Clustered Sparse Structural Equation Modeling for Heterogeneous Data

Joint analysis with clustering and structural equation modeling is one of the most popular approaches to analyzing heterogeneous data. The methods involved in this approach estimate a path diagram of the same shape for each cluster and interpret the clusters according to the magnitude of the coefficients. However, these methods have problems with difficulty in interpreting the coefficients when the number of clusters and/or paths increases and are unable to deal with any situation where the path diagram for each cluster is different. To tackle these problems, we propose two methods for simplifying the path structure and facilitating interpretation by estimating a different form of path diagram for each cluster using sparse estimation. The proposed methods and related methods are compared using numerical simulation and real data examples. The proposed methods are superior to the existing methods in terms of both fitting and interpretation.