In this paper, we develop a mixed stochastic approximation expectation-maximization (MSAEM) algorithm coupled with a Gibbs sampler to compute the marginalized maximum a posteriori estimate (MMAPE) of a confirmatory multidimensional four-parameter normal ogive (M4PNO) model. The proposed MSAEM algorithm not only has the computational advantages of…

Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models that are widely used in educational and psychological measurement. A key component of CDMs is the Q-matrix characterizing the dependence structure between the items and the latent attributes. Additionally, researchers also assume in many applications certain…

Multidimensional Item Response Theory (MIRT) is widely used in educational and psychological assessment and evaluation. With the increasing size of modern assessment data, many existing estimation methods become computationally demanding and hence they are not scalable to big data, especially for the multidimensional three-parameter and…

Large-scale assessments are supported by a large item pool. An important task in test development is to assign items into scales that measure different characteristics of individuals, and a popular approach is cluster analysis of items. Classical methods in cluster analysis, such as the hierarchical clustering, K-means method, and latent-class…