A diagnostic tree model for polytomous responses with multiple strategies

Ma, Wenchao

doi:10.1111/bmsp.12137

Cited by 26 publications

(19 citation statements)

References 46 publications

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“…Third, only the dichotomous scoring item and dichotomous attribute were modeled in the proposed model. It would be meaningful and practical to extend the current model to consider polytomous scoring items (e.g., Ma, 2019;von Davier, 2008) and polytomous attributes (e.g., Karelitz, 2008;Zhan, Wang, & Li, 2019). Fourth, notably, the generalizability of the findings of this study is dependent upon the limitations of the design of the simulation studies, such as a fixed number of attributes and assuming the Q-matrix is correct.…”

Section: Summary and Discussionmentioning

confidence: 95%

Deterministic Inputs, Noisy Mixed Modeling for Identifying Coexisting Condensation Rules

Zhan¹

2020

Preprint

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In cognitive diagnosis models, the condensation rule reflects how latent attributes influence individuals’ observed item responses. Multiple condensation rules may be involved in an item simultaneously. The purpose of this study is to present a new cognitive diagnosis model that considers such coexisting condensation rules while keeping the model as simple as possible. Inspired by but different from the mixture/hybrid item response models, the deterministic-inputs, noisy mixture (DINMix) model is proposed. Specifically, the DINMix model focuses on the mixture of condensation rules employed in the latent responses instead of the mixture of latent groups in the population. Two simulation studies were conducted to evaluate the psychometric properties of the proposed model. The results indicate that the model parameters for the DINMix model can be well recovered, and the DINMix model can adaptively and accurately identify coexisting condensation rules. Two empirical examples are also analyzed to illustrate the applicability and advantages of the proposed model. The results indicate that in many, if not all, test applications, no single condensation rule can be expected to be contained in all the items.

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Section: Summary and Discussionmentioning

confidence: 95%

Deterministic Inputs, Noisy Mixed Modeling for Identifying Coexisting Condensation Rules

Zhan¹

2020

Preprint

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“…We also found that the Q‐matrix in the real data was complete based on the procedure of Köhn and Chiu (), indicating that all latent classes are distinguishable. Nevertheless, the evaluation of local identifiability of the GMS‐LLM, by checking whether the information matrix is positive definite as in von Davier () and Ma (), failed as a result of numerical problems caused by the boundary estimates. A possible approach to boundary solutions is to employ the posterior mode estimation, which has been discussed by DeCarlo () in the CDM contexts.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Last, the GMS‐CDMs can be viewed as a variant of the DTM of Ma (), which incorporates CDMs into tree models to accommodate multiple strategies for polytomous response data from constructed‐response items. Similar to the DTM approach, the GMS‐CDMs proposed in this paper can be presented using the tree diagram, as shown in Figure , where the first node (i.e., X 0 ) represents the task for strategy selection with M possible outcomes for M strategies.…”

Section: A Generalized Multiple‐strategy Modelmentioning

confidence: 99%

“…One of these is the Unified model (DiBello, Stout, & Roussos, ), which, unfortunately, cannot be estimated statistically. The diagnostic tree model (DTM; Ma, ) is another CDM that allows multiple strategies used in polytomous response data from constructed‐response items. However, it requires that the strategy used by each student for an item can be identified, which is challenging for dichotomous response data from multiple‐choice items.…”

Section: Introductionmentioning

confidence: 99%

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Cognitive diagnosis models for multiple strategies

Guo

2019

Brit J Math & Statis

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Cognitive diagnosis models (CDMs) have been used as psychometric tools in educational assessments to estimate students' proficiency profiles. However, most CDMs assume that all students adopt the same strategy when approaching problems in an assessment, which may not be the case in practice. This study develops a generalized multiple-strategy CDM for dichotomous response data. The proposed model provides a unified framework to accommodate various condensation rules (e.g., conjunctive, disjunctive, and additive) and different strategy selection approaches (i.e., probability-matching, over-matching, and maximizing). Model parameters are estimated using the marginal maximum likelihood estimation via expectation-maximization algorithm. Simulation studies showed that the parameters of the proposed model can be adequately recovered and that the proposed model was relatively robust to some types of model misspecifications. A set of real data was analysed as well to illustrate the use of the proposed model in practice.

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“…Attributes are discrete in nature rather than continuous, with usually only two levels indicating if the examinees mastered or did not master each specific attribute. CDM is a very active area of research (e.g., [6,7]). Some of the latest developments are in the area of cognitive diagnostic CAT (CD-CAT).…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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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.

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A diagnostic tree model for polytomous responses with multiple strategies

Cited by 26 publications

References 46 publications

Deterministic Inputs, Noisy Mixed Modeling for Identifying Coexisting Condensation Rules

Deterministic Inputs, Noisy Mixed Modeling for Identifying Coexisting Condensation Rules

Cognitive diagnosis models for multiple strategies

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

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