Data

• Activity Number: 114
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Daniel Nettleton*+ and Long Qu
• Companies: Iowa State University and BioStatSolutions
• Keywords: Backward variable selection ; High dimensional data ; Microarray ; Relative variable importance

Abstract

We consider the relative variable importance problem for the multiresponse permutation procedure (MRPP), a permutation test for the equality of multiple multivariate distributions. The MRPP is based on the sum of pairwise distances between multivariate observations within each treatment group. To identify important variables in the multivariate observations, we introduce hypothetical weights for each dimension in the distance measure and make continuous approximations to the discrete permutation p-value through kernel smoothing. We then define our relative variable importance measure by the partial derivatives of the approximated continuous p-value with respect to the hypothetical weights. We evaluate the effectiveness of this and a related variable importance measure compared to univariate tests via simulation. We also develop an iterative backward variable selection algorithm and apply our algorithm to high dimensional genomics problems. Our proposed method is advantageous in that it allows the importance of each variable to be assessed in the presence of all other variables, even when the number of variables greatly exceeds the sample size.