A Tutorial on Cognitive Diagnosis Modeling for Characterizing Mental Health Symptom Profiles Using Existing Item Responses.

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.

Improving reliability estimation in cognitive diagnosis modeling.

Cognitive diagnosis models (CDMs) are used in educational, clinical, or personnel selection settings to classify respondents with respect to discrete attributes, identifying strengths and needs, and thus allowing to provide tailored training/treatment. As in any assessment, an accurate reliability estimation is crucial for valid score interpretations. In this sense, most CDM reliability indices are based on the posterior probabilities of the estimated attribute profiles. These posteriors are traditionally computed using point estimates for the model parameters as approximations to their populational values. If the uncertainty around these parameters is unaccounted for, the posteriors may be overly peaked, deriving into overestimated reliabilities. This article presents a multiple imputation (MI) procedure to integrate out the model parameters in the estimation of the posterior distributions, thus correcting the reliability estimation. A simulation study was conducted to compare the MI procedure with the traditional reliability estimation. Five factors were manipulated: the attribute structure, the CDM model (DINA and G-DINA), test length, sample size, and item quality. Additionally, an illustration using the Examination for the Certificate of Proficiency in English data was analyzed. The effect of sample size was studied by sampling subsets of subjects from the complete data. In both studies, the traditional reliability estimation systematically provided overestimated reliabilities, whereas the MI procedure offered more accurate results. Accordingly, practitioners in small educational or clinical settings should be aware that the reliability estimation using model parameter point estimates may be positively biased. R codes for the MI procedure are made available.

A dual process item response theory model for polytomous multidimensional forced-choice items.

The use of multidimensional forced-choice (MFC) items to assess non-cognitive traits such as personality, interests and values in psychological tests has a long history, because MFC items show strengths in preventing response bias. Recently, there has been a surge of interest in developing item response theory (IRT) models for MFC items. However, nearly all of the existing IRT models have been developed for MFC items with binary scores. Real tests use MFC items with more than two categories; such items are more informative than their binary counterparts. This study developed a new IRT model for polytomous MFC items based on the cognitive model of choice, which describes the cognitive processes underlying humans' preferential choice behaviours. The new model is unique in its ability to account for the ipsative nature of polytomous MFC items, to assess individual psychological differentiation in interests, values and emotions, and to compare the differentiation levels of latent traits between individuals. Simulation studies were conducted to examine the parameter recovery of the new model with existing computer programs. The results showed that both statement parameters and person parameters were well recovered when the sample size was sufficient. The more complete the linking of the statements was, the more accurate the parameter estimation was. This paper provides an empirical example of a career interest test using four-category MFC items. Although some aspects of the model (e.g., the nature of the person parameters) require additional validation, our approach appears promising.

Bridging Parametric and Nonparametric Methods in Cognitive Diagnosis.

A number of parametric and nonparametric methods for estimating cognitive diagnosis models (CDMs) have been developed and applied in a wide range of contexts. However, in the literature, a wide chasm exists between these two families of methods, and their relationship to each other is not well understood. In this paper, we propose a unified estimation framework to bridge the divide between parametric and nonparametric methods in cognitive diagnosis to better understand their relationship. We also develop iterative joint estimation algorithms and establish consistency properties within the proposed framework. Lastly, we present comprehensive simulation results to compare different methods and provide practical recommendations on the appropriate use of the proposed framework in various CDM contexts.

An Empirical Q-Matrix Validation Method for the Polytomous G-DINA Model.

A number of empirically based Q-matrix validation methods are available in the literature, all of which were developed for cognitive diagnosis models (CDMs) involving dichotomous attributes. However, in many applications, it is more instructionally relevant to classify students into more than two categories (e.g., no mastery, basic mastery, and advanced mastery). To extend the practical utility of CDMs, methods for validating the Q-matrix for CDMs that measure polytomous attributes are needed. This study focuses on validating the Q-matrix of the generalized deterministic input, noisy, "and" gate model for polytomous attributes (pG-DINA). The pGDI, an extension of the G-DINA model discrimination index, is proposed for polytomous attributes. The pGDI serves as the basis of a validation method that can be used not only to identify potential misspecified q-entries, but also to suggest more appropriate attribute-level specifications. The theoretical properties of the pGDI are underpinned by several mathematical proofs, whereas its practical viability is examined using simulation studies covering various conditions. The results show that the method can accurately identify misspecified q-entries and suggest the correct attribute-level specifications, particularly when high-quality items are involved. The pGDI is applied to a proportional reasoning test that measures several polytomous attributes.

Computerized Adaptive Testing for Ipsative Tests with Multidimensional Pairwise-Comparison Items: Algorithm Development and Applications.

A computerized adaptive testing (CAT) solution for tests with multidimensional pairwise-comparison (MPC) items, aiming to measure career interest, value, and personality, is rare. This paper proposes new item selection and exposure control methods for CAT with dichotomous and polytomous MPC items and present simulation study results. The results show that the procedures are effective in selecting items and controlling within-person statement exposure with no loss of efficiency. Implications are discussed in two applications of the proposed CAT procedures: a work attitude test with dichotomous MPC items and a career interest assessment with polytomous MPC items.

Evaluation of the Linear Composite Conjecture for Unidimensional IRT Scale for Multidimensional Responses.

The linear composite direction represents, theoretically, where the unidimensional scale would lie within a multidimensional latent space. Using compensatory multidimensional IRT, the linear composite can be derived from the structure of the items and the latent distribution. The purpose of this study was to evaluate the validity of the linear composite conjecture and examine how well a fitted unidimensional IRT model approximates the linear composite direction in a multidimensional latent space. Simulation experiment results overall show that the fitted unidimensional IRT model sufficiently approximates linear composite direction when correlation between bivariate latent variables is positive. When the correlation between bivariate latent variables is negative, instability occurs when the fitted unidimensional IRT model is used to approximate linear composite direction. A real data experiment was also conducted using 20 items from a multiple-choice mathematics test from American College Testing.

Digital competence as a protective factor against gaming addiction in children and adolescents: A cross-sectional study in Hong Kong.

Background: Digital competence can help children and adolescents engage with technology for acquiring new knowledge and for broadening social contact and support, while reducing the risk of inappropriate media use. This study investigated the effects of digital competence on the risk of gaming addiction among children and adolescents. We explored whether students with good digital competence were protected from the adverse effects of media use and the risk of gaming addiction. Methods: 1956 students (690 primary and 1266 secondary) completed a digital competence assessment and a self-report questionnaire on their mental health status, use of digital devices, and experiences of cyberbullying. Multiple regression analyses with further mediation and moderation analyses were performed to investigate the association of digital competence with gaming addiction and mental health in children and adolescents. Findings: Regression analyses showed that children and adolescents with better digital competence were less likely to develop gaming addiction (ß = -0.144, p < 0.0001) and experienced less cyberbullying behaviour as perpetrators (ß = -0.169, p < 0.0001) and as victims (ß = -0.121, p < 0.0001). Digital competence was found to mediate the relationship between digital device usage time and gaming addiction. Interpretation: Digital competence is associated with less gaming addiction and could potentially lead to better mental wellbeing by reducing the risks of gaming addiction and cyberbullying. Education that promotes digital competence is essential to maximize the benefits of media use, while reducing the potential adverse effects from the inappropriate use of digital devices. Funding: This study was supported by a grant from the Research Grants Council of the HKSAR Government (#T44-707/16N) under the Theme-based Research Scheme.

Detecting Differential Item Functioning Using Multiple-Group Cognitive Diagnosis Models.

This study proposes a multiple-group cognitive diagnosis model to account for the fact that students in different groups may use distinct attributes or use the same attributes but in different manners (e.g., conjunctive, disjunctive, and compensatory) to solve problems. Based on the proposed model, this study systematically investigates the performance of the likelihood ratio (LR) test and Wald test in detecting differential item functioning (DIF). A forward anchor item search procedure was also proposed to identify a set of anchor items with invariant item parameters across groups. Results showed that the LR and Wald tests with the forward anchor item search algorithm produced better calibrated Type I error rates than the ordinary LR and Wald tests, especially when items were of low quality. A set of real data were also analyzed to illustrate the use of these DIF detection procedures.

Balancing fit and parsimony to improve Q-matrix validation.

The Q-matrix identifies the subset of attributes measured by each item in the cognitive diagnosis modelling framework. Usually constructed by domain experts, the Q-matrix might contain some misspecifications, disrupting classification accuracy. Empirical Q-matrix validation methods such as the general discrimination index (GDI) and Wald have shown promising results in addressing this problem. However, a cut-off point is used in both methods, which might be suboptimal. To address this limitation, the Hull method is proposed and evaluated in the present study. This method aims to find the optimal balance between fit and parsimony, and it is flexible enough to be used either with a measure of item discrimination (the proportion of variance accounted for, PVAF) or a coefficient of determination (pseudo-R2 ). Results from a simulation study showed that the Hull method consistently showed the best performance and shortest computation time, especially when used with the PVAF. The Wald method also performed very well overall, while the GDI method obtained poor results when the number of attributes was high. The absence of a cut-off point provides greater flexibility to the Hull method, and it places it as a comprehensive solution to the Q-matrix specification problem in applied settings. This proposal is illustrated using real data.

A Blocked-CAT Procedure for CD-CAT.

This article introduces a blocked-design procedure for cognitive diagnosis computerized adaptive testing (CD-CAT), which allows examinees to review items and change their answers during test administration. Four blocking versions of the new procedure were proposed. In addition, the impact of several factors, namely, item quality, generating model, block size, and test length, on the classification rates was investigated. Three popular item selection indices in CD-CAT were used and their efficiency compared using the new procedure. An additional study was carried out to examine the potential benefit of item review. The results showed that the new procedure is promising in that allowing item review resulted only in a small loss in attribute classification accuracy under some conditions. Moreover, using a blocked-design CD-CAT is beneficial to the extent that it alleviates the negative impact of test anxiety on examinees' true performance.

Estimation approaches in cognitive diagnosis modeling when attributes are hierarchically structured.

BACKGROUND: Although research in cognitive psychology suggests refraining from investigating cognitive skills inisolation, many cognitive diagnosis model (CDM) examples do not take hierarchical attribute structures into account. When hierarchical relationships among the attributes are not considered, CDM estimates may be biased. METHOD: The current study, through simulation and real data analyses, examines the impact of different MMLE-EM approaches on the item and person parameter estimates of the G-DINA, DINA and DINO models when attributes have a hierarchical structure. A number of estimation approaches that can result from modifying either the Q-matrix or prior distribution are proposed. Impact of the proposed approaches on item parameter estimation accuracy and attribute classification are investigated. RESULTS: For the G-DINA model estimation, the Q-matrix type (i.e, explicit vs. implicit) has greater impact than structuring the prior distribution. Specifically, explicit Q-matrices result in better item parameter recovery and higher correct classification rates. In contrast, structuring the prior distribution is more influential on item and person parameter estimates for the reduced models. When prior distribution is structured, the Q-matrix type has almost no influence on item and person parameter estimates of the DINA and DINO models. CONCLUSION: We can conclude that the Q-matrix type has a significant impact on CDM estimation, especially when the estimating model is G-DINA.

An empirical Q-matrix validation method for the sequential generalized DINA model.

As a core component of most cognitive diagnosis models, the Q-matrix, or item and attribute association matrix, is typically developed by domain experts, and tends to be subjective. It is critical to validate the Q-matrix empirically because a misspecified Q-matrix could result in erroneous attribute estimation. Most existing Q-matrix validation procedures are developed for dichotomous responses. However, in this paper, we propose a method to empirically detect and correct the misspecifications in the Q-matrix for graded response data based on the sequential generalized deterministic inputs, noisy 'and' gate (G-DINA) model. The proposed Q-matrix validation procedure is implemented in a stepwise manner based on the Wald test and an effect size measure. The feasibility of the proposed method is examined using simulation studies. Also, a set of data from the Trends in International Mathematics and Science Study (TIMSS) 2011 mathematics assessment is analysed for illustration.

Adapting cognitive diagnosis computerized adaptive testing item selection rules to traditional item response theory.

Currently, there are two predominant approaches in adaptive testing. One, referred to as cognitive diagnosis computerized adaptive testing (CD-CAT), is based on cognitive diagnosis models, and the other, the traditional CAT, is based on item response theory. The present study evaluates the performance of two item selection rules (ISRs) originally developed in the CD-CAT framework, the double Kullback-Leibler information (DKL) and the generalized deterministic inputs, noisy "and" gate model discrimination index (GDI), in the context of traditional CAT. The accuracy and test security associated with these two ISRs are compared to those of the point Fisher information and weighted KL using a simulation study. The impact of the trait level estimation method is also investigated. The results show that the new ISRs, particularly DKL, could be used to improve the accuracy of CAT. Better accuracy for DKL is achieved at the expense of higher item overlap rate. Differences among the item selection rules become smaller as the test gets longer. The two CD-CAT ISRs select different types of items: items with the highest possible a parameter with DKL, and items with the lowest possible c parameter with GDI. Regarding the trait level estimator, expected a posteriori method is generally better in the first stages of the CAT, and converges with the maximum likelihood method when a medium to large number of items are involved. The use of DKL can be recommended in low-stakes settings where test security is less of a concern.

Improving Robustness in Q-Matrix Validation Using an Iterative and Dynamic Procedure.

In the context of cognitive diagnosis models (CDMs), a Q-matrix reflects the correspondence between attributes and items. The Q-matrix construction process is typically subjective in nature, which may lead to misspecifications. All this can negatively affect the attribute classification accuracy. In response, several methods of empirical Q-matrix validation have been developed. The general discrimination index (GDI) method has some relevant advantages such as the possibility of being applied to several CDMs. However, the estimation of the GDI relies on the estimation of the latent group sizes and success probabilities, which is made with the original (possibly misspecified) Q-matrix. This can be a problem, especially in those situations in which there is a great uncertainty about the Q-matrix specification. To address this, the present study investigates the iterative application of the GDI method, where only one item is modified at each step of the iterative procedure, and the required cutoff is updated considering the new parameter estimates. A simulation study was conducted to test the performance of the new procedure. Results showed that the performance of the GDI method improved when the application was iterative at the item level and an appropriate cutoff point was used. This was most notable when the original Q-matrix misspecification rate was high, where the proposed procedure performed better 96.5% of the times. The results are illustrated using Tatsuoka's fraction-subtraction data set.

Estimating CDMs Using the Slice-Within-Gibbs Sampler.

In this paper, the slice-within-Gibbs sampler has been introduced as a method for estimating cognitive diagnosis models (CDMs). Compared with other Bayesian methods, the slice-within-Gibbs sampler can employ a wide-range of prior specifications; moreover, it can also be applied to complex CDMs with the aid of auxiliary variables, especially when applying different identifiability constraints. To evaluate its performances, two simulation studies were conducted. The first study confirmed the viability of the slice-within-Gibbs sampler in estimating CDMs, mainly including G-DINA and DINA models. The second study compared the slice-within-Gibbs sampler with other commonly used Markov Chain Monte Carlo algorithms, and the results showed that the slice-within-Gibbs sampler converged much faster than the Metropolis-Hastings algorithm and more flexible than the Gibbs sampling in choosing the distributions of priors. Finally, a fraction subtraction dataset was analyzed to illustrate the use of the slice-within-Gibbs sampler in the context of CDMs.

Computerized Adaptive Testing for Cognitively Based Multiple-Choice Data.

Cognitive diagnosis models (CDMs) are latent class models that hold great promise for providing diagnostic information about student knowledge profiles. The increasing use of computers in classrooms enhances the advantages of CDMs for more efficient diagnostic testing by using adaptive algorithms, referred to as cognitive diagnosis computerized adaptive testing (CD-CAT). When multiple-choice items are involved, CD-CAT can be further improved by using polytomous scoring (i.e., considering the specific options students choose), instead of dichotomous scoring (i.e., marking answers as either right or wrong). In this study, the authors propose and evaluate the performance of the Jensen-Shannon divergence (JSD) index as an item selection method for the multiple-choice deterministic inputs, noisy "and" gate (MC-DINA) model. Attribute classification accuracy and item usage are evaluated under different conditions of item quality and test termination rule. The proposed approach is compared with the random selection method and an approximate approach based on dichotomized responses. The results show that under the MC-DINA model, JSD improves the attribute classification accuracy significantly by considering the information from distractors, even with a very short test length. This result has important implications in practical classroom settings as it can allow for dramatically reduced testing times, thus resulting in more targeted learning opportunities.

Multivariate Higher-Order IRT Model and MCMC Algorithm for Linking Individual Participant Data From Multiple Studies.

Many clinical and psychological constructs are conceptualized to have multivariate higher-order constructs that give rise to multidimensional lower-order traits. Although recent measurement models and computing algorithms can accommodate item response data with a higher-order structure, there are few measurement models and computing techniques that can be employed in the context of complex research synthesis, such as meta-analysis of individual participant data or integrative data analysis. The current study was aimed at modeling complex item responses that can arise when underlying domain-specific, lower-order traits are hierarchically related to multiple higher-order traits for individual participant data from multiple studies. We formulated a multi-group, multivariate higher-order item response theory (HO-IRT) model from a Bayesian perspective and developed a new Markov chain Monte Carlo (MCMC) algorithm to simultaneously estimate the (a) structural parameters of the first- and second-order latent traits across multiple groups and (b) item parameters of the model. Results from a simulation study support the feasibility of the MCMC algorithm. From the analysis of real data, we found that a bivariate HO-IRT model with different correlation/covariance structures for different studies fit the data best, compared to a univariate HO-IRT model or other alternate models with unreasonable assumptions (i.e., the same means and covariances across studies). Although more work is needed to further develop the method and to disseminate it, the multi-group multivariate HO-IRT model holds promise to derive a common metric for individual participant data from multiple studies in research synthesis studies for robust inference and for new discoveries.

Trajectories and predictors of response in youth anxiety CBT: Integrative data analysis.

OBJECTIVE: Integrative data analysis was used to combine existing data from nine trials of cognitive-behavioral therapy (CBT) for anxious youth (N = 832) and identify trajectories of symptom change and predictors of trajectories. METHOD: Youth- and parent-reported anxiety symptoms were combined using item-response theory models. Growth mixture modeling assessed for trajectories of treatment response across pre-, mid-, and posttreatment and 1-year follow-up. Pretreatment client demographic and clinical traits and treatment modality (individual- and family-based CBT) were examined as predictors of trajectory classes. RESULTS: Growth mixture modeling supported three trajectory classes based on parent-reported symptoms: steady responders, rapid responders, and delayed improvement. A 4-class model was supported for youth-reported symptoms: steady responders, rapid responders, delayed improvement, and low-symptom responders. Delayed improvement classes were predicted by higher number of diagnoses (parent and youth report). Receiving family CBT predicted membership in the delayed improvement class compared to all other classes and membership in the steady responder class compared with rapid responders (youth report). Rapid responders were predicted by older age (parent report) and higher number of diagnoses (parent report). Low-symptom responders were more likely to be male (youth report). CONCLUSIONS: Integrative data analysis identified distinct patterns of symptom change. Diagnostic complexity, age, gender, and treatment modality differentiated response classes. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Introducing the General Polytomous Diagnosis Modeling Framework.

Although considerable developments have been added to the cognitive diagnosis modeling literature recently, most have been conducted for dichotomous responses only. This research proposes a general cognitive diagnosis model for polytomous responses-the general polytomous diagnosis model (GPDM), which combines the G-DINA modeling process for dichotomous responses with the item-splitting process for polytomous responses. The polytomous items are specified similar to dichotomous items in the Q-matrix, and the MML estimation is implemented using an EM algorithm. Under the general framework, different saturated forms, and some reduced forms, can be transformed linearly. Model assessment and adjustment under the dichotomous context can be extended to polytomous responses. This simulation study demonstrates the effectiveness of the model when comparing the two response types. The real-data example further illustrates how the proposed model can make a difference in practice.