Identifying Latent Structures in Restricted Latent Class Models
Gongjun Xu, University of Michigan
This talk focuses on a family of restricted latent structure models with wide applications in psychological and educational assessments, where the model parameters are restricted via a latent structure matrix to reflect pre-specified assumptions on the latent attributes. Such a structure matrix is often provided by experts and assumed to be correct upon construction, yet it may be subjective and misspecified. Recognizing this problem, researchers have been developing methods to estimate the structure matrix from data. However, the fundamental issue of the identifiability of the restricted latent class models has not been addressed until now. In this talk, we first introduce identifiability conditions that ensure the estimability of the structure matrix and the model parameters. The results provide theoretical justification for the existing estimation methods as well as a guideline for the related experimental designs. With the theoretical development, we further propose a likelihood-based method to estimate the latent structure. Simulation studies and data analysis are also presented to examine the performance of the proposed method.
Note: Seminars are free and open to the public. Reception to follow.