Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications
Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications
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DOI：
10.1080/01621459.2019.1635485
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发表时间：
2019-07-20
影响因子：
3.7
通讯作者：
Zhang, Siliang
中科院分区：
文献类型：
--
作者：
Chen, Yunxiao;Li, Xiaoou;Zhang, Siliang
摘要：潜在因素模型广泛用于测量社会和行为科学（包括心理学、教育和营销）中未观察到的潜在特征。当以验证性方式使用时，设计信息被合并为相应参数的零约束，从而产生结构化（验证性）潜在因素模型。在本文中，我们研究此类设计信息如何影响结构化潜在因素模型的可识别性和估计。通过渐近和非渐近分析获得见解。我们的渐近结果是在明显变量的数量和样本大小都存在差异的情况下建立的，这是由于大规模数据的应用而产生的。在此体系下，我们定义了潜在因素的结构可识别性，并建立了确保结构可识别性的充分必要条件。此外，我们提出了一种估计器，当结构可识别性成立时，该估计器被证明是一致的且速率最优。最后，推导出该估计量的非渐近误差界，通过该界限进一步量化设计信息的影响。我们的结果揭示了教育和心理学中大规模测量的设计，并对测量的有效性和可靠性产生了重要影响。
Abstract–Latent factor models are widely used to measure unobserved latent traits in social and behavioral sciences, including psychology, education, and marketing. When used in a confirmatory manner, design information is incorporated as zero constraints on corresponding parameters, yielding structured (confirmatory) latent factor models. In this article, we study how such design information affects the identifiability and the estimation of a structured latent factor model. Insights are gained through both asymptotic and nonasymptotic analyses. Our asymptotic results are established under a regime where both the number of manifest variables and the sample size diverge, motivated by applications to large-scale data. Under this regime, we define the structural identifiability of the latent factors and establish necessary and sufficient conditions that ensure structural identifiability. In addition, we propose an estimator which is shown to be consistent and rate optimal when structural identifiability holds. Finally, a nonasymptotic error bound is derived for this estimator, through which the effect of design information is further quantified. Our results shed lights on the design of large-scale measurement in education and psychology and have important implications on measurement validity and reliability.