Model Selection and Estimation in Regression with Grouped Variables

TLDR

Selecting grouped variables for accurate regression prediction is a common problem, exemplified by multifactor ANOVA, and is traditionally addressed using methods such as the lasso, LARS, and non‑negative garrote for individual variable selection. The study aims to evaluate extensions of the lasso, LARS, and non‑negative garrote for factor selection, focusing on estimation accuracy rather than stepwise elimination. The authors develop efficient algorithms extending these methods for factor selection, analyze their similarities and differences, and illustrate them with simulations and real data. The extended methods outperform traditional stepwise backward elimination in factor selection tasks.

Abstract

Summary We consider the problem of selecting grouped variables (factors) for accurate prediction in regression. Such a problem arises naturally in many practical situations with the multifactor analysis-of-variance problem as the most important and well-known example. Instead of selecting factors by stepwise backward elimination, we focus on the accuracy of estimation and consider extensions of the lasso, the LARS algorithm and the non-negative garrotte for factor selection. The lasso, the LARS algorithm and the non-negative garrotte are recently proposed regression methods that can be used to select individual variables. We study and propose efficient algorithms for the extensions of these methods for factor selection and show that these extensions give superior performance to the traditional stepwise backward elimination method in factor selection problems. We study the similarities and the differences between these methods. Simulations and real examples are used to illustrate the methods.