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 Q -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.

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 models (DCMs) can be used to track the cognitive learning states of students across multiple time points or over repeated measurements. This study developed an effective variational Bayes (VB) inference method for hidden Markov longitudinal general DCMs. The simulations performed in this study verified the validity of the proposed algorithm for satisfactorily recovering true parameters. Simulation and applied data analyses were conducted to compare the proposed VB method to Markov chain Monte Carlo (MCMC) sampling. The results revealed that the parameter estimates provided by the VB method were consistent with the MCMC method with the additional benefit of a faster estimation time. The comparative simulation also indicated differences between the two methods in terms of posterior standard deviation and coverage of 95% credible intervals. Thus, with limited computational resources and time, the proposed VB method can output estimations comparable to that of MCMC.

Previous longitudinal assessment experiences for multidimensional continuous latent constructs suggested that the set of anchor items should be proportionally representative of the total test forms in content and statistical characteristics and that they should be loaded on every domain in multidimensional tests. In such cases, the set of items containing the unit Q-matrix, which is the smallest unit representing the whole test, seems to be the natural choice for anchor items. Two simulation studies were conducted to verify the applicability of these existing insights to longitudinal learning diagnostic assessments (LDAs). The results mainly indicated that there is no effect on the classification accuracy regardless of the unit Q-matrix in the anchor items, and even not including the anchor items has no impact on the classification accuracy. The findings of this brief study may ease practitioners\' worries regarding anchor-item settings in the practice application of longitudinal LDAs.

The forced-choice (FC) item formats used for noncognitive tests typically develop a set of response options that measure different traits and instruct respondents to make judgments among these options in terms of their preference to control the response biases that are commonly observed in normative tests. Diagnostic classification models (DCMs) can provide information regarding the mastery status of test takers on latent discrete variables and are more commonly used for cognitive tests employed in educational settings than for noncognitive tests. The purpose of this study is to develop a new class of DCM for FC items under the higher-order DCM framework to meet the practical demands of simultaneously controlling for response biases and providing diagnostic classification information. By conducting a series of simulations and calibrating the model parameters with a Bayesian estimation, the study shows that, in general, the model parameters can be recovered satisfactorily with the use of long tests and large samples. More attributes improve the precision of the second-order latent trait estimation in a long test, but decrease the classification accuracy and the estimation quality of the structural parameters. When statements are allowed to load on two distinct attributes in paired comparison items, the specific-attribute condition produces better a parameter estimation than the overlap-attribute condition. Finally, an empirical analysis related to work-motivation measures is presented to demonstrate the applications and implications of the new model.

Diagnostic classification models (DCMs) have been used to classify examinees into groups based on their possession status of a set of latent traits. In addition to traditional item-based scoring approaches, examinees may be scored based on their completion of a series of small and similar tasks. Those scores are usually considered as count variables. To model count scores, this study proposes a new class of DCMs that uses the negative binomial distribution at its core. We explained the proposed model framework and demonstrated its use through an operational example. Simulation studies were conducted to evaluate the performance of the proposed model and compare it with the Poisson-based DCM.

When developing ordinal rating scales, we may include potentially unordered response options such as \"Neither Agree nor Disagree,\" \"Neutral,\" \"Don\'t Know,\" \"No Opinion,\" or \"Hard to Say.\" To handle responses to a mixture of ordered and unordered options, Huggins-Manley et al. (2018) proposed a class of semi-ordered models under the unidimensional item response theory framework. This study extends the concept of semi-ordered models into the area of diagnostic classification models. Specifically, we propose a flexible framework of semi-ordered DCMs that accommodates most earlier DCMs and allows for analyzing the relationship between those potentially unordered responses and the measured traits. Results from an operational study and two simulation studies show that the proposed framework can incorporate both ordered and non-ordered responses into the estimation of the latent traits and thus provide useful information about both the items and the respondents.

Assessments with a large amount of small, similar, or often repetitive tasks are being used in educational, neurocognitive, and psychological contexts. For example, respondents are asked to recognize numbers or letters from a large pool of those and the number of correct answers is a count variable. In 1960, George Rasch developed the Rasch Poisson counts model (RPCM) to handle that type of assessment. This article extends the RPCM into the world of diagnostic classification models (DCMs) where a Poisson distribution is applied to traditional DCMs. A framework of Poisson DCMs is proposed and demonstrated through an operational dataset. This study aims to be exploratory with recommendations for future research given in the end.

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.

In research applications, mental health problems such as alcohol-related problems and depression are commonly assessed and evaluated using scale scores or latent trait scores derived from factor analysis or item response theory models. This tutorial paper demonstrates the use of cognitive diagnosis models (CDMs) as an alternative approach to characterizing mental health problems of young adults when item-level data are available. Existing measurement approaches focus on estimating the general severity of a given mental health problem at the scale level as a unidimensional construct without accounting for other symptoms of related mental health problems. The prevailing approaches may ignore clinically meaningful presentations of related symptoms at the item level. The current study illustrates CDMs using item-level data from college students (40 items from 719 respondents; 34.6% men, 83.9% White, and 16.3% first-year students). Specifically, we evaluated the constellation of four postulated domains (i.e., alcohol-related problems, anxiety, hostility, and depression) as a set of attribute profiles using CDMs. After accounting for the impact of each attribute (i.e., postulated domain) on the estimates of attribute profiles, the results demonstrated that when items or attributes have limited information, CDMs can utilize item-level information in the associated attributes to generate potentially meaningful estimates and profiles, compared to analyzing each attribute independently. We introduce a novel visual inspection aid, the lens plot, for quantifying this gain. CDMs may be a useful analytical tool to capture respondents\' risk and resilience for prevention research.