Fuzzy clusterwise generalized structured component analysis

Generalized Structured Component Analysis (GSCA) was recently introduced by Hwang and Takane (2004) as a component-based approach to path analysis with latent variables. The parameters of GSCA are estimated by pooling data across respondents under the implicit assumption that they all come from a single, homogenous group. However, as has been empirically demonstrated by various researchers across a number of areas of inquiry, such aggregate analyses can often mask the true structure in data when respondent heterogeneity is present. In this paper, GSCA is generalized to a fuzzy clustering framework so as to account for potential group-level respondent heterogeneity. An alternating least-squares procedure is developed and technically described for parameter estimation. A small-scale Monte Carlo study involving synthetic data is carried out to compare the performance between the proposed method and an extant approach. In addition, an empirical application concerning alcohol use among adolescents from US northwestern urban areas is presented to illustrate the usefulness of the proposed method. Finally, a number of directions for future research are provided.