Informative Measures of Significance for Constructing Lasso Weights

Abstract: 

When part of the regressors can act on both the response and some of the other explanatory variables, the already challenging problem of selecting variables in a p>n context becomes more difficult. This seminar presentation is motivated by a health study in mice which measures for two different diet groups of size ten each, a total of 185 microbial percentages as well as changes in nine phenotypes related to bodyweight regulation. Interest lies in understanding how diet and gut microflora diversity affect the phenotypes. The data has more variables than observations and diet is known to act directly on the phenotypes as well as on some or potentially all of the microbial percentages. I will present a recent methodology for variable selection in this context that links the concept of q-values from multiple testing to the weighted Lasso. I will then show that different informative measures of significance to q-values, such as partial correlation coefficients or Benjamini-Hochberg adjusted p-values, give similarly promising performance as when using q-values. Joint work with Raymond J Carroll (Texas A&M); Tanya P Garcia (Texas A&M); Rosemary L Walzem (Texas A&M).