Heredity, Regularization, and Model Selection for Multilevel Data

• Activity Number: 302
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Elizabeth Stone*+ and Alan Izenman
• Companies: Temple University and Temple University
• Keywords: Multilevel modeling ; regularization ; strong heredity

Abstract

Regularized estimation and selection procedures for multilevel models have proven to be successful in reducing instability of estimates and producing viable candidate models. However, these algorithms may select interaction terms while excluding one or more parent terms (e.g., main effects). This violates the model-building principle of heredity, in which higher order terms are included in a model only when the associated lower terms are also included. Our estimation procedure addresses this problem by applying strong heredity control in both the fixed- and random-effects parts of a two-level, cross-sectional Gaussian linear model. Control is invoked with an l_1 penalty in which individual terms are weighted by what we call importance ratios of regularized to unconstrained parameter estimates. Applications to simulated data and to the High School and Beyond educational data set show promise in producing estimates comparable to other regularization algorithms while producing candidate models that adhere to principles of heredity. There are many challenges inherent in this line of research, and we present areas that would benefit from further development.