Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent attributes explain the dependence of observed variables in a highly structured fashion. Usually, the maximum marginal likelihood estimation approach is adopted for SLAMs, treating the latent attributes as random effects. The increasing scope of modern assessment data involves large numbers of observed variables and high-dimensional latent attributes. This poses challenges to classical estimation methods and requires new methodology and understanding of latent variable modeling. Motivated by this, we consider the joint maximum likelihood estimation (MLE) approach to SLAMs, treating latent attributes as fixed unknown parameters. We investigate estimability, consistency, and computation in the regime where sample size, number of variables, and number of latent attributes all can diverge. We establish the statistical consistency of the joint MLE and propose efficient algorithms that scale well to large-scale data for several popular SLAMs. Simulation studies demonstrate the superior empirical performance of the proposed methods. An application to real data from an international educational assessment gives interpretable findings of cognitive diagnosis.
翻译:结构性隐性属性模型(SLAMs)是由在教育、心理学和流行病学中广泛使用的离散潜伏变量模型组成的组合,用于模拟多变量绝对数据。ASLM认为,多离散潜在属性可以以结构化高度的方式解释所观测变量的依赖性。通常,对SLMS采用最大的边际可能性估算方法,将潜在属性作为随机效应处理。现代评估数据的范围不断扩大,涉及大量观测到的变量和高维潜伏属性。这给传统估算方法带来了挑战,要求采用新的方法和理解潜在变量模型。为此,我们考虑对SLMMS采取联合最大可能性估算(MLE)方法,将潜在属性作为固定的未知参数处理。我们在抽样大小、变量数量和潜在属性数量可能各不相同的系统中,对可解释性、一致性和计算方法进行了调查。我们建立了联合MLE的统计一致性,并为一些广尺度的数据提出了高效算法。模拟研究表明了拟议方法的高级实证性表现。从国际教育评估中得出了可解释的认知性诊断结果。