The recent “Every Student Succeed Act" encourages schools to use an innovative assessment to provide feedback about students’ mastery level of grade-level content standards. Mastery of a skill requires the ability to complete the task with not only accuracy but also fluency. This paper offers a new sight on using both response times and response accuracy to measure fluency with cognitive diagnosis model framework. Defining fluency as the highest level of a categorical latent attribute, a polytomous response accuracy model and two forms of response time models are proposed to infer fluency jointly. A Bayesian estimation approach is developed to calibrate the newly proposed models. These models were applied to analyze data collected from a spatial rotation test. Results demonstrate that compared with the traditional CDM that using response accuracy only, the proposed joint models were able to reveal more information regarding test takers’ spatial skills. A set of simulation studies were conducted to evaluate the accuracy of model estimation algorithm and illustrate the various degrees of model complexities.

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.

Cognitive diagnostic models (CDMs) are a popular family of discrete latent variable models that model students’ mastery or deficiency of multiple fine-grained skills. CDMs have been most widely used to model categorical item response data such as binary or polytomous responses. With advances in technology and the emergence of varying test formats in modern educational assessments, new response types, including continuous responses such as response times, and count-valued responses from tests with repetitive tasks or eye-tracking sensors, have also become available. Variants of CDMs have been proposed recently for modeling such responses. However, whether these extended CDMs are identifiable and estimable is entirely unknown. We propose a very general cognitive diagnostic modeling framework for arbitrary types of multivariate responses with minimal assumptions, and establish identifiability in this general setting. Surprisingly, we prove that our general-response CDMs are identifiable under $\mathbf{Q}$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\textbf{Q}}$$\end{document}-matrix-based conditions similar to those for traditional categorical-response CDMs. Our conclusions set up a new paradigm of identifiable general-response CDMs. We propose an EM algorithm to efficiently estimate a broad class of exponential family-based general-response CDMs. We conduct simulation studies under various response types. The simulation results not only corroborate our identifiability theory, but also demonstrate the superior empirical performance of our estimation algorithms. We illustrate our methodology by applying it to a TIMSS 2019 response time dataset.

A common assessment research design is the single-group pre-test/post-test design in which examinees are administered an assessment before instruction and then another assessment after instruction. In this type of study, the primary objective is to measure growth in examinees, individually and collectively. In an item response theory (IRT) framework, longitudinal IRT models can be used to assess growth in examinee ability over time. In a diagnostic classification model (DCM) framework, assessing growth translates to measuring changes in attribute mastery status over time, thereby providing a categorical, criterion-referenced interpretation of growth. This study introduces the Transition Diagnostic Classification Model (TDCM), which combines latent transition analysis with the log-linear cognitive diagnosis model to provide methodology for analyzing growth in a general DCM framework. Simulation study results indicate that the proposed model is flexible, provides accurate and reliable classifications, and is quite robust to violations to measurement invariance over time. The TDCM is used to analyze pre-test/post-test data from a diagnostic mathematics assessment.

Process data refer to data recorded in computer-based assessments (CBAs) that reflect respondents’ problem-solving processes and provide greater insight into how respondents solve problems, in addition to how well they solve them. Using the rich information contained in process data, this study proposed an item expansion method to analyze action-level process data from the perspective of diagnostic classification in order to comprehensively understand respondents’ problem-solving competence. The proposed method cannot only estimate respondents’ problem-solving ability along a continuum, but also classify respondents according to their problem-solving skills. To illustrate the application and advantages of the proposed method, a Programme for International Student Assessment (PISA) problem-solving item was used. The results indicated that (a) the estimated latent classes provided more detailed diagnoses of respondents’ problem-solving skills than the observed score categories; (b) although only one item was used, the estimated higher-order latent ability reflected the respondents’ problem-solving ability more accurately than the unidimensional latent ability estimated from the outcome data; and (c) interactions among problem-solving skills followed the conjunctive condensation rule, which indicated that the specific action sequence appeared only when a respondent mastered all required problem solving skills. In conclusion, the proposed diagnostic classification approach is feasible and promising analyzing process data.

The asymptotic classification theory of cognitive diagnosis (ACTCD) provided the theoretical foundation for using clustering methods that do not rely on a parametric statistical model for assigning examinees to proficiency classes. Like general diagnostic classification models, clustering methods can be useful in situations where the true diagnostic classification model (DCM) underlying the data is unknown and possibly misspecified, or the items of a test conform to a mix of multiple DCMs. Clustering methods can also be an option when fitting advanced and complex DCMs encounters computational difficulties. These can range from the use of excessive CPU times to plain computational infeasibility. However, the propositions of the ACTCD have only been proven for the Deterministic Input Noisy Output “AND” gate (DINA) model and the Deterministic Input Noisy Output “OR” gate (DINO) model. For other DCMs, there does not exist a theoretical justification to use clustering for assigning examinees to proficiency classes. But if clustering is to be used legitimately, then the ACTCD must cover a larger number of DCMs than just the DINA model and the DINO model. Thus, the purpose of this article is to prove the theoretical propositions of the ACTCD for two other important DCMs, the Reduced Reparameterized Unified Model and the General Diagnostic Model.