Selecting the most appropriate cognitive diagnosis model (CDM) for an item is a challenging process. Although general CDMs provide better model-data fit, specific CDMs have more straightforward interpretations, are more stable, and can provide more accurate classifications when used correctly. Recently, the Wald test has been proposed to determine at the item level whether a general CDM can be replaced by specific CDMs without a significant loss in model-data fit. The current study examines the practical consequence of the test by evaluating whether the attribute-vector classification based on CDMs selected by the Wald test is better than that based on general CDMs. Although the Wald test can detect the true underlying model for certain CDMs, it is yet unclear how effective it is at distinguishing among the wider range of CDMs found in the literature. This study investigates the relative similarity of the various CDMs through the use of the newly developed dissimiliarity index, and explores the implications for the Wald test. Simulations show that the Wald test cannot distinguish among additive models due to their inherent similarity, but this does not impede the ability of the test to provide higher correct classification rates than general CDMs, particularly when the sample size is small and items are of low quality. An empirical example is included to demonstrate the viability of the procedure.

In this article, a testlet hierarchical diagnostic classification model (TH-DCM) was introduced to take both attribute hierarchies and item bundles into account. The expectation-maximization algorithm with an analytic dimension reduction technique was used for parameter estimation. A simulation study was conducted to assess the parameter recovery of the proposed model under varied conditions, and to compare TH-DCM with testlet higher-order CDM (THO-DCM; Hansen, M. (2013). Hierarchical item response models for cognitive diagnosis (Unpublished doctoral dissertation). UCLA; Zhan, P., Li, X., Wang, W.-C., Bian, Y., & Wang, L. (2015). The multidimensional testlet-effect cognitive diagnostic models. Acta Psychologica Sinica, 47(5), 689. https://doi.org/10.3724/SP.J.1041.2015.00689 ). Results showed that (1) ignoring large testlet effects worsened parameter recovery, (2) DCMs assuming equal testlet effects within each testlet performed as well as the testlet model assuming unequal testlet effects under most conditions, (3) misspecifications in joint attribute distribution had an differential impact on parameter recovery, and (4) THO-DCM seems to be a robust alternative to TH-DCM under some hierarchical structures. A set of real data was also analyzed for illustration.

Despite the increasing popularity, cognitive diagnosis models have been criticized for limited utility for small samples. In this study, the authors proposed to use Bayes modal (BM) estimation and monotonic constraints to stabilize item parameter estimation and facilitate person classification in small samples based on the generalized deterministic input noisy “and” gate (G-DINA) model. Both simulation study and real data analysis were used to assess the utility of the BM estimation and monotonic constraints. Results showed that in small samples, (a) the G-DINA model with BM estimation is more likely to converge successfully, (b) when prior distributions are specified reasonably, and monotonicity is not violated, the BM estimation with monotonicity tends to produce more stable item parameter estimates and more accurate person classification, and (c) the G-DINA model using the BM estimation with monotonicity is less likely to overfit the data and shows higher predictive power.

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.