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Diagnostic classification models (DCMs) have seen wide applications in educational and psychological measurement, especially in formative assessment. DCMs in the presence of testlets have been studied in recent literature. A key ingredient in the statistical modeling and analysis of testlet-based DCMs is the superposition of two latent structures, the attribute profile and the testlet effect. This paper extends the standard testlet DINA (T-DINA) model to accommodate the potential correlation between the two latent structures. Model identifiability is studied and a set of sufficient conditions are proposed. As a byproduct, the identifiability of the standard T-DINA is also established. The proposed model is applied to a dataset from the 2015 Programme for International Student Assessment. Comparisons are made with DINA and T-DINA, showing that there is substantial improvement in terms of the goodness of fit. Simulations are conducted to assess the performance of the new method under various settings. 

Diagnostic classification tests are designed to assess examinees’ discrete mastery status on a set of skills or attributes. Such tests have gained increas- ing attention in educational and psychological measurement. We review diagnostic classification models and their applications to testing and learning, discuss their statistical and machine learning connections and related challenges, and introduce some contemporary and future extensions. 

Time limits are imposed on many computer-based assessments, and it is common to observe exami- nees who run out of time, resulting in missingness due to not-reached items. The present study proposes an approach to account for the missing mechanisms of not-reached items via response time censoring. The censoring mechanism is directly incorporated into the observed likelihood of item responses and response times. A marginal maximum likelihood estimator is proposed, and its asymptotic properties are estab- lished. The proposed method was evaluated and compared to several alternative approaches that ignore the censoring through simulation studies. An empirical study based on the PISA 2018 Science Test was further conducted. 

Multidimensional unfolding methods are widely used for visualizing item response data. Such methods project respondents and items simultaneously onto a low-dimensional Eu- clidian space, in which respondents and items are represented by ideal points, with person- person, item-item, and person-item similarities being captured by the Euclidian distances between the points. In this paper, we study the visualization of multidimensional unfold- ing from a statistical perspective. We cast multidimensional unfolding into an estimation problem, where the respondent and item ideal points are treated as parameters to be esti- mated. An estimator is then proposed for the simultaneous estimation of these parameters. Asymptotic theory is provided for the recovery of the ideal points, shedding lights on the validity of model-based visualization. An alternating projected gradient descent algorithm is proposed for the parameter estimation. We provide two illustrative examples, one on users’ movie rating and the other on senate roll call voting. 

The bifactor model and its extensions are multidimensional latent vari- able models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psycho- logical assessments, these multidimensional latent variable models may suffer from nonidentifiability, which can further lead to inconsistent parameter estimation and invalid inference. The current work provides a relatively complete characterization of identifiability for linear and dichotomous bifactor models and the linear extended bifactor model with correlated subdimensions. In addition, similar results for the two-tier models are developed. Illustrative examples on checking model identifia- bility by inspecting the factor loading structure are provided. Simulation studies examine the estimation consistency when the identifiability conditions are/are not satisfied.