Parameter Invariance and Skill Attribute Continuity in the DINA Model

2018 ◽  
Vol 55 (2) ◽  
pp. 264-280
Author(s):  
Daniel M. Bolt ◽  
Jee-Seon Kim
Keyword(s):  
Dina Model ◽  
Parameter Invariance

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.

A New Method of Q-matrix Validation Based on DINA Model

2013 ◽  
Vol 44 (4) ◽  
pp. 558-568 ◽  
Author(s):  
Dong-Bo TU ◽  
Yan CAI ◽  
Hai-Qi DAI
Keyword(s):  
New Method ◽  
Dina Model ◽  
Q Matrix

scholarly journals Q-Matrix Refinement Based on Item Fit Statistic RMSEA

2018 ◽  
Vol 43 (7) ◽  
pp. 527-542 ◽  
Author(s):  
Chunhua Kang ◽  
Yakun Yang ◽  
Pingfei Zeng
Keyword(s):  
Search Algorithm ◽  
Delta Method ◽  
Mean Square ◽  
Simulation Studies ◽  
Response Data ◽  
Item Fit ◽  
Dina Model ◽  
Q Matrix ◽  
Diagnosis Model ◽  
Effectiveness And Efficiency

A Q-matrix, which reflects how attributes are measured for each item, is necessary when applying a cognitive diagnosis model to an assessment. In most cases, the Q-matrix is constructed by experts in the field and may be subjective and incorrect. One efficient method to refine the Q-matrix is to employ a suitable statistic that is calculated using response data. However, this approach is limited by its need to estimate all items in the Q-matrix even if only some are incorrect. To address this challenge, this study proposes an item fit statistic root mean square error approximation (RMSEA) for validating a Q-matrix with the deterministic inputs, noisy, “and” (DINA) model. Using a search algorithm, two simulation studies were performed to evaluate the effectiveness and efficiency of the proposed method at recovering Q-matrices. Results showed that using RMSEA can help define attributes in a Q-matrix. A comparison with the existing Delta method and residual sum of squares (RSS) method revealed that the proposed method had higher mean recovery rates and can be used to identify and correct Q-matrix misspecifications. When no error exists in the Q-matrix, the proposed method does not modify the correct Q-matrix.

scholarly journals Multilevel Modeling of Cognitive Diagnostic Assessment: The Multilevel DINA Example

2018 ◽  
Vol 43 (1) ◽  
pp. 34-50 ◽  
Author(s):  
Wen-Chung Wang ◽  
Xue-Lan Qiu
Keyword(s):  
Continuous Variable ◽  
Parameter Recovery ◽  
Dina Model ◽  
Variable Approach ◽  
Item Level ◽  
Multivariate Bernoulli ◽  
Level Model ◽  
Log Linear ◽  
Latent Attribute ◽  
Mathematics And Science

Many multilevel linear and item response theory models have been developed to account for multilevel data structures. However, most existing cognitive diagnostic models (CDMs) are unilevel in nature and become inapplicable when data have a multilevel structure. In this study, using the log-linear CDM as the item-level model, multilevel CDMs were developed based on the latent continuous variable approach and the multivariate Bernoulli distribution approach. In a series of simulations, the newly developed multilevel deterministic input, noisy, and gate (DINA) model was used as an example to evaluate the parameter recovery and consequences of ignoring the multilevel structures. The results indicated that all parameters in the new multilevel DINA were recovered fairly well by using the freeware Just Another Gibbs Sampler (JAGS) and that ignoring multilevel structures by fitting the standard unilevel DINA model resulted in poor estimates for the student-level covariates and underestimated standard errors, as well as led to poor recovery for the latent attribute profiles for individuals. An empirical example using the 2003 Trends in International Mathematics and Science Study eighth-grade mathematical test was provided.

Variational Bayes Inference for the DINA Model

2020 ◽  
Vol 45 (5) ◽  
pp. 569-597
Author(s):  
Kazuhiro Yamaguchi ◽  
Kensuke Okada
Keyword(s):  
Real Data ◽  
Variational Bayes ◽  
Diagnostic Assessment ◽  
Model Parameters ◽  
Mcmc Method ◽  
Inference Method ◽  
Bayes Inference ◽  
Dina Model ◽  
Mcmc Estimation ◽  
Parameter Values

In this article, we propose a variational Bayes (VB) inference method for the deterministic input noisy AND gate model of cognitive diagnostic assessment. The proposed method, which applies the iterative algorithm for optimization, is derived based on the optimal variational posteriors of the model parameters. The proposed VB inference enables much faster computation than the existing Markov chain Monte Carlo (MCMC) method, while still offering the benefits of a full Bayesian framework. A simulation study revealed that the proposed VB estimation adequately recovered the parameter values. Moreover, an example using real data revealed that the proposed VB inference method provided similar estimates to MCMC estimation with much faster computation.

A method of Q-matrix validation based symmetrised Kullback–Leibler divergence for the DINA model

2019 ◽  
Vol 12 (4) ◽  
pp. 537-547
Author(s):  
Jinxin Guo ◽  
Xin Xu ◽  
Jian Tao ◽  
Ningzhong Shi
Keyword(s):  
Dina Model ◽  
Leibler Divergence ◽  
Q Matrix
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