This article proposes a class of cognitive diagnosis models (CDMs) for polytomously scored items with different link functions. Many existing polytomous CDMs can be considered as special cases of the proposed class of polytomous CDMs. Simulation studies were carried out to investigate the feasibility of the proposed CDMs and the performance of…

This study aims to conduct differential item functioning analyses in the context of cognitive diagnosis assessments using various formulations of the Wald test. In implementing the Wald test, two scenarios are considered: one where the underlying reduced model can be assumed; and another where a saturated CDM is used. Illustration of the different…

Categorical data become increasingly ubiquitous in the modern big data era. In this dissertation, we propose novel statistical learning and inference methods for large-scale categorical data, focusing on latent variable models and their applications to psychometrics. In psychometric assessments, the subjects' underlying aptitude often cannot be…

The demand for diagnostic feedback has triggered extensive research on cognitive diagnostic models (CDMs), such as the deterministic input, noisy output "and" gate (DINA) model. This study explored two Q-matrix specifications with the DINA model in a statewide large-scale mathematics assessment. The first Q-matrix was developed based on…

This study proposes explanatory cognitive diagnostic model (CDM) jointly incorporating responses and response times (RTs) with the inclusion of item covariates related to both item responses and RTs. The joint modeling of item responses and RTs intends to provide more information for cognitive diagnosis while item covariates can be used to predict…

Measurement models need to properly delineate the real aspect of examinees' response processes for measurement accuracy purposes. To avoid invalid inferences, fit of examinees' response data to the model is studied through "person-fit" statistics. Misfit between the examinee response data and measurement model may be due to invalid…

In this article, we systematically introduce the just another Gibbs sampler (JAGS) software program to fit common Bayesian cognitive diagnosis models (CDMs) including the deterministic inputs, noisy "and" gate model; the deterministic inputs, noisy "or" gate model; the linear logistic model; the reduced reparameterized unified…

Purpose: Well-designed assessment methodologies and various cognitive diagnosis models (CDMs) to extract diagnostic information about examinees' individual strengths and weaknesses have been developed. Due to this novelty, as well as educational specialists' lack of familiarity with CDMs, their applications are not widespread. This article aims at…

In this study, it was aimed to investigate the impact of different missing data handling methods on DINA model parameter estimation and classification accuracy. In the study, simulated data were used and the data were generated by manipulating the number of items and sample size. In the generated data, two different missing data mechanisms…

Solving a constructed-response item usually requires successfully performing a sequence of tasks. Each task could involve different attributes, and those required attributes may be "condensed" in various ways to produce the responses. The sequential generalized deterministic input noisy "and" gate model is a general cognitive…

Competence data from low-stakes educational large-scale assessment studies allow for evaluating relationships between competencies and other variables. The impact of item-level nonresponse has not been investigated with regard to statistics that determine the size of these relationships (e.g., correlations, regression coefficients). Classical…

Diagnostic classification models (DCMs, also known as cognitive diagnosis models) hold the promise of providing detailed classroom information about the skills a student has or has not mastered. Specifically, DCMs are special cases of constrained latent class models where classes are defined based on mastery/nonmastery of a set of attributes (or…

This dissertation aims to investigate the effect size measures of differential item functioning (DIF) detection in the context of cognitive diagnostic models (CDMs). A variety of DIF detection techniques have been developed in the context of CDMs. However, most of the DIF detection procedures focus on the null hypothesis significance test. Few…

We provide evidence of validity for a newly developed diagnostic competence model of operation sense, by both (a) describing the theoretically substantiated development of the competence model in close association with its use within a large-scale formative assessment and (b) providing empirical evidence for the theoretically described cognitive…

A primary purpose of cognitive diagnosis models (CDMs) is to classify examinees based on their attribute patterns. The Q-matrix (Tatsuoka, 1985), a common component of all CDMs, specifies the relationship between the set of required dichotomous attributes and the test items. Since a Q-matrix is often developed by content-knowledge experts and can…