scholarly journals Using JAGS for Bayesian Cognitive Diagnosis Modeling: A Tutorial

2019 ◽  
Vol 44 (4) ◽  
pp. 473-503 ◽  
Author(s):  
Peida Zhan ◽  
Hong Jiao ◽  
Kaiwen Man ◽  
Lijun Wang
Keyword(s):  
Gibbs Sampler ◽  
Logistic Model ◽  
Structural Model ◽  
Higher Order ◽  
Unified Model ◽  
Cognitive Diagnosis ◽  
Cognitive Diagnosis Models ◽  
Log Linear ◽  
Linear Logistic Model ◽  
Or Gate

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 model; and the log-linear CDM (LCDM). Further, we introduce the unstructured latent structural model and the higher order latent structural model. We also show how to extend these models to consider polytomous attributes, the testlet effect, and longitudinal diagnosis. Finally, we present an empirical example as a tutorial to illustrate how to use JAGS codes in R.

Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables

Psychometrika ◽  
2008 ◽  
Vol 74 (2) ◽  
pp. 191-210 ◽  
Author(s):  
Robert A. Henson ◽  
Jonathan L. Templin ◽  
John T. Willse
Keyword(s):  
Latent Variables ◽  
Linear Models ◽  
Cognitive Diagnosis ◽  
Cognitive Diagnosis Models ◽  
Log Linear

Development and Application of an Exploratory Reduced Reparameterized Unified Model

2018 ◽  
Vol 44 (1) ◽  
pp. 3-24 ◽  
Author(s):  
Steven Andrew Culpepper ◽  
Yinghan Chen
Keyword(s):  
Bayesian Methods ◽  
Unified Model ◽  
Cognitive Diagnosis ◽  
Simulation Studies ◽  
Binary Matrix ◽  
Data Set ◽  
Cognitive Diagnosis Models ◽  
Item Parameters ◽  
Attribute Hierarchy ◽  
Q Matrix

Exploratory cognitive diagnosis models (CDMs) estimate the Q matrix, which is a binary matrix that indicates the attributes needed for affirmative responses to each item. Estimation of Q is an important next step for improving classifications and broadening application of CDMs. Prior research primarily focused on an exploratory version of the restrictive deterministic-input, noisy-and-gate model, and research is needed to develop exploratory methods for more flexible CDMs. We consider Bayesian methods for estimating an exploratory version of the more flexible reduced reparameterized unified model (rRUM). We show that estimating the rRUM Q matrix is complicated by a confound between elements of Q and the rRUM item parameters. A Bayesian framework is presented that accurately recovers Q using a spike–slab prior for item parameters to select the required attributes for each item. We present Monte Carlo simulation studies, demonstrating the developed algorithm improves upon prior Bayesian methods for estimating the rRUM Q matrix. We apply the developed method to the Examination for the Certificate of Proficiency in English data set. The results provide evidence of five attributes with a partially ordered attribute hierarchy.

scholarly journals A Sequential Higher Order Latent Structural Model for Hierarchical Attributes in Cognitive Diagnostic Assessments

2019 ◽  
Vol 44 (1) ◽  
pp. 65-83 ◽  
Author(s):  
Peida Zhan ◽  
Wenchao Ma ◽  
Hong Jiao ◽  
Shuliang Ding
Keyword(s):  
Structural Model ◽  
Latent Trait ◽  
Simulated Data ◽  
Hierarchical Structures ◽  
Higher Order ◽  
Order Structure ◽  
Cognitive Diagnosis Models ◽  
Attribute Hierarchy ◽  
Latent Attribute ◽  
Attribute Space

The higher-order structure and attribute hierarchical structure are two popular approaches to defining the latent attribute space in cognitive diagnosis models. However, to our knowledge, it is still impossible to integrate them to accommodate the higher-order latent trait and hierarchical attributes simultaneously. To address this issue, this article proposed a sequential higher-order latent structural model (LSM) by incorporating various hierarchical structures into a higher-order latent structure. The feasibility of the proposed higher-order LSM was examined using simulated data. Results indicated that, in conjunction with the deterministic-inputs, noisy “and” gate model, the sequential higher-order LSM produced considerable improvement in person classification accuracy compared with the conventional higher-order LSM, when a certain attribute hierarchy existed. An empirical example was presented as well to illustrate the application of the proposed LSM.

On Permissible Attribute Classes in Noncompensatory Cognitive Diagnosis Models

Methodology ◽  
2014 ◽  
Vol 10 (3) ◽  
pp. 100-107 ◽  
Author(s):  
Jürgen Groß ◽  
Ann Cathrice George
Keyword(s):  
Diagnostic Information ◽  
Cognitive Diagnosis ◽  
Latent Classes ◽  
Psychometric Test ◽  
Cognitive Diagnosis Models ◽  
Dina Model

When a psychometric test has been completed by a number of examinees, an afterward analysis of required skills or attributes may improve the extraction of diagnostic information. Relying upon the retrospectively specified item-by-attribute matrix, such an investigation may be carried out by classifying examinees into latent classes, consisting of subsets of required attributes. Specifically, various cognitive diagnosis models may be applied to serve this purpose. In this article it is shown that the permission of all possible attribute combinations as latent classes can have an undesired effect in the classification process, and it is demonstrated how an appropriate elimination of specific classes may improve the classification results. As an easy example, the popular deterministic input, noisy “and” gate (DINA) model is applied to Tatsuoka’s famous fraction subtraction data, and results are compared to current discussions in the literature.

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