Model Selection with Lasso in Multi-group Structural Equation Models

Abstract

A Structural Equations Modeling analysis of multiple groups often involves specification of cross-group parameter equality constraints. In this paper, we present a technique for estimating the differences and equalities in parameters between groups using L1-penalized estimation (also known as the Lasso). We present the general model formulation and provide an algorithm for estimating the parameters across a range of penalization levels and a procedure for determining the amount of penalization. We also provide two case studies, one with a model including only observed variables, and one with a model with latent variables. Further, we conduct a simulation study to investigate some properties of the method.