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Activity Number: 652 - Genomics, Metabolomics, Microbiome and NextGen Sequencing
Type: Contributed
Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
Sponsor: Biometrics Section
Abstract #304241
Title: Post-Selection Inference for Regression Models with Linear Constraints, with an Application to Microbiome Data
Author(s): Jiarui Lu* and Hongzhe Li
Companies: University of Pennsylvania and University of Pennsylvania
Keywords: Post-selection inference; Linear constraints; Model selection; Compositional Data

Linear models with linear constraints naturally arise in many applications. Examples include regression analysis of microbiome compositional data, where linear models with a group of linear constraints have been developed to explore the association between taxa and outcome of interests. However, statistical inference for these models are not trivial due to both the high dimensionality and the linear constraints. In this paper, we consider the post-selection inference problem for linear models with linear equality and inequality constraints. We present methods for constructing the confidence intervals for the selected coefficients, which are chosen based on a Lasso-type estimator with linear constraints. These confidence intervals are interpreted as having desired coverage probability when conditioned on the selected model. Simulations are conducted for different settings and the results show the validity of our method in providing valid confidence intervals after variable selection. We also applied our method to a gut microbiome dataset to study the association between taxa compositional and BMI.

Authors who are presenting talks have a * after their name.

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