Identifying Latent Structures in Restricted Latent Class Models

• 成果类型: Article
• 署名作者: Xu, Gongjun; Shang, Zhuoran
• 署名单位: University of Michigan System; University of Michigan; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1340889
• 发表日期: 2018
• 页码: 1284-1295
• 关键词: dina model; q-matrix; CLASSIFICATION; Identifiability; selection; identification

摘要

This article 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 prespecified 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 article is to establish identifiability conditions that ensure the estimability of the structure matrix. With the theoretical development, the second part of the article 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 dataset in educational assessment. Supplementary materials for this article are available online.