Variable Selection via the Lasso-Type Regularization for Structural Equation Models

• Activity Number: 41
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Kei Hirose*+ and Sadanori Konishi
• Companies: Kyushu University and Kyushu University
• Keywords: Factor analysis ; Grouped weighted lasso ; lasso-type regularization ; Model selection criterion ; Structural equation modeling ; Variable selection

Abstract

Variable selection is an important topic in statistical analysis. Over the past 10 years, a regularization procedure which imposes the lasso-type penalty on parameters has been widely used in regression analysis. In this paper, we consider the problem of variable selection via the $L_1$ regularization for factor analysis models. Since each observed variable is controlled by multiple parameters, the ordinary lasso cannot be directly applied. We treat these parameters as grouped parameters and then propose a regularization method via the grouped lasso. The weight of the grouped lasso penalty is adjusted so that the proper penalties are imposed on each variable. Furthermore, a model selection criterion is derived to select the number of factors and regularization parameters. Our proposed procedure can be extended to deal with the problem of variable selection for structural equation models.