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We propose a dynamic multiplicative factor model for process data arising from complex problem-solving items, an emerging type of data in large-scale educational assessment. The proposed model can be viewed as an extension of the classical frailty models developed in survival analysis for multivariate recurrent event times, but with two important distinctions: (i) the factor (frailty) is of primary interest; (ii) covariates are internal and embedded in the factor. It allows…

探索性层级因子分析及其在心理测量中的应用AI 解读

Hierarchical factor models, which include the bifactor model as a special case, are useful in social and behavioural sciences for measuring hierarchically structured constructs. Specifying a hierarchical factor model involves imposing hierarchically structured zero constraints on a factor loading matrix, which is often challenging. Therefore, an exploratory analysis is needed to learn the hierarchical factor structure from data. Unfortunately, there does not exist an…

精确探索性双因子分析：基于约束的优化方法AI 解读

Bi-factor analysis is a form of confirmatory factor analysis widely used in psychological and educational measurement. The use of a bi-factor model requires the specification of an explicit bi-factor structure on the relationship between the observed variables and the group factors. In practice, the bi-factor structure is sometimes unknown, in which case an exploratory form of bi-factor analysis is needed to find the bi-factor structure. Unfortunately, there are few methods…

高维重复事件的动态因子分析AI 解读

Recurrent event time data arise in many studies, including biomedicine, public health, marketing, and social media analysis. High-dimensional recurrent event data involving many event types and observations have become prevalent with advances in information technology. This paper proposes a semiparametric dynamic factor model for the dimension reduction of high-dimensional recurrent event data. The proposed model imposes a low-dimensional structure on the mean intensity…

项目反应理论：教育与心理测量的统计框架AI 解读

Item response theory (IRT) has become one of the most popular statistical models for psychometrics, a field of study concerned with the theory and techniques of psychological measurement. The IRT models are latent factor models tailored to the analysis, interpretation, and prediction of individuals' behaviors in answering a set of measurement items that typically involve categorical response data. Many important questions of measurement are directly or indirectly answered…