Identifying Latent Structures in Restricted Latent Class Models
This paper focuses on a family of restricted latent structure models with wide applications in psychological and educational assessment, where the model parameters are restricted via a latent structure matrix to reflect pre-specified assumptions on the latent attributes. Such a latent 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 matrix from data. However, the fundamental issue of the identifiability of the latent structure matrix has not been addressed until now. The first goal of this paper is to establish identifiability conditions that ensure the estimability of the structure matrix. With the theoretical development, the second part of the paper proposes a likelihood-based method to estimate the latent structure from the data. Simulation studies show that the proposed method outperforms the existing approaches. We further illustrate the method through a data set in educational assessment.